NCERT Exemplar Problems Class 8 Science Chapter 12 Friction

Multiple Choice Questions 

Question. 1 Whenever the surfaces in contact tend to move or move with respect to each other, the force of friction comes into play
(a) only if the objects are solid
(b) only if one of the two objects is liquid
(c) only if one of the two objects is gaseous
(d) irrespective of whether the objects are solids, liquids or gases
Answer. (d) Force of friction acts in solids, liquids and gases and opposes the motion with respect to each other.

Question. 2 In’figure, a boy is shows pushing the box from right to left.

The force of friction will act on the box
(a) from right to left (<-) (b) from left to right (->)
(c) vertically downwards (i) (d) vertically upwards (T)
Answer. (b) The force of friction will be from left to right (-4) because the friction force always acts in opposite direction to the motion.

Question. 3 To sharpen the blade of a knife by rubbing it against a surface, which of the following will be most suitable?
(a) Stone (b) Plastic block (c) Wooden block (d) Class block
Answer. (a) Stone will be more suitable because it will exert greater reaction and hence greater friction force which sharpen the blade of a knife easily by rubbing.

Question. 4 A toy car released with the same initial speed will travel farthest on
(a) muddy surface
(b) polished marble surface
(c) cemented surface
(d) brick surface
Answer. (b) It will go farthest on the surface having least frictional force, i.e. the polished marble surface.

Question. 5 If we apply oil on door hinges, the friction will
(a) increase
(b) decrease
(c) disappear altogether
(d) will remain unchanged
Answer. (b) The friction will decrease because oil acts as a lubricant which reduce friction.

Question. 6 Which of the following statements is incorrect?
(a) Friction acts on a ball rolling along the ground
(b) Friction acts on a boat moving on water
(c) Friction acts on a bicycle moving on a smooth road
(d) Friction does not act on a ball moving through air
Answer. (d) Friction will act in case of ball moving through air always.

Question. 7 A boy rolls a rubber ball on a wooden surface. The ball travels a short distance before coming to rest. To make the same, ball travel longer distance before coming to rest, he may (a) spread a carpet on the wooden surface
(b) cover the ball with a piece of cloth
(c) sprinkle talcum powder on the wooden surface
(d) sprinkle sand on the wooden surface
Answer. (c) Talcum powder reduces friction force and the ball will cover longer distance.

Question. 8 In a large commercial complex there are four ways to reach the main road. One of the path has loose soil, the second is laid with polished marble, the third is laid with bricks and the fourth has gravel surface. It is raining heavily and Paheli wishes to reach the main road. The path on which she is least likely to slip is
(a) loose soil
(b) polished marble (c) bricks
(d) gravel
Answer. (d) She should use gravel surface path because only in this path. She will have sufficient friction force to walk easily.

Very Short Answer Type Questions

Question. 9 Two blocks of iron of different masses are kept on a cemented floor as shown in the figure. Which one of them would require a larger force to move it from the rest position?

Answer. The block having mass 2 units will require larger force to move it from the rest position because friction force increases as the mass of object increases and hence larger mass require a larger force to move from the rest position.

Question. 10 Will force of friction come into play when a rain drop rolls down a glass window pane?
Answer. Yes, friction comes into play when two surfaces are in contact, e.g. glass and water in this case..

Question. 11 Two boys are riding their bicycles on the same concrete road. One has new tyres on his bicycle while the other has tyres that are old and used. Which of them is more likely to slip while moving through a patch of the road which has lubricating oil spilled over it?
Answer. The boy having the tyres which are old and used is most likely to slip because these tyres will experience less friction force which is insufficient to move on the oily road.

Question. 12 Figure shows two boys applying force on a box. If the magnitude of the force applied by each is equal, will the box experience any force of friction?

Answer.No, the force applied by both boys is equal.
So, net force will be zero and hence friction force will not come into play.

Question. 13 Imagine that an object is falling through a long straight glass tube held vertical, air has been removed completely from the tube. The object does i not touch the walls of the tube. Will the object experience any force of
friction?
Answer. No, the object will not experience any frictional force because to experience the force of friction, two surfaces must be there and there is only one surface in this case.

Short Answer Type Questions

Question. 14 You might have noticed that when used for a long time, slippers with rubber soles become slippery. Explain the reason.
Answer. It is due to continuousrubbing of soles with the ground, the spikes on the sole get damaged slowly and the soles become slippery.

Question. 15 Is there a force of friction between the wheels of a moving train and iron rails? If yes, name the type of friction. If an air cushion can be introduced between the wheel and the rail, what effect will it have on the friction?
Answer. Yes, there is always a force of friction between the wheels of a moving train and iron rails. The name of this friction is rolling friction, since the wheels are rolling on the track.
On introducing air cushion, the frictional force becomes less, since there is no contact between rails and wheels.

Question. 16 Cartilage is present in the joints of our body which helps in their smooth movement. With advancing age, this cartilage wears off. How would this affect the movement of joints?
Answer. Cartilage is present in the joints of our body, reduces friction during movement of joints. But on wearing off this cartilage, the force of friction increases due to which the smoothness of movement decreases and one feels the joint pain.

Question. 17 While playing tug of war, Preeti felt that the rope was slipping through her hands. Suggest a way out for her to prevent this.

Answer. To prevent slipping of the rope from hands, Preeti has to make her hands somewhat non-smooth, so she can rub her hands by introducing the sand between them.

Question. 18 The handle of a cricket bat or a badminton racquet is usually rough. Explain the reason.
Answer. The handle of a cricket bat or a badminton racquet is rough, so that while playing, the bat or badminton racquet does not slip away from the hands of the player.
Roughness is responsible for the frictional force between handle of the bat or a badminton racquet and’hands, without which gripping is not possible.

Question. 19 Explain why the surface of mortar and pestle (silbatta) used for grinding is etched again after prolonged use.
Answer. After prolonged use, the mortar and pestle loose the roughness, due to which frictional force reduces and it does not work properly. So, we have to etch it to makelt rough again.

Question. 20 A marble is allowed to roll down an inclined plane from a fixed height. At the foot of the-inclined plane, it moves on a horizontal surface (a) covered with silk cloth (b) covered with a layer of sand and (c) covered with a glass sheet. On which surface, will the marble move the shortest distance. Give reason for your answer.
Answer. Marble will move the shortest distance on the layer of sand because it will exert a greater force of friction on the marble and other two surfaces like silk cloth and giass sheet will exerta lesser friction force comparatively.

Question. 21 A father and son pushed their car to bring it to the side of road as it had stalled in the middle of the road. They experienced that although they had to push with all their might initially to move the car, the push required to keep the car rolling was smaller, once the car started rolling. Explain.
Answer. When the car is at rest, we have to apply greater force to set the car in motion which value is more. As the car starts moving, the friction changes into the rolling friction which is always less than the previous one. . . ,,
So, we have to exert the lesser force to keep it in motion.

Question. 22 When the cutting edge of a knife is put against a fast rotating stone to sharpen it, sparks are seen to fly. Explain the reason.
Answer. Due to the friction between cutting edge of a knife and stone, the temperature of the knife and hence stone increases and it increases to such a level that the sparks are produced which can be seen while sharpening it.

Question. 23 We have two identical metal sheets. One of them is rubbed with sand paper and the other with ordinary paper. The one rubbed with sand paper shines more than the other. Give reason.
Answer. While rubbing with sandpaper, more frictional force is produced between the layers of metal sheet and sandpaper which causes more force on dust particles and they are removed easily, so it will shine more.
But in case of ordinary paper, the force of friction is not sufficient to remove all the dust, so it will shine less in this case.

Question. 24 While travelling on a rickshaw, you might have experienced that if the seat cover is very smooth, you tend to slip when brakes are applied suddenly. Explain.
Answer. If the seat cover of rickshaw is very smooth, then the friction between our body and the seat is very small.
Therefore, when the brakes are applied, we tend to slip.

Long Answer Type Question

Question. 25 Two friends are trying to push a heavy load as shown in the figure below. Suggest a way which will make this task easier for them.

Answer. They can put rollers below the heavy load. Since, the rolling friction is smaller than the sliding friction. Therefore, putting rollers below the heavy load will make this task easier for them because rolling reduces friction.

The post NCERT Exemplar Problems Class 8 Science Friction appeared first on Learn CBSE.

NCERT  Exemplar Problems Class 8 Mathematics Chapter 1 Rational Numbers

Multiple Choice Questions
Question . 1 A number which can be expressed as \(\frac { p }{ q }\) , where p and q are integers and \( q\neq 0\) is
(a) natural number (b) whole number
(c) integer (d) rational number
Solution. (d) A number which can be expressed as \(\frac { p }{ q }\), where p and q are integers and \( q\neq 0\) is a rational number.

Question . 2 A number of the form \(\frac { p }{ q }\) is said to be a rational number, if
(a) p, q are integers (b) p, q are integers and \( q\neq 0\)
(c) p, q are integers and \( p\neq 0\) (d) p, q are integers and \( p\neq 0\), also \( q\neq 0\)
Solution. (b) A number of the form \(\frac { p }{ q }\) is said to be a rational number, if p and q are integers and

Question . 3 The numerical expression \( \frac { 3 }{ 8 } +\frac { (-5) }{ 7 } =\frac { -19 }{ 56 }\) shows that
(a)rational numbers are closed under addition
(b) rational numbers are not closed under addition
(c) rational numbers are closed under multiplication
(d) addition of rational numbers is not commutative
Solution. (b) We have \( \frac { 3 }{ 8 } +\frac { (-5) }{ 7 } =\frac { -19 }{ 56 }\)
Show that rational numbers are closed under addition.
[\(\frac { 3 }{ 8 }\) and\( \frac { -5 }{ 7 }\) are rational numbers and their addition is \(\frac { -19 }{ 56 }\) which is also a rational number]
Note The sum of any two rational numbers is always a rational number.

Question . 4 Which of the following is not true?
(a) rational numbers are closed under addition
(b) rational numbers are closed under subtraction
(c) rational numbers are closed under multiplication
(d) rational numbers are closed under division
Solution. (d) Rational numbers are not closed under division.
As, 1 and 0 are the rational numbers but \( \frac { 1 }{ 0 }\) is not defined.

Question . 5 \(-\frac { 3 }{ 8 } +\frac { 1 }{ 7 } =\frac { 1 }{ 7 } +[\frac { -3 }{ 8 } ]\) is an example to show that
(a) addition of rational numbers is commutative
(b) rational numbers are closed under addition
(c) addition of rational numbers is associative
(d) rational numbers are distributive under addition
Solution.

Clearly, a + b = b + a
So, addition is communication for rational numbers

Question . 6 Which of the following expressions shows that rational numbers are associative under multiplication.

Solution.

So, a x (b  x c) = (a x b) x c
Hence, the given expression shows that rational numbers are associative under multiplication.

Question . 7 Zero (0) is
(a) the identity for addition of rational numbers
(b) the identity for subtraction of rational numbers
(c) the identity for multiplication of rational numbers
(d) the identity for  division of rational numbers
Solution . (a) Zero (0) is the identity for addition of rational numbers.
That means,
If a is a rational number.
Then, a+0=0+a = a
Note Zero (0) is also the additive identity for integers and whole number as well.

Question . 8 One (1) is
(a) the identity for addition of rational numbers
(b) the identity for subtraction of rational numbers
(c) the identity for multiplication of rational numbers
(d) the identity for division of rational numbers
Solution . (c) One (1) is the identity for multiplication of rational numbers.
That means,
If a is  a rational number.
Then, a-1 = 1-a = a
Note One (1) is the multiplication identity for integers and whole number also.

Question . 9 The additive inverse  of \(\frac { -7 }{ 19 }\) is

Solution . (b) We know that, if a and b are the additive inverse of each other, then a + b = 0
Suppose, x is the additive inverse of \(\frac { -7 }{ 19 }\)

Question . 10 Multiplicative inverse of a negative rational number is
(a) a positive rational number (b) a negative rational number
(c) 0 (d) 1
Solution. (b) We know that, the product of two rational numbers is 1, taken they are multiplication inverse of each other, e.g.
Suppose, p is negative rational number, i.e.
\(\frac { 1 }{ p }\) is the  multiplicative inverse of-p, then, -p x \(\frac { 1 }{ -p }\) = 1
Hence, multiplicative inverse of a negative rational number is a negative rational number.

Question. 11 If x + 0 = 0 + x = x, which is rational number, then 0 is called
(a) identity for addition of rational numbers
(b) additive inverse of  x
(c) multiplicative inverse of x
(d) reciprocal of x
Solution . (a) We know that, the sum of any rational number and zero (0) is the rational number itself.
Now, x + 0 = 0+ x= x, which is a rational number, then 0 is called identity for addition of rational numbers.

Question . 12 To get the product 1,  we should multiply \( \frac { 8 }{ 21 }\) by

Solution .

Question . 13 – (-x) is same as
(a)-x (b)x (c)\(\frac { 1 }{ x }\) (d)\(\frac { -1 }{ x }\)
Solution . (b) -(-x) = x
Negative of negative rational number is equal to positive rational number.

Question . 14 The multiplicative inverse of \( -1\frac { 1 }{ 7 }\) is

Solution . (d) We know that, if the product of two rational numbers is 1, then they are multiplicative inverse of each other.

Question . 15 If x is any rational number, then x + 0 is equal to
(a)x (b) 0 (c)-x (d) Not defined
Solution . (a) If x is any rational number, then x + 0 = x [0 is the additive identity]

Question . 16  The reciprocal of 1 is ;
(a) 1 (b) -1 (c) 0 (d) Not defined
Solution . (a) The reciprocal of 1 is the number itself.

Question . 17  The reciprocal of -1 is
(a) 1 (b) -1 (c) 0 (d) Not defined
Solution . (b) The reciprocal of -1 is the number itself.

Question . 18 The reciprocal of 0 is
(a) 1 (b) -1 (c) 0 (d) Not defined
Solution . (d) The reciprocal of 0 is not defined.

Question . 19 The reciprocal of any rational number \(\frac { p }{ q }\) , where p and q are integers and \( q\neq 0\) is
(a)\(\frac { p }{ q }\) (b)1 (c)0 (d)\(\frac { q }{ p }\)
Solution . (d) The reciprocal of any rational number \(\frac { p }{ q }\), where p and q are integers and \( q\neq 0\) is \(\frac { q }{ p }\)

Question . 20 If y is the reciprocal of rational number x, then the reciprocal of y will be
(a)x (b) y (c) \(\frac { x }{ y }\) (d) \(\frac { y }{ x }\)
Solution . (a) If y be the reciprocal of rational number x, i.e. y = \(\frac { 1 }{ x }\) or x = \(\frac { 1 }{ y }\).
Hence, the reciprocal of y will be x.

Question .21

Solution .

Question . 22 Which of the following is an example of distributive property of multiplication over addition for rational numbers.

Solution . We know that, the distributive property of multiplication over addition for rational numbers can be expressed as a x (b + c) = ab + ac, where a, b and c are rational numbers.

is the example of distributive property of multiplication over addition for rational numbers.

Question . 23 Between two given rational numbers, we can find
(a) one and only one rational number
(b) only two rational numbers
(c) only ten rational numbers
(d) infinitely many rational numbers
Solution . (d) We can find infinite many rational numbers between two given rational numbers.

Question .24

(a) Between x and y
(b) Less than x and y both
(c) Greater than x and y both
(d) Less than x but greater than y
Solution .

Question . 25 Which of the following statements is always true?

Solution .

Fill in the Blanks
In questions 26 to 47, fill in the blanks to make the statements true.
Question . 26 The equivalent of \( \frac { 5 }{ 7 } \) whose numerator is 45, is —.
Solution .

Question . 27 The equivalent rational number of \( \frac { 7 }{ 9} \) , whose denominator is 45 is——————.
Solution .

Question . 28 Between the numbers \(\frac {15 }{ 20} \) and \(\frac { 35 }{ 40} \), the greater number is———————-.
Solution .

Question . 29 The reciprocal of a positive rational number is—————.
Solution .

Question . 30 The reciprocal of a negative rational number is——————–.
Solution .

Question. 31 Zero has————reciprocal.
Solution .

Question. 32 The numbers ————–and————–are their own reciprocal.
Solution .

Question . 33 If y is the reciprocal of x, then the reciprocal of \({ y }^{ 2 }\) in terms of x will be—————-.
Solution .

Question . 34

Solution .

Question . 35

Solution .

Question . 36 The negative of 1 is—————-.
Solution . -1 The negative of 1 is -1.

Question . 37

Solution .

Question . 38 \(\frac { -5 }{ 7 }\) is———————than -3.
Solution .

Question . 39 There are rational numbers between any two rational numbers.
Solution . Infinite
There are infinite rational numbers between any two rational numbers.

Question . 40 The rational numbers \(\frac { 1 }{ 3 }\) and \(\frac { -1 }{ 3 }\) are on the sides of zero on the number line.
Solution .

Question . 41 The negative of a negative rational number is always a—————-rational
number.
Solution. positive
Let x be a positive rational number.
Then, – x be a negative rational number.
Now, negative of a negative rational number = – (- x)= x =positive rational number.

Question . 42 Rational numbers can be added or multiplied in any————-.
Solution . order
Rational numbers can be added or multiplied in any order and this concept is known as commutative property.

Question . 43 The reciprocal of \(\frac { -5 }{ 7 }\) is——————.
Solution .

Question . 44 The multiplicative inverse of \(\frac { 4 }{ 3 }\) is———–.
Solution .

Question . 45 The rational number 10.11 in the form \(\frac { p }{ q }\) is ——–.
Solution .

Question .46

Solution .

Question . 47 The two rational numbers lying between -2 and -5 with denominator as 1 are———–and————.
Solution .

True/False
In questions 48 to 99, state whether the given statements are True or False.
Question . 48 If \(\frac { x }{ y }\)is a rational number, then y is always a whole number.
Solution .

Question . 49 If \(\frac { p }{ q }\) is a rational number, then p Cannot be equal to zero.
Solution .

Question . 50 If \(\frac { r }{ s }\) is a rational number, then s cannot be equal to zero.
Solution .

Question . 51 \(\frac { 5 }{ 6 }\) lies between \(\frac { 2 }{ 3 }\) and 1.
Solution .

Question . 52 \(\frac { 5 }{ 10 }\) lies between \(\frac { 1 }{ 2 }\) and 1.
Solution .

Question . 53 \(\frac { 5 }{ 10 }\) lies between -3 and 4.
Solution .

Question . 54 \(\frac { 9 }{ 6 }\) lies between 1 and 2.
Solution .

Question . 55 If \(a\neq 0\) the multiplicative inverse of \(\frac { a }{ b }\) is \(\frac { b }{ a }\) .
Solution .

Question . 56 The multiplicative inverse of \(\frac { -3 }{ 5 }\) is \(\frac { 5 }{ 3 }\) .
Solution .

Question . 57 The additive inverse of \(\frac { 1 }{ 2 }\) is -2.
Solution .

Question . 58

Solution .

Question . 59 For every rational number x, x + 1 = x.
Solution . False
For every rational number , x + 0 = x

Question . 60

Solution .

Question . 61 The reciprocal of a non-zero rational number \(\frac { q }{ p }\) is the rational number \(\frac { q }{ p }\).
Solution .False
The reciprocal of a non-zero rational number \(\frac { q }{ p }\) . is the rational number\(\frac { p }{ q }\)

Question . 62 If x + y = 0, then -y is known as the negative of x, where x and y are rational numbers.
Solution . False
If x and y are rational numbers and x+ y = 0.
Then, y is known as the negative of x.

Question . 63 The negative of the negative of any rational number is the number itself.
Solution . True
Let x be a positive rational number. Then, -x be a negative rational number.
Now, negative of negative rational number = -(-x)= x = Positive rational number

Question . 64 The negative of 0 does not exist.
Solution . True
Since, zero is neither a positive integer nor a negative integer.

Question . 65 The negative of 1 is 1 itself.
Solution . False
The negative of 1 is -1.

Question . 66 For all rational numbers x and y,x-y = y- x
Solution . False
For all rational numbers x and y,
x-y = -(y-x)

Question . 67 For all rational numbers x and y, x x y = y x x.
Solution . True
For all rational numbers x and y,
x x y= y x x

Question . 68 For every rational number x, x x 0 = x.
Solution . False
For every rational number x,
x x 0 = 0

Question . 69 For every rational numbers x, y and z, x + (y x z) = (x + y) x (x + z)
Solution . False
For all rational numbers a, b and c.
a(b + c) = ab+ ac

Question . 70 For all rational numbers a, b and c,a (b + c) = ab + bc.
Solution . False
As, addition is not distributive over multiplication.

Question . 71 1 is the only number which is its own reciprocal.
Solution . False
Reciprocal of 1 is 1 and reciprocal of -1 is -1.

Question . 72 -1 is not the reciprocal of any rational number.
Solution . False
-1 is the reciprocal of -1.

Question . 73 For any rational number x, x + (-1) = – x.
Solution . False
For every rational number x,
x x (-1) = – x

Question . 74 For rational numbers x and y, if x < y, then x – y is a positive rational number.
Solution .

Question . 75 If x and y are negative rational numbers, then so is x + y.
Solution .

Question . 76 Between any two rational numbers there are exactly ten rational . numbers.
Solution . False
There are infinite rational numbers between any two rational numbers.

Question . 77 Rational numbers are closed under addition and multiplication but not under subtraction.
Solution . False
Rational numbers are closed under addition, subtraction and multiplication.

Question . 78 Subtraction of rational number is commutative.
Solution . False
Subtraction of rational numbers is not commutative, i.e. \(a-b\neq b-a\)
where, a and b are rational numbers.

Question . 79 \(-\frac { 3 }{ 4 }\) is smaller than -2 .
Solution .

Question . 80 0 is a rational number.
Solution .

Question . 81 All positive rational numbers lie between 0 and 1000.
Solution . False
Infinite positive rational numbers lie on the right side of 0 on the number line.

Question. 82 The population of India in 2004-05 is a rational number.
Solution. True
The population of India in 2004-05 is a rational number.

Question. 83 There are countless rational numbers between \(-\frac { 5 }{ 6 }\) and \(-\frac { 8 }{ 9 }\).
Solution.

Question. 84

Solution.

Question. 85 The rational number \(-\frac { 57 }{ 23 }\) lies to the left of zero on the number line.
Solution. False
Since,\(-\frac { 57 }{ 23 }\) is a positive rational number.
So, it lies on the right of zero on the number line.

Question .86 The rational number \(-\frac { 7 }{ -4 }\) lies to the right of zero on the number line.
Solution . False
Since, \(-\frac { 7 }{ -4 }\) is a negative rational number.
So, it lies on the left of zero on the number line.

Question .87 The rational number \(-\frac { -8 }{ -3 }\) lies neither to the right nor to the left of zero on the number line.
Solution . False
\(-\frac { -8 }{ -3 }\) = \(-\frac { 8 }{ 3 }\) is a positive rational number.
Hence, it lies on the right of zero on the number line.

Question . 88 The rational numbers \(-\frac { 1 }{ 2 }\) and -1 are on the opposite sides of zero on the number tine.
Solution . True
Since, positive rational number and negative rational number are on the opposite sides of zero on the number line.’
Hence, \(-\frac { 1 }{ 2 }\) and -1 are on the opposite sides of zero on the number line.

Question . 89 Every fraction is a rational number.
Solution .

Question . 90 Every integer is a rational number.
Solution . True
Every integer is a rational number whose denominator remain 1.

Question . 91 The rational numbers can be represented on the number line.
Solution . True
The rational numbers can be represented on the number line.

Question . 92 The negative of a negative rational number is a positive rational number.
Solution . True
Let be a positive rational number.
Then, – x be the negative rational number.
Hence, negative of negative rational number = – (- x)= x = Positive rational number

Question . 93 If x and y are two rational numbers such that x > y, then x – y is always a positive rational number.
Solution . True
If x and y are two rational numbers such that x > y.
Then, there are three possible cases, i.e.
Case I x and y both are positive. ‘
Case II x is positive and y is negative.
Case III x and y both are negative.
In all three cases, x – y is always a positive rational number.

Question . 94 0 is the smallest rational number.
Solution . False
As the smallest rational number does not exist.

Question .95 Every whole number is an integer.
Solution .True
W (whole numbers) = {0,1,2, 3 }
Z (integers) = {…- 3, – 2, -1, 0,1,2, 3,…}
Every whole number is an integer, but every integer is not a whole number.

Question .96 Every whole number is a rational number.
Solution .True
Every whole number can be written in the form of \(-\frac { p }{ q }\), where p, q are integers and \(q\neq 0\).
Hence, every whole number is a rational number.

Question . 97 0 is whole number but it is not a rational number.
Solution . False
0 is a whole number and also a rational number.

Question . 98 The rational numbers \(-\frac { 1 }{ 2 }\)and \(-\frac -{ 5 }{ 2}\) are on the opposite sides of zero on the number line.
Solution . True
Positive rational number and negative rational number remain on opposite sides of zero on the number line.

Question .99 Rational numbers can be added (or multiplied) in any order

Solution .

Question . 100 Solve the following, select the rational numbers from the list which are also the integers.

Solution . From the given rational numbers, the numbers whose denominator is 1 and the numbers whose numerator is the multiple of denominator are the integers.

Question . 101 Select those which can be written as a rational number with denominator 4 in their lowest form

Solution . From the given rational numbers, the number with denominator 4 in their lowest form is \(-\frac { 5 }{ -4 }\)

Question . 102 Using suitable rearrangement and find the sum

Solution .

Question . 103 Verify – (-x) = x for

Solution .

Question . 104 Give one example each to show that the rational numbers are closed under addition, subtraction and multiplication. Are rational numbers closed under division? Give two examples in support of your answer.
Solution . We know that, rational numbers are closed under addition, subtraction and multiplication. We can understand this from the following examples.
Rational numbers are closed under addition


But rational are not closed under division. If zero is excluded from the collection of rational numbers, then we can say that rational numbers are closed under division.

Question . 105 Verify the property x + y = y + x of rational numbers by taking

Solution .

Question . 106 Simplify each of the following by using suitable property. Also, name the property.

Solution .

Question . 107

Solution .

Question . 108 Verify the property x x y = y x x of rational numbers by using

Solution .

Question . 109 Verify the property x x (y x z)=i.(x x y) x z of rational numbers by using

Solution .

Question . 110 Verify the property x x (y + z) = x x y + x x z of rational numbers by taking

Solution .

Question . 111 Use the distributivity of multiplication of rational numbers over addition to simplify

Solution .

Question. 112 Simplify

Solution .

Question. 113 Identify the rational number that does not belong with the other three. Explain your reasoning

Solution . does not belong with the other three. Since,\( \frac { -7 }{ 3 }\) as it is smaller than -1 whereas rest of the numbers are greater than -1.

Question. 114 The cost of \( \frac { 19 }{ 4 }\) m of wire is Rs \( \frac { 171 }{ 2 }\) Find the cost of one metre of the wire.
Solution .

Question. 115 A train travels \( \frac { 1445 }{ 2 }\) km in \( \frac { 17 }{ 2 }\) h. Find the speed of the train in km/h.
Solution .

Question. 116 If 16 shirts of equal size can be made out of 24m of cloth, how much cloth is needed for making one shirt?
Solution . If 16 shirts are to be made by cloth of 24 m
Then, 1 shirt is to be made by cloth of = \( \frac { 24 }{ 16 }\) m = \( \frac { 3 }{ 2 }\) m = 1.5 m
Hence, 1.5 m cloth is needed for making one shirt.

Question. 117 \( \frac { 7 }{ 11 }\) of all the money in Hamid’s bank account is Rs 77000. How much money does Hamid have in his bank account?
Solution .

Question. 118 A 117\( \frac { 1 }{ 3 }\) m long rope is cut into equal pieces measuring 7\( \frac { 1 }{ 3 }\) m each. How many such small pieces are these?
Solution .

Question. 119 \( \frac { 1 }{ 6 }\) of the class students are above average, \( \frac { 1 }{ 4 }\) are average and rest are below average. If there are 48 students in all, how many students are below average in the class?
Solution . Number of above average students = \( \frac { 1 }{ 6 }\) of the class students
Number of average students = \( \frac { 1 }{ 4 }\)of the class students

Question. 120 \( \frac { 2 }{ 5 }\)of total number of students of a school come by car while \( \frac { 1 }{ 4 }\) of students come by bus to school. All the other students walk to school of which \( \frac { 1 }{ 3 }\)walk on their own and the rest are escorted by their parents. If 224 students come to school walking on their own, how many students study in that school?
Solution .

The post NCERT Exemplar Problems Class 8 Mathematics Rational Numbers appeared first on Learn CBSE.

NCERT Exemplar Problems Class 8 Science Chapter 13 Sound

Multiple Choice Questions (MCQs)

Question 1
A list of mediums is given below
(i) Wood (ii) Water
(iii) Air (iv) Vacuum
In which of these mediums can sound travel?
(a) (i) and (ii) (b) (i), (ii) and (iii)
(c) (iii) and (iv) (d) (ii), (iii) and (iv)
Answer.
(b) Sound requires any medium to travel but in vacuum there is no medium, so sound cannot travel through them.

Question 2
The loudness of sound depends on
(a) its amplitude (b) its time period
(c) its frequency (d) its speed
Answer.
(a) Sound will be loud when its amplitude is large and sound will be soft when its amplitude is small hence, loudness of sound depends upon its amplitude.

Question 3
Which of the following statements are correct?
(i) Sound is produced by vibrations.
(ii)Sound requires a medium for propagation.
(iii)Light and sound both require a medium for propagation.
(iv)Sound travels slower than light.
(a) (i) and (ii) (b) (i), (ii) and (iii)
(c) (ii), (iii) and (iv) (d) (i), (ii) and (iv)
Answer.
(d) Because light can travel in vacuum also but it is only sound which requires medium to travel.

Question 4
An object is vibrating at 50 Hz. What is its time period?
(a) 0.02 s (b) 2 s
(c) 0.2 s (d) 20 s
Answer.

Question 5
order to reduce the loudness of a sound, we have to
(a) decrease its frequency of vibration of the sound
(b) increase its frequency of vibration of the sound
(c) decrease its amplitude of vibration of the sound
(d) increase its amplitude of vibration of the sound
Answer.
(c)Since, loudness depends upon amplitude, so it can be increased by increasing amplitude and it can be decreased by decreasing amplitude.

Question 6
Loudness of sound is measured in units of
(a) decibel (dB) (b) hertz (Hz)
(c) metre (m) (d) metre/second(m/s)
Answer.
(a) Unit of loudness of sound is decibel (dB). ,,

Question 7
The loudness of sound is determined by its
(a) amplitude of vibration
(b) ratio of amplitude and frequency of vibration •(c) frequency of vibration
(d) product of amplitude and frequency of vibration
Answer.
(a) Loudness of sound is determined by the amplitude of its vibrations.

Question 8
1 Hz is equal to
(a) 1 vibration per minute (b) 10 vibrations per minute
(c) 60 vibrations per minute (d) 600 vibrations per minute
Answer.
(c) 1 Hz = 1 vibration per second = 60 vibrations per minute

Question 9 Pitch of sound is determined by its
(a) frequency (b) speed
(c) amplitude (d) loudness
Answer.
(a) Pitch or shrillness is determined by the frequency of sound.

Question 10
Ultrasound has frequency of vibration
(a) between 20 and 20000 Hz
(b) below 20 Hz
(c) above 20000 Hz
(d) between 500 and 10000 Hz
Answer.
(c) Ultrasound has frequency of vibration above 20000 Hz.

Question 11
Lightning can be seen at the moment when it occurs. Paheli observes lightning in her area. She hears the sound 5 s after she observed lightning. How far is she from the place where lightning occurs?
(speed of sound = 330 m/s).
Answer.

Question 12
Does any part of our body vibrate when we speak? Name the part.
Answer.
Yes, while speaking the part which vibrates is called vocal cords. It is below the throat and creates vibrations while speaking.

Question 13
Boojho saw a cracker burst at night at a distance from his house. He heard the sound of the cracker a little later after seeing the cracker burst. Give reason for the delay in hearing the sound.
Answer.
The light travels faster than sound. So, the light from the cracker reaches faster than that of sound of the cracker.
Speed of light in air = 3 x 108 m/s
Speed of sound in air = 330 m/s

Question14
When we hear a sound, does any part of our body vibrate? Name the part.
Answer.
Yes, It is the eardrum which vibrates and sends vibrations to the inner ear, when we hear any sound.

Question 15
Name two musical instruments which produce sound by vibrating strings.
Answer.
Guitar and sitar are the two musical instruments which produce the sound by vibrating strings.

Question 16
A simple pendulum makes 10 oscillations in 20 s. What is the time period and frequency of its oscillations?
Answer.
Given, number of oscillations = 10
Time taken = 20 s
As, we know that the number of oscillations per second is frequency.

Question 17
We have learnt that vibration is necessary for producing sound. Explain why the sound produced by every vibrating body cannot be heard by us.
Answer.
Since, range of frequency for every vibrating body is different. But we can hear the vibrations which lies between the range of frequencies from 20 Hz to 20000 Hz, so sound of every vibrating body cannot be heard by us.

Question18
Suppose a stick is struck against a frying pan in vacuum. Will the frying > pan vibrate? Will we be able to hear the sound? Explain.
Answer.
Yes, the frying pan will vibrate.
Since, it is being hit by the stick but vibrations need a medium to travel and there is no
medium in vacuum, so we’cannot hear the vibrations produced.

Question19
Two astronauts are floating close to each other in space. Can they talk to
each other without using any special device? Give reasons.
Answer.
No, they cannot talk to each other without using any special device because there is no medium in space and sound needs medium to travel.

Question20
List three sources of noise pollution in your locality.
Answer.
Sources of noise pollution gre .
(i) Horns of vehicles
(ii)Loudspeakers of temples
(iii)Generators running without silencers

Question 21
We have a stringed musical instrument. The string is plucked in the middle first with a force of greater magnitude and then with a force of  smaller magnitude. In which case would the instrument produce a louder
sound?
Answer.
It will create more loud sound in case of string stretched with a greater force because amplitude is greater in this case and loudness depends on the amplitude. Greater will be the loudness, greater will be the amplitude.

Question 22
How is sound produced and how is it transmitted and heard by us?
Answer.
Sound is produced when any object starts vibrating by any means.
These vibrations travel from the source all around the environment through the particles of the environment, thus, it reaches to its destination, i.e. our ear.
Now, it enters our ear and travels down a canal at the end of which a thin membrane is stretched tightly known as eardrum. The eardrum sends vibrations to inner part of the ear and finally reaches to the brain and we hear the sounds.

Question 23
An alarm bell is kept inside a vessel as shown in figure. A person standing close to it can distinctly hear the sound of alarm. Now, if the air inside the vessel is removed completely, how will the loudness of alarm get affected for the same person?

Answer.
Initially, the person is able to hear the sound coming from air and water distinctly. But after sometime, when the air is completely removed from the bottle, the sound will pass through the water and not reached to man.
So, the man will not hear the sound which was coming through the air initially.

Question 24
The town hall building is situated close to Boojho’s house. There is a clock on the top of the townhall building which rings the bell every hour. Boojho has noticed that the sound of the clock appears to be much clearer at night. Explain.
Answer.
We know that speed, pitch, loudness all are initiated with a vibration. During the day, there is a number of vibrations around us. So, the sound coming from the clock gets disturbed and amplitude of vibrations becomes small.
But during the night, there are not such multiple vibrations in the environment. So, sound is more clear. Further,-“the dew factor at night increases the speed of sound as moisture level increases.

Long Answer Type Question

Question 25
Suggest three measures to limit noise pollution in your locality.
Answer.
The following measures to limit noise pollution in our locality is given as:
(i) The industries which produce noise should be setup away from the residential areas.
(ii)The television and the music systems should be run at the low volumes.
(iii)The aircraft engines, transport vehicles, industrial machines and home appliances ’ must be installed with siltncing devices.

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NCERT Exemplar Problems Class 8 Mathematics  Chapter 2 Data Handling

Multiple Choice Questions
Question. 1 The height of a rectangle in a histogram shows the
(a) width of the class (b) upper limit of the class
(c) lower limit of the class (d) frequency of the class
Answer. (d) The height of a rectangle in a histogram shows the frequency of the class,
Note The number of times a particular observation occurs in a given data, is called its frequency.

Question. 2 A geometric representation showing the relationship between a whole and its parts, is a
(a) pie chart (b) histogram
(c) bar graph 4 (d) pictograph
Answer. (a) Data can also be represented by using a pie chart (circle graph), It shows the relationship between a whole and its parts,

Question. 3 In a pie chart, the total angle at the centre of the circle is
(a) 180° (b) 360°
(c) 270° (d) 90°
Answer. (b) The total angle at the centre of the circle is 360°.

Question. 4 The range of the data 30, 61, 55, 56, 60, 20, 26, 46, 28, 56 is
(a) 26 (b) 30
(c) 41 (d) 61
Answer. (c) Range of data = Maximum value – Minimum value = 61 – 20 = 41

Question. 5 Which of the following is not a random experiment?
(a) Tossing a coin
(b) Rolling a die
(c) Choosing a card from a deck of 52 cards
(d) Throwing a stone from the roof of a building
Answer. (d) Tossing a coin, rolling a die and choosing a card from a deck of 52 cards are the random experiments, as we don’t have an idea about the output of these experiments. But if we throw a stone from the roof of a building, we know the output, it will fail on the ground.

Question. 6 What is the probability of choosing a vowel from the alphabets?

Answer.Total number of alphabets = 26
Total number of vowels =5

Question. 7 In a school, only 3 out of 5 students can participate in a competition. What is the probability of the students who do not make it to the competition?
(a) 0.65 (b) 0.4
(c) 0.45 (d) 0.6
Answer. (b) Given, 3 out of 5 students can participate in a competition, i.e. 2 out of 5 students cannot participate in a competition.
Hence, probability of students who do not make it to competition \(\frac { 2 }{ 5 }\) = 0.4
Students of a class voted for their favourite colour and a pie chart was prepared based on the data collected.
Observe the pie chart given below and answer the questions 8-10 based on it.

Question.8 Which colour received \(\frac { 1 }{ 5 } \) of the votes?
(a) Red (b) Blue
(c) Green (d) Yellow
Answer.

Question. 9 If 400 students voted in all, then how many did vote ‘Others’ colour as their favourite?
(a)6 (b) 20 (c)24 (d) 40
Answer. (c) If total number of votes = 400
Then, number of votes in favour of ‘Others’ = 6% of 400 =\(\frac { 6 }{ 100 } \) x 400= \(\frac { 3 }{ 50 } \) x 400= 24

Question. 10 Which of the following is a reasonable conclusion for the given data?
(a) \(\frac { 1 }{ 20 } \) th student voted for blue colour 20
(b) Green is the least popular colour
(c) The number of students who voted for red colour, is two times the number of students who voted for yellow colour
(d) Number of students liking together yellow and green colours is approximately the same as those for red colour
Answer. (d) Number of students liking together yellow and green colours is (14+ 20)% i.e. 34%, which is approximately the same as those for red (35%).

Question. 11 Listed below are the temperatures in °C for 10 days.
-6,-8, 0,3, 2, 0,1, 5,4,4 ‘
What is the range of the data?
(b) 13°C (d) 12°C
Answer. (b) Range of data = Maximum temperature – Minimum temperature = 5-(-8)= 5+8= 13 Hence, the range of data is 13°C.

Question. 12 Ram put some buttons on the table. There were 4 blue, 7 red, 3 black and 6 white buttons in all. All of a sudden, a cat jumped on the table and knocked out one button on the floor. What is the probability that the button on the floor
(a)\(\frac { 7 }{ 20 } \)
(b)\(\frac { 3 }{ 5 } \)
(c)\(\frac { 1 }{ 5 } \)
(d)\(\frac { 1 }{ 4 } \)
Answer. (c) Total number of buttons = 4+ 7+ 3+ 6 = 20

Question. 13 Rahul, Varun and Yash are playing a game of spinning a coloured wheel. Rahul wins, if spinner lands on red. Varun wins, if spinner lands on blue. Yash wins, if it lands on green. Which of the following spinners should be used to make the game fair?

(a) (i) (b) (ii) (c) (iii) (d) (iv)
Answer. (d) The figure (iv) should be selected to make the game fair as the area occupied by each colour is equal. Hence, the chance of winning for each person is equal.

Question. 14 In a frequency distribution with classes 0-10,10-20 etc., the size of the class intervals is 10. The lower limit of fourth class is
(a) 40 (b) 50 (c) 20 (d) 30
Answer. (d) Given classes are 0-10 and 10-20.
As, the class of given classes is 10, so the next classes will be 20-30 and 30-40.
As, the fourth class is 30-40.
Hence, the lower limit of fourth class is 30.

Question. 15 A coin is tossed 200 times and head appeared 120 times. The probability of getting a head in this experiment is
(a)\(\frac { 2 }{ 5 } \) (b)\(\frac { 3 }{ 5 } \) (c)\(\frac { 1 }{ 5 } \) (d)\(\frac { 4 }{ 5 } \)
Answer. (b) Given, head appeared 120 times, if a coin is tossed 200 times. Then,
probability of getting a head in this experiment=

Question. 16 Data collected in a survey shows that 40% of the buyers are interested in buying a particular brand of toothpaste. The central angle of the sector of the pie chart representing this information is
(a) 120° (b) 150°
(c) 144° (d) 40°
Answer. (c) Percentage of buyers who selected the particular brand of toothpaste = 40%
Central angle of the sector of pie chart representing the above information
=40% of central angle
= \(\frac { 40 }{ 100 } \) x 360° = 144°

Question. 17 Monthly salary of a person is ? 15000. The central angle of the sector representing his eiqjenses on food and house rent on a pie chart is 60°. The amount he spends on food and house rent, is
(a) Rs. 5000 (b) Rs. 2500
(c) Rs. 6000 (d) Rs. 9000
Answer. (b) Central angle of the sector representing his expenses on food and house rent on a pie chart =60°
Part of the monthly salary he is expending on food and house rent = \(\frac { 60° }{ 360° } \)= \(\frac { 1 }{ 6 } \)
Hence, the amount he spends on food and house rent =\(\frac { 1 }{ 6 } \) x Monthly salary
\(\frac { 1 }{ 6 } \)x 15000=Rs. 2500

Question. 18 The following pie chart*gives the distribution of constituents in the human body. The central angle of the sector showing the distribution of protein and other constituents is

(a)108° (b) 54° (c)30° (d)216°
Answer. (a) Distribution of protein and other constituents in human body = 16+14 = 30%
Central angle of the sector showing the distribution of protein and other constituents
= \(\frac { 30 }{ 100 } \) x 360° = 108°

Question. 19 Rohan and Shalu are playing with 5 cards as shown in the given figure. What is the probability of Rohan picking a card without seeing, that has the number 2 on it?

(a)\(\frac { 2 }{ 5 } \) (b)\(\frac { 1 }{ 5 } \) (c) \(\frac { 3 }{ 5 } \) (d)\(\frac { 4 }{ 5 } \)
Answer. (a) Total number of cards = 5
Number of cards having 2 on it = 2
Probability of Rohan picking a card without seeing, that has the number 2 on it \(\frac { 2 }{ 5 } \)

In questions 20 to 22, the following pie chart represents the distribution of proteins in parts of human body.
Question. 20 What is the ratio of distribution of proteins in the muscles to that of proteins in the bones?
(a) 3 : 1 (b) 1 : 2
(c) 1 : 3 (d) 2 : 1
Answer.Distribution of protein in muscles =\(\frac { 1 }{ 3 } \)
Distribution of protein in bones = \(\frac { 1 }{ 6 } \)
Ratio of distribution of proteins in the muscles to that of proteins in the bones
= \(\frac { 1 }{ 3 } \): \(\frac { 1 }{ 5 } \) =\(\frac { 1 }{ 3 } \) x \(\frac { 1 }{ 5 } \)
= 2:1

Question. 21 What is the central angle of the sector (in the above pie chart) representing skin and bones together?
(a) 36° (b) 60° (c) 90° (d) 96°
Answer.

Question. 22 What is the central angle of the sector representing hormones enzymes and other proteins?
(a) 120° (b) 144° (c)156° (d)176°
Answer.

Question. 23 A coin is tossed 12 times and the outcomes are observed as shown below:

Answer.Total number of times coin tossed =12
Total number of occurrence of head = 5
The chance of occurrence of head = \(\frac { Number of times head appeared }{ Numberoftimesacoinistossed }\)
= \(\frac { 5 }{ 12 } \)

Question. 24 Total number of outcomes, when a ball is drawn from a bag which contains 3 red, 5 black and 4 blue balls, is
(a) 8 (b) 7 (c) 9 (d) 12
Answer. (d) Given, a bag contains 3 red, 5 black and 4 blue balls.
Then, total number of outcomes = Total number of balls = 3+ 5+ 4 = 12

Question. 25 A graph showing two sets of data simultaneously is known as
(a) pictograph (b) histogram
(c) pie chart (d) double bar graph
Answer. (d) A graph showing two sets of data simultaneously is known as double bar graph.

Question. 26 Size of the class 150-175 is
(a) 150 (b) 175
(c) 25 (d) -25
Answer. (c) Size of the class 150-175 = Upper limit – Lower limit = 175 -150 = 25

Question. 27 In a throw of a die, the probability of getting the number 7 is
(a)\(\frac { 1 }{ 2 } \) (b)\(\frac { 1 }{ 6 } \)
(c)1 (d) 0
Answer. (d) In a die, there are only 6 numbers, which are 1,2, 3, 4, 5 and 6.
Hence, there is no possibility of number 7.
Therefore, probability of getting the number 7 is 0.

Question. 28 Data represented using circles is known as
(a) bar graph (b) histogram
(c) pictograph (d) pie chart
Answer. (d) Data represented using circles is known as pie chart.
Note Bar graph Data using bars of different heights in a graphical display is known as bar graph (bar chart).
Histogram Grouped data can be represented by a histogram.
Pictograph Data using pictures and symbols to represent the statistical information is known as pictograph.

Question. 29 Tally marks are used to find
(a) class intervals (b) range (c) frequency (d) upper limit
Answer. (c) Tally marks are used to find the frequency of the observations.

Question. 30 Upper limit of class interval 75-85 is
(a) 10 (b)-10 (c)75 (d) 85
Answer. (d) Upper limit of class interval 75-85 is 85.

Note The upper value of class interval is called its upper class limit and lower value of a class interval is called lower class limit

Question. 31 Numbers 1 to 5 are written on separate slips, i.e. one number on one slip and put in a box. Wahida pick a slip from the box without looking at it. What is the probability that the slip bears an odd number?
(a)\(\frac { 1 }{ 5 } \) (b)\(\frac { 2 }{ 5 } \) (c)\(\frac { 3 }{ 5 } \) (d)\(\frac { 4 }{ 5 } \)
Answer. (c) Numbers on the slips are 1,2, 3, 4 and 5.
Odd numbers = 1,3, 5
Number of slips bears an odd number = 3
Probability that the slip bears an odd number =\(\frac { Number of slips bears an odd number }{ Total number of slips }\)
=\(\frac { 3 }{ 5 } \)

Question.32 A glass jar contains 6 red, 5 green, 4 blue and 5 yellow marbles of same size. Hari takes out a marble from the jar at random. What is the probability that the chosen marble is of red colour?

(a)\(\frac { 7 }{ 10 } \) (b) \(\frac { 3 }{ 10 } \) (c) \(\frac { 4 }{ 5 } \) (d)\(\frac { 2 }{ 5 } \)
Answer.As, jar contains 6 red, 5 green, 4 blue and 5 yellow marbles of same size. Then, probability that the chosen marble is of red colour

Question. 33 A coin is tossed two timgs. The number of possible outcomes is
(a) 1 (b) 2 (0 3 (d) 4
Answer. (d) Number of possible outcomes is 4, i.e. HH, HT, TH, TT.

Question. 34 A coin is tossed three times. The number of possible outcomes is
(a) 3 (b) 4 (0 6 (d) 8
Answer. (d) Number of possible outcomes is 8, i.e. HHH, HHT, HTH, THH, TTH, THT, HTT, TTT.

Question. 35 A die is tossed two times. The number of possible outcomes is (a) 12 (b) 24 (c)36 (d) 30
Answer. (c) Number of possible outcomes is 36,
i.e. (1,1), (1, 2), (1,3), (1,4), (1,5), (1,6)
(2, 1), (2, 2), (2, 3)…. (2, 6)
(3,1), (3,2), (3,3)…. (3,6)
(4, 1), (4,2)…. (4,6)
(5, 1), (5,2)…. (5,6)
(6,1),(6, 2)…. (6,6)

Fill in the Blanks
In questions 36 to 58, fill in the blanks to make the statements true.

Question. 36 Data available in an unorganised form is called…………… data.
Answer. raw
Data available in an unorganised form is called raw data.

Question. 37 In the class interval 20-30, the lower class limit is…………
Answer. 20
In the class interval 20-30, the lower class limit is 20.

Question. 38 In the class interval 26-33, 33 is known as……….
Answer. upper class limit
In class interval 26-33, 33 is known as upper class limit.

Question. 39 The range of the data 6, 8, 16, 22, 8, 20, 7, 25 is………….
Answer. 19
Range .of the given data = Maximum value – Minimum value = 25 – 6 = 19

Question. 40 A pie chart is used to compare …………….. to a whole.
Answer. a part
A pie chart is used to compare a part to a whole.

Question. 41 In the experiment of tossing a coin one time, the outcome is either……………..or…………………
Answer. head, tail On tossing a coin one time, the outcome’can-be head or tail.

Question. 42 When a die is rolled, the six possible outcomes are……………. .
Answer. 1,2, 3, 4, 5, 6
When a die is rolled, then the six possible outcomes are 1,2, 3, 4, 5 and 6.

Question. 43 Each outcome or a collection of outcomes in an experiment makes an ………………..
Answer. event
Each outcome or a collection of outcomes in an experiment makes an event.

Question. 44 An experiment whose outcomes cannot be predicted exactly in advance, is called a…………… experiment.
Answer. random
An experiment whose outcomes cannot be predicted exactly in advance, is called a random experiment.

Question. 45 The difference between the upper and lower limits of a class interval is called the……………….. of the class interval.
Answer. size
The difference between the upper and lower limits of a class interval is called the size of the class interval.

Question. 46 The sixth class interval for a grouped data whose first two class intervals are 10-15 and 15-20 is ………………..
Answer. 35-40
From the first two intervals, we can observe that the class size is 5. So, the sixth class interval will be 35-40.
Histogram given below shows the number of people owning the different number of books. Answer 47 to 50 based on it.

Question. 47 The total number of people surveyed is……………. .
Answer. 35
Total number of people surveyed = 8 + 14 +-5 + 6 + 2 = 35

Question. 48 The number of people owning books more than 60 is…………………. .
Answer. 8
The number of people owning books more than 60 = 6 + 2 = 8

Question. 49 The number of people owning books less than 40 is……………….. .
Answer. 22
The number of people owning books less than 40 = 8 + 14 = 22

Question. 50 The number of people having books more than 20 and less than 40 is …………………..
Answer. 14
The number of people having books more than 20 but less than 40 = 14

Question. 51 The number of times a particular observation occurs in a given data, is called its………………. .
Answer. frequency
The number of times an observation occurs in a given data, is called its frequency.

Question. 52 When the number of observations is large, the observations are usually organised in groups of equal width, called………………….. .
Answer. class Intervals
When the number of observations is large, the observations are usually organised in groups of equal width, called class intervals.

Question. 53 The total number of outcomes when a coin is tossed, is……………… .
Answer. 2
The total number of outcomes’when a coin is tossed, is 2 i.e. head or tail.

Question. 54 The class size of the interval 80-85 is…………… .
Answer. 5
Class size of the interval 80-85 = Upper class limit – Lower class limit= 85-80=5

Question. 55 In a histogram,……………. are drawn with width equal to a class interval
without leaving any gap in between.
Answer. bars
In a histogram, bars are drawn with width equal to a class interval without leaving any gap in between.

Question. 56 When a die is thrown, outcomes 1, 2, 3, 4, 5, 6 are equally ………………..
Answer. likely
When a die is thrown, outcomes 1, 2, 3, 4, 5, 6 are equally likely. As, their chances to appear are equal.

Question. 57 In a histogram, class intervals and frequencies are taken along …………. axis and …………… axis.
Answer. X, Y
In a histogram, class intervals are taken along X-axis and frequencies are taken along Y-axis.

Question. 58 In the class intervals 10-20 and 20-30 respectively, 20 lies in the class……………… .
Answer. 20-30
In the class intervals 10-20 and 20-30 respectively, 20 lies in the class 20-30.

True/False
In questions 59 to 81, state whether the statements are True or False.

Question. 59 In a pie chart, a whole circle is divided into sectors.
Answer. True
In a pie chart, a whole circle is divided into sectors.

Question. 60 The central angle of a sector in a pie chart cannot be more than 180°.
Answer. False
The central angle of a sector in a pie chart can be more than 180°, but not more than 360°.

Question. 61 Sum of all the central angles in a pie chart is 360°.
Answer. True
Sum of all the central angles in a pie chart is 360°.

Question. 62 In a pie chart, two central angles can be of 180°.
Answer. True
In a pie chart, two central angles can be of 180°.

Question. 63 In a pie chart, two or more central angles can be equal.
Answer. True
In a pie chart, two or more central angles can be equal.

Question. 64 Getting a prime number on throwing a die is an event.
Answer. True
Getting a prime number on throwing a die is an event.

Question. 65 9 students got full marks.
Answer. True
9 students got full marks.

Question. 66 The frequency of less than 8 marks is 29.
Answer. False
The frequency of less than 8 marks = 5+10+8 = 23

Question. 67 The frequency of more than 8 marks is 21.
Answer. True
The frequency of more than 8 marks = 12 + 9 = 21

Question. 68 10 marks has the highest frequency.
Answer. False
9 Marks has the highest frequency.

Question. 69 If the fifth class interval is 60-65 and fourth class interval is 55-60, then the first class interval is 45-50.
Answer. False
If fifth class interval is 60-65 and fourth class interval is 55-60, then third class interval is 50-55, second class interval is 45-50 and first class interval is 40-45.

Question. 70 From the histogram given below, we can say that 1500 males above the age of 20 are literate.

Answer. False
Number of literate males above the age of 20 yr= 600 + 800 + 500 = 1900

Question. 71 The class size of the class interval 60-58 is 8.
Answer. True
Class size of the class interval 60-68 = Upper class limit – Lower class limit = 68 – 60= 8

Question. 72 If a pair of coins is tossed, then the number of outcomes are 2.
Answer. False
When a pair of coins is tossed, then the number of outcomes are 4, i.e. HH, HT, TH and TT.

Question. 73 On throwing a die once, the probability of occurrence of an even number \(\frac { 1 }{ 2 } \)
Answer. True
On throwing a die, the occurrence of even numbers can be as 2, 4 and 6.
Hence, probability of occurrence of a even number =\(\frac { Number of even numbers on a die}{ Total numbers on a die } \)
=\(\frac { 3 }{ 6 } \)=\(\frac { 1 }{ 2 } \)

Question. 74 On throwing a die once, the probability of occurrence of a composite number is \(\frac { 1 }{ 2 } \) .
Answer. False
On throwing a die, the occurrence of composite numbers can be as 4, 6.
Hence, probability of occurrence of a composite number
=\(\frac { Number of composite numbers on a die }{Total numbers on a die } \)
=\(\frac { 2 }{ 6 } \)=\(\frac { 1 }{ 3 } \)

Question. 75 From the given pie chart, we can infer that production of Manganese is least in state B.

Answer. False
From the given pie chart, we cannot infer that production of manganese is least in state B. Unless we know the central angle for it.

Question. 76 One or more outcomes of an experiment make an event.
Answer. True
One or more outcomes of an experiment make an event.

Question. 77 The probability of getting number 6 in a throw of a die is Similarly,\(\frac { 1 }{ 6 } \)
the probability of getting a number 5 is \(\frac { 1 }{ 5 } \)
Answer. False
The probability of getting number 6 or number 5 on a throw of a die = \(\frac { 1 }{ 6 } \)

Question. 78 The probability of getting a prime number is the same as that of a composite number in a throw of die.
Answer. False
In throw of a die, the occurrence of prime numbers can be as 2, 3, 5 and occurrence of composite numbers can be as 4, 6.
Hence, the probability of getting a prime number is 3/6 and of getting is 2/61, which is a composite not same.

Question. 79 In a throw of a die, the probability of getting an even number is the same as that of getting an odd number.
Answer. True
In throw of a die, the occurrence of even numbers can be as 2, 4, 6 and the occurrence of odd numbers can be as 1,3, 5.
Hence, probability of getting an even number is same as that of getting an odd number on a throw of a die.

Question. 80 To verify Pythagoras theorem is a random experiment.
Answer. False
Verifying Pythagoras theorem is not a random experiment, because we already know the result.

Question. 81 The following pictorial representation of data is a histogram.

Answer. True

Question. 82 Given below is a frequency distribution table. Read it and answer the questions that follow.

(a) What is the lower limit of the second class interval?
(b) What is the upper limit of the last class interval?
(c) What is the frequency of the third class?
(d) Which interval has a frequency of 10?
(e) Which interval has the lowest frequency?
(f) What is the class size?
Answer. (a) The lower limit of second class interval (20-30) is 20.
(b) The .upper limit of the last class interval (50-60) is 60.
(c) The frequency of the third class (30-40) is 4.
(d) The interval (20-30) has a frequency of 10.
(e) The interval (30-40) has the lowest frequency, i.e. 4.
(f) We know that,
Class size = Upper class limit – Lower class limit Consider first class, i.e. 10-20, then class size = 20-10 = 10

Question. 83 The top speeds of thirty different land animals have been organised into a frequency table. Draw a histogram for the given data.

Answer.

Question. 84 Given below is a pie chart showing the time spend by a group of 350 children in different games. Observe it and answer the questions that follow.

(a) How many children spend atleast one hour in playing games?
(b) How many children spend more than 2 h in playing games?
(c) How many children spend 3 or lesser hours in playing games?
(d) Which is greater, number of children who spend 2 hours or more per . day or number of children who play for less than one hour?
Answer. (a) Number of children who spend atleast 1 h in playing games i.e. the number of children playing 1 h or more than 1 h
= (Total number of children) – (Number of children spend less than 1 h)
= 350-6% of 350
= 350- \(\frac { 6 }{ 100 } \) x350
= 350 – 21 = 329
(b) Number of children who spend more than 2 h in playing games
= (34 + 10 + 4)%of the total number of students
= 48% of 350
= \(\frac { 48 }{ 100} \) x350 = 168
(c) Number of children who spend 3 or lesser hours in playing games
= (34 + 30 + 16 + 6)% of total number of students
= 86% of 350
= \(\frac { 86 }{ 100 } \) x350= 301
(d) Number of children who spend 2 h or more per day in playing games
= (30 + 34 + 10 + 4)% of total number of students = 78% of total number of students
Number of children who spend less than one hour = 6% of total number of students
Clearly, number of children who play for 2 h or more per day is greater than the number of children who play for less than 1 h.

Question. 85 The pie chart given below shows the result of a survey carried out to find the modes of travel used by the children to go to school. Study the pie chart and answer the questions that follow.

(a) What is the most common mode of transport?
(b) What fraction of children travel by car?
(c) If 18 children trfvelby car, how many children took part in the survey?
(d) By which two modes of transport are equal number of children travelling?
Answer. (a) The central angle is maximum for bus, hence bus is the most common mode of transport.
(b) Fraction of children travelled by car = \(\frac { Central angle }{ 360° } \) = \(\frac { 90° }{ 360° } \)
= \(\frac { 1 }{ 4 } \)
(c) We know that, fraction of children travel by car =\(\frac { 1 }{ 4 } \)
Hence, total number of children travelled by car = \(\frac { 1 }{ 4 } \) x Total number of children
=> 18 =\(\frac { 1 }{ 4 } \)x Total number of children
Total number of children =18 x 4 = 72
(d) The central angle made up the sectors representing cycle and walk are same. Hence, the cycle and walk are two modes of transport, by which equal number of children are travelling.

Question. 86 A die is rolled once. What is the probability that the number on top will be
(a) odd (b) greater than 5 (c) a multiple of 3
(d) less than 1 (e) a factor of 36 (f) a factor of 6
Answer.

Question. 87 Classify the following statements under appropriate headings.
(a) Getting the sum of angles of a triangle as 180°.
(b) India winning a cricket match against Pakistan.
(c) Sun setting in the evening.
(d) Getting 7 when a die is thrown.
(e) Sun rising from the West.
(f) Winning a racing competition by you.

Answer.(a) Certain to happen, because the sum of the angles of a triangle is 180°.
(b) May or may not happen, as the result of the match is unpredictable.
(c) Certain to happen, as the Sun always set in the evening.
(d) Impossible to happen, as there are only 6 possible outcomes on throwing a die, i.e. 1,2, 3, 4, 5 and 6.
(e) Impossible to happen, as the Sun rise from East.
(f) May or may not happen, as the winning of the competition is unpredictable.

Question. 88 Study the pie chart given below depicting the marks scored by a student in an examination out of 540. Find the marks obtained by him in each subject.
Answer.

Question. 89 Ritwik draws a ball from a bag that contains white and yellow balls.The probability of choosing a white ball is [/latex]\frac { 2 }{ 9 } [/latex]. If the total number of balls in the bag is 36, then find the number of yellow balls.
Answer.

Question. 90 Look at the histogram below and answer the questions that follow.

(a) How many students have height more than or equal to 135 cm, but less than 150 cm ?
(b) Which class interval has the least number of students?
(c) What is class size?
(d) How many students have height less than 140 cm?
Answer. (a) Number of students who have height more than or equal to 135 cm, but less than 150 cm = 14+ 18+ 10 = 42
(b) The class interval 150-155 has the least number of students, i.e. 4.
(c) We-know, class size = Upper class limit – Lower class limit Consider any class, say (125-130), then class size = 130-125 = 5 Hence, the class size is 5.
(d) Number of students who have height less than 140 cm = 6 + 8 + 14 = 28

Question. 91 Following are the numbers of members in 25 families of a village:
6, .8, 7, 7, 6, 5, 3, 2, 5, 6, 8, 7, 7, 4, 3, 6, 6,6, 7, 5, 4, 3, 3, 2, 5 Prepare a frequency distribution table for the data using class intervals 0-2, 2-4 etc.
Answer.

Question. 92 Draw a histogram to represent the frequency distribution, in question 91.
Answer.

Question. 93 The marks obtained (out of 20) by 30 students of a class in a test are as follows:
14, 16, 15, 11, 15, 14, 13, 16, 8, 10, 7, 11, 18, 15, 14,
19, 20, 7, 10, 13, 12, 14, 15, 13, 16, 17, 14, 11, 10, 20.
Prepare a frequency distribution table for the above data using class intervals of equal width in which one class interval is 4-8 (excluding 8 and including 4).
Answer.

Question. 94 Prepare a histogram from the frequency distribution table obtained in question 93.
Answer.

Question. 95 The weights (in kg) of 30 students of a class are as follows:
39, 38, 36, 38, 40, 42, 43, 44, 33, 33, 31, 45, 46, 38, 37,
31, 30, 39, 41, 41, 46, 36, 35, 34, 39, 43, 32, 37, 29, 26
Prepare a frequency distribution table using one class interval as (30-35), 35 not included.
(i) Which class has the least frequency?
(ii) Which class has the maximum frequency?
Answer.

Question. 96 Shoes of the following brands are sold in November 2007 at a shoe store. Construct a pie chart for the given data.

Answer.

Question. 97 The following pie chart depicts the expenditure of a state government under different heads:

(i) If the total spending is 10 crore, how much money was spent on roads?
(ii) How many times is the amount of money spents on education compared to the amount spent on roads?
(iii) What fraction of the total expenditure is spents on both roads and public welfare together?
Answer.

Question. 98 The following data represents the different number of animals in a zoo. Prepare a pie chart for the given data.

Answer.

Question. 99 Playing cards
(a) From a pack of cards, the following cards are kept face down:

Suhail wins if he picks up face card. Find probability of Suhail winning?
(b) Now, the following cards are added to the above cards:

What is the probability of Suhail winning now ? Reshma wins, if she picks up a 4. What is the probability of Reshma winning? [Queen, King and Jack cards are called face cards.]
Answer.

Question. 100 Construct a frequency distribution table for the following weights (in grams] of 35 mangoes, using the equal class intervals, one of them is 40-45 (45 not included):
30, 40, 45, 32, 43, 50, 55, 62, 70, 70, 61, 62, 53, 52, 50, 42, 35, 37, 53, 55, 65, 70, 73, 74, 45, 46, 58, 59, 60, 62, 74, 34, 35, 70, 68
(a) How many classes are there in the frequency distribution table?
(b) Which weight group has the highest frequency?
Answer.

Question. 101 Complete the following table.

Find the total number of persons, whose weights are given in the above table.
Answer.

Question. 102 Draw a histogram for the following data.

Answer.

Question. 103 In a hypothetical sample of 20 people, the amount of money (in t thousands) with each was found to be as follows:
114, 108, 100, 98, 101, 109, 117, 119, 126, 131,
136, 143, 156, 169, 182, 195, 207, 219, 235, 118
Draw a histogram of the frequency distribution, taking one of the class intervals as 50-100.
Answer. Before preparing histogram of the given data, we will prepare the frequency distribution table.

Question. 104 The below histogram shows the number of literate females in the age group of 10 yr to 40 yr in a town.

(a) Write the classes assuming all the classes are of equal width.
(b) What is the classes width?
(c) In which age group, are literate females the least?
(d) In which age group, is the number of literate females the highest?
Answer. (a) As we know that, the age group of 10 yr to 40 yr is to be divided into classes of equal width, starting with 10. Then, the classes of equal width can be written as . 10-15,15-20,20-25,25-30, 30-35,35-40 ,
(b) The width of the classes is 5, as the difference .between upper class limit and lower class limit is 5.
(c) In the age group of 10-15, the number of literate females is the least.
(d) In the age group of 15-20, the number of literate females is the highest.

Question. 105 The following histogram shows the frequency distribution of teaching experiences of 30 teachers in various schools:

(a) What is the class width?
(b) How many teachers are having the maximum teaching experience and how many have the least teaching experience?
(c) How many teachers have teaching experience of 10 to 20 years?
Answer. (a) In the histogram, we see that the class width Is 5.
(b) By the histogram, it is clear that two teachers have the maximum teaching experience,i.e. 15-20 years, and five teachers have the least teaching experience, i.e. 0-5 years.
(c) The number of teachers having experience from 10 to 20 years, is 7 + 2, i.e. 9.

Question. 106 In a district, the number of branches of different banks is given below:

Draw a pie chart for this data.
Answer.

Question. 107 For the development of basic infrastructure in a district, a project of Rs 108 crore approved by Development Bank is as follows:

Draw a pie chart for this data.
Answer.

Question. 108 In the time table of a school, periods allotted per week to different teaching subjects are given below.

Draw a pie chart for this data.
Answer.

Question. 109 A survey was carried out to find the favourite beverage preferred by a certain group of young people. The following pie chart shows the findings of this survey.

From this pie chart, answer the following:
(i) Which type of beverage is liked by the maximum number of people?
(ii) If 45 people like tea, how many people were surveyed?
Answer.

Question. 110 The following data represents the approximate percentage of water in various oceans. Prepare a pie chart of the given data.

Answer.

Question. 111 At a birthday party, the children spin a wheel to get a gift.

Find the probability of
(a) getting a ball (b) getting a toy car
(c) getting any toy except a chocolate.
Answer.

Question. 112 Sonia picks up a card from the given cards

Find the probability of getting (a) an odd number (b) a Y card
(c) a G card (d) a B card bearing number greater than 7.
Answer.

Identify which symbol should appear in each sector of questions 113 and 114.
Question. 113

Answer.

Question. 114

Answer.

Question. 115 A financial counsellor gave a client this pie chart describing how to budget his income. If the client brings home ? 50000 each month, how much should he spend in each category?

Answer.

Question. 116 Following is a pie chart showing the amount spent (in Rs thousands) by a company on various modes of advertising for a product.Now, answer the following questions.
(i) Which type of media advertising is the greatest amount of the total?
(ii) Which type of media advertising is the least amount of the total?

Answer.(i) The greatest amount of the total is spent in the advertisement of newspaper, i.e. Rs 42.
(ii) The least amount of the total is spent in the advertisement of radio, i.e. Rs 7 thousand.

The post NCERT Exemplar Problems Class 8 Mathematics Data Handling appeared first on Learn CBSE.

Indian Economy on the Eve of Independence NCERT Solutions for Class 11 Indian Econmonic Developtment

NCERT TEXTUAL QUESTIONS WITH ANSWERS

Question 1. What was the focus of the economic policies pursued by the colonial government in India? What were the impacts of these policies?
Answer. The economic policies pursued by the colonial government in India were concerned more with the protection and promotion of the economic interests of their home country rather than with the development of the Indian economy.
Thus, at the time of independence in 1947, India was a poor and underdeveloped country. At that time, agriculture was in a poor condition and mineral resources were not fully used. There were only a few industries and many of the cottage and small-scale industries had declined under the British rule. Millions of people were unemployed, not because they were unwilling to work but because there were no jobs to be found. The per capita income of Indians was one of the lowest in the world, indicating that the average Indian was extremly poor and could not afford even the basic necessities of life. For instance, the staple food of average Indian consisted of rice, wheat and millets (like jowar and bajra). Most Indians could not afford to buy nutritious and balanced diet. The vast majority of people in India led a miserable life.

Question 2. Name some notable economists who estimated India’s per capita income during the colonial period.
Answer. Dadabhai Naoroji, V.K.R.V. Rao, Wiliam Digby, Findlay Shirras and R.C. Desai.

Question 3. What were the main causes of India’s agricultural stagnation during the colonial period?
Answer. Indian agriculture was primitive and stagnant. The main causes of stagnation of agriculture sector were as follows:
1. Land Tenure System. There were three forms of Land tenure system introduced by the British rulers in India. These were:
(a) Zamindari system
(b) Mahalwari system
(c) Ryotwari system
In the Zamindari system, Zamindars or landlords were the owners of land. The actual collections by Zamindars was much higher than what they had to pay to the Government. Zamindari system led to multiplication of middlemen between cultivators and Government, absentee landlordism, exploitation of peasants by unsympathetic agents and enmity between landlords and tenants. Under the system, intermediaries benefited at the cost of both actual cultivators and the state.
2. Commercialisation of Agriculture. Commercialisation of agriculture means production of crops for sale in the market rather than for self consumption. Farmers were forced to cultivate commercial crops like Indigo. Indigo was required by the textile industry in Britain for dyeing of the textile. As a result, there was fall in the production of food crops. The farmers had to suffer from frequent occurence of famine. Indian agriculture was transformed into a raw material exporting sector for England.
3. Partition of the Country. Partition of the country in 1947 also adversely affected India’s agricultural production. The rich food producing areas of West Punjab and Sindh went to Pakistan. It created food crisis in the country. Also, the whole of fertile land under jute production went to East Pakistan. The jute industry was most severely affected due to partition.
Thus, Indian agriculture became backward, stagnant and non-vibrant under the British rule. Indian Economy on the Eve of Independence .

Question 4. Name some modem industries which were in operation in our country at the time of independence.
Answer. The Tata Iron and Steel company (TISCO) was incorporated in August 1907 in India. It established
its first plant in Jamshedpur (Bihar). Some other industries which had their modest beginning after Second World War were: sugar, cement, chemical and paper industries.

Question 5. What was the two-fold motive behind the systematic de-industrialisation effected by the British in pre-independent India?
Answer. De-industrialisation-Decline of India Handicraft Industry. Britishers followed the policy of systematically de-industrialising India. The primary motive behind the de-industrialisation by , the British government was two-fold:
(a) to get raw materials from India at cheap rates in order to reduce India to a mere exporter of raw materials to the British industries.
(b) to sell British manufactured goods in Indian market at higher prices.In this way, they exploited India through the device of double exploitation.

Question 6. The traditional handicraft industries were mined under the British mle. Do you agree with this view? Give reasons in support of your answer.
Answer. The main cause of exploitation of traditional handicraft industries was de-industrialisation introduced by British rulers in India. They got raw materials from India at cheap rates and reduced India to a mere exporter of raw materials to the British industries. They sold British manufactured goods in Indian market at higher prices.
It resulted in decline of world famous traditional handicrafts. Britishers followed discriminatort tariff policy. It allowed free export of raw materials from India and free import of British final goods to India, but placed heavy duty on the export of Indian handicrafts. In this way, Indian . markets were full of manufactured goods from Britain which were low priced. Indian handicrafts 1 started losing both domestic market and export market. Ultimately, the handicraft industry declined.

Question 7. What objectives did the British intend to achieve through their policies of infrastructure development in India?
Answer. During the British rule, some basic infrastructure was developed in the form of railways, water transport, ports, post and telegraph, etc. However, the real intention behind these developments 1 was to serve their own colonial interest.
The main motives of British rulers behind the development of infrastructure in India were:
(a) To have effective control and administration over the vast Indian territory. For this, Britishers linked important administrative and military centres through railway lines.
(b) To earn profits through foreign trade. For this they linked railways with major ports and the marketing centres (or Mandies).
(c) To create an opportunity for profitable investment of British funds in India.
(d) To mobilise army within India and carrying out raw materials through roads to the nearest railway station or to the port to send it to Britain.

Question 8. Critically appraise some of the shortfalls of the industrial policy pursued by the British. colonial administration.
Answer. The state of Indian industrial sector on the eve of independence was as follows:
1. De-industrialisation—Decline of Indian Handicraft Industry. Britishers followed the policy of systematically de-industrialising India. The primary motive behind the de-industrialisation by the British government was two-fold.
(a) to get raw materials from India at cheap rates in order to reduce India to a mere exporter of raw materials to the British industries.
(b) to sell British manufactured goods in Indian market at higher prices.
In this way, they exploited India through the device of double exploitation. It resulted in decline of world famous traditional handicrafts. Britishers followed dis-criminatory tariff policy. It allowed free export of raw materials from India and free import of British final goods to India, but placed heavy duty on the export of Indian handicrafts. In this way, Indian markets were full of manufactured goods from Britain which were low priced. Indian handicrafts started losing both domestic market and export market. Ultimately, the handicraft industry declined.
2. Lopsided Modem Industrial Structure. Unbalanced and lopsided structure of Indian industries is again a legacy of the British rule in India. British rulers neither permitted modernisation of industries nor did they encourage the growth of heavy industries in India. The period 1850-55 saw the establishment of the first cotton mill, first jute mill and the first coal mine. By the end of 19th century, there were 194 cotton mills and 36 jute mills. The cotton textile mills were located in the western parts of the country, in the states of Maharashtra and Gujarat.
Jute mills in BengaT were established mainly by British capitalists. First iron and steel industry during British rule was Tata Iron and Steel company (TISCO) incorporated in August 1907 in Jamshedpur (Bihar). Some other industries which had their modest beginning after Second World War were: sugar, cement, chemical and paper industries.
3. Capital Goods Industries were Lacking. The policy of Britishers was simply to develop those industries which would never be competitive to the British industry. They always wanted Indians to be dependent on Britain for the supply of capital goods and heavy equipments. Thus, the development of a few consumer goods industries was witnessed during the British rule. The heavy industries were, by and large, conspicuous by their absence. This resulted in an unbalanced and lopsided growth of industries in India.
4. Limited Operation of the Public Sector. Public sector was confined to railways, power generation, communi-cation, ports and some other departmental under-takings.

Question 9. What do you understand by the drain of Indian wealth during the colonial period?
Answer. Drain of wealth means that economic policies of the British in India were primarily motivated to snatch maximum benefits from India’s trade. India’s foreign trade generated large export surplus. This export surplus did not result in any flow of gold or silver into India. There was drain of India’s wealth into Britain. It is clear from the following facts :
(a) The surplus was used to make payments for the expenses incurred by the office set up by the colonial government in Britain.
(b) The surplus was used to pay expenses on war fought by the British government.
(c) Surplus was used to pay for the import of invisible items.

Question 10. Which is regarded as the defining year to mark the demographic transition from its first to the second decisive stage?
Answer. 1921 is the defining year. It is called ‘Year of Great Divide’.

Question 11. Give a quantitative appraisal of India’s demographic profile during the colonial period.
Answer. The demographic condition on the eve of independence was as follows:
1. High Birth Rate and Death Rate. High birth rate and high death rate are treated as indices of backwardness of a country. Both birth rate and death rate were very high at 48 and 40 per thousand of persons res-pectively.
2. High Infant Mortality Rate. If refers to death rate of children below the age of one year. It was about 18 per thousand live births.
3. Low Life Expectancy. Life expectancy means the number of years that a new bom child on an average is expected to live. It was as low as 32 years.
4. Mass Illiteracy. Mass illiteracy among the people of a country is taken as an indicator of its poverty and backwardness. The population census of 1941 (which was the last census under the British rule) estimated the literacy rate at 17 per cent. This means that 83 per cent of the total population was illiterate.
5. Low Standard of Living. At the time of independence, people used to spend between 80 to 90 percent of their income on basic necessities, that is on food, clothing and housing. Even then, people did not get adequate quantity of food or clothing or housing and millions of people starved, went naked and lived in huts or in the open. Moreover, some parts of India came under severe famine conditions. The famines were so severe that millions died. One of the worst famines in India was the Bengal famine of 1943, when three million people died.

Question 12. Highlight the salient features of India’s pre-independence occupational structure.
Answer. Occupational structure means the distribution of work-force among different sectors of an economy. The state of occupational structure on the eve of independence was as follows:
1. Pre-dominance of Agriculture Sector. The agricultural sector accounted for the largest share of work-force, which was 72 per cent. The manufacturing and service sectors accounted for 10 per cent and 18 per cent respectively.
2. Growing Regional Variations. There was growing regional variation. In the states of Tamil Nadu, Andhra Pradesh, Kerala, Karnataka, Maharashtra and West Bengal, the dependence of the workforce on the agricultural sector declined. On the other hand, there was increase in the share of work force in the agriculture sector in the states of Orissa, Rajasthan and Punjab.
Thus, India’s occupational structure was static and imbalanced.

Question 13. Underscore some of India’s most crucial economic challenges at the time of independence.
Answer. Most crucial economic challenges at the time of independence were:
(a) Little industrialisation and decline of handicrafts.
(b) Low agricultural output and high imports of grains.
(c) Low figure of national income and per capita income which showed extreme poverty.
(d) Very sluggish economic progress.’
(e) Unemployment and underemployment.
(f) Very high infant mortality rate, low life expectancy and low standard of living.

Question 14. When was India’s first official census operation undertaken?
Answer. First official census was undertaken in the year 1881.

Question 15. Indicate the volume and direction of trade at the time of independence.
Answer. India has been an important trading nation since ancient times. But the restrictive policies of commodity production, trade and tariff pursued by the British government adversely affected the structure, composition and volume of India’s foreign trade. The state of India’s foreign trade on the eve of independence was as follows:
1. Net Exporter of Raw Material and Importer of Finished Goods. India became an exporter of primary products such as raw silk, cotton, wool, sugar, indigo, jute, etc. and an importer of finished consumer goods like cotton, silk and woollen clothes and capital goods like light machinery produced in the factories of Britain. UK was the chief supplier to India contributing to over 31 per cent of total import at the time of independence. The principal item of import was food grains and by 1947 food grain imports had touched the level of 3 million tonnes.
2. Britain had Monopoly Control on Foreign Trade. Opening of Suez Canal in 1869 served as a direct route for the ships operating between India and Britain. The canal connected Port Said on the Mediterranean Sea with the Gulf of Suez. It provided a direct trade route for ships operating between European or American ports and ports located in South Asia, East Africa and Oceania.
It reduced the cost of transportation and made access to the Indian market easier. In other words, the exploitation of Indian market was now easier. British maintained monopoly control over India’s foreign trade. More than half of India’s foreign trade was with Britain. British allowed trade with few other countries like China, Ceylon (Sri Lanka) and Persia (Iran).

Question 16. Were there any positive contributions made by the British in India? Discuss.
Answer. British rule exploited India in many ways. But, the ways to achieve the motives sometimes yield positive effects. Their exploitative programmes and policies resulted in some positive impact on India. Some of these positive effects were:
(a) Commercialisation of agriculture implied a good breakthrough in agriculture and resulted in self-sufficiency in fiSodgrain production.
(b) The development of infrastructure, railways and roadways generated new opportunities for economic and social growth and broke cultural and geographical barriers.
(c) Railways promoted commercialisation of agriculture through long distance movement of goods and it enabled people to move from one place to another easily.
(d) The supply of food and essentials could be made available to drought affected areas through transportation.
(e) Indian economy witnessed a huge expansion of monetary system and growth in production through division of labour and specialisation.

The post Indian Economy on the Eve of Independence NCERT Solutions for Class 11 Indian Econmonic Developtment appeared first on Learn CBSE.

Indian Economy 1950-1990 NCERT Solutions for Class 11 Indian Econmonic Developtment

NCERT TEXTUAL QUESTIONS WITH ANSWERS

Question 1. Define a plan.
Answer. Plan is a document showing detailed scheme, program and strategy worked out in advance for fulfilling an objective.

Question 2. Why did India opt for planning?
Answer. India achieved independence in 1947. The colonial government left India in a poor, backward and stagnant situation. From that time efforts have been made to solve people’s problems in a sovereign Indian republic through a system of federal parliamentary democracy. Political independence has no meaning without economic prosperity. Planning was undertaken to sustain political independence and generate economic prosperity.

Question 3. Why should plans have goals?
Answer. Plans should have goals or objectives which the country wants to achieve in a specific time period. Without goals, the planners would not know which sector of the economy should be developed on a priority’basis.

Question 4. What are miracle seeds?
Answer. Miracle seeds are the high yielding variety of seeds which combined with assured water supply, fertilizer, insecticides, etc. would result in high production levels.

Question 5. What is marketable surplus?
Answer. It is that part of the agricultural produce which is sold in the market by the farmer.

Question 6. Explain the need and type of land reforms implemented in the agriculture sector.
Answer. In India, there existed a large army of middlemen like zamindars, mahalwars and ryotwars, who collected rent from the actual cultivators and deposited a part of it to the government as land revenue. They treated cultivators as slaves. The measure of abolition of intermediaries was adopted to make direct link between actual tillers and government, and to pass forests, wasteland, etc. to state government.
Tenancy Reforms are concerned with:
(a) Regulation of Rent
(b) Security of Tenure
(c) Ownership Rights for Tenants.
Reorganisation of Agriculture is concerned with:
(a) Redistribution of Land
(b) Consolidation of Holdings
(c) Co-operative Farming.

Question 7. What is Green Revolution? Why was it implemented and how did it benefit the farmers? Explain in brief.
Answer. Green Revolution. This strategy, which was launched in October 1965, has been given different names such as, New Agricultural Strategy (NAS), or Seed-Fertilizers Water Technology.
Before adopting the New Agricultural Strategy (NAS), the state of Indian agriculture was as follows:
(a) there was low and erratic growth,
(b) there was extreme regional unevenness and growing interclass inequality,
(c) there were serious droughts for two consecutive years
(d) there was a war with Pakistan
(e) USA denied India PL 480 imports.
India decided to get rid of this dependence on foreign aid in such a vital matter as food supply.
And that was the genesis of our Green Revolution, i.e., biochemical technology to step up output per acre by using scientifically inclined techniques and methods of production.
Benefits of Green Revolution.
(i) Increase in Income. Since the Green Revolution was limited to wheat and rice for a number of years, its benefits were enjoyed by wheat and rice growing areas of Punjab, Haryana, Western Uttar Pradesh and Andhra Pradesh. The income of farmers in these States grew sharply. Green Revolution succeeded in removing rural poverty in these States.
(ii) Impact on Social Revolution. Along with economic revolution there was a social revolution. The old social beliefs and customs were destroyed and people were willing to accept changes in technology, seeds and fertilizers.’ The traditional methods of farming were transformed into modern methods of farming.
(iii) Increase in Employment. Green Revolution solved the problem of seasonal unemployment to a great extent because with the possibility of growing more than one crop on a piece of land, more working hands were needed throughout the year. Also, package inputs reqired better irrigation facilities which raised the employment rate.

Question 8. Explain ‘growth with equity’ as a planning objective.
Answer. Economic Growth is an increase in the aggregate output of goods and services in a country in a given period of time. Equity refers to reduction in inequality of income or wealth, uplifting weaker sections of the society and equal distribution of economic power. Higher levels of growth and social justice are two main objectives of India’s economic planning. When these two objectives are clubbed together, it is called development with social justice.

Question 9. Does modernisation as a planning objective create contradiction in the light of employment generation? Explain.
Answer. Modernisation as a planning objective implies use of advanced technology. Advanced technology requires less labour per unit of output. Thus, modernisation creates unemployment.

Question 10. Why was it necessary for a developing country like India to follow self-reliance as a planning
objective?
Answer. On the eve of independence, India was poor, stagnant and backward. There were heavy imports of foodgrains. It was important to be self-reliance.
Features of Self reliance are:
(a) Self-sufficiency in foodgrains.
(b) Fall in foreign aid and reduced dependence on imports which is possible when there is growth in domestic production.
(c) Rise in exports.
(d) Rise in contribution of industries in grass domestic product.

Question 11. What is sectoral composition of an economy? Is it necessary that the service sector should contribute maximum to GDP of an economy? Comment.
Answer. The contribution made by each of these sectors in the GDP of a country is called sectoral composition of the economy. If the service sector or tertiary sector contributes maximum to GDP of an economy, then the country is economically developed.

Question 12. Why was public sector given a leading role in industrial development during the planning period?
Answer. Public sector has been playing a very significant role in the development of industries in the following way:
(a) Creation of a strong industrial base.
(b) Development of Infrastructure.
(c) Development of backward areas.
(d) To mobilise savings and earn foreign exchange.
(e) To prevent concentration of economic power.
(f) To promote equality of income and wealth distri-bution.
(g) To provide employment.
(h) to promote import substitution.

Question 13. Explain the statement that green revolution enabled the government to procure sufficient foodgrains to build its stocks that could be used during times of shortage.
Answer. Green revolution refers to the tremendous increase in agricultural production and productivity that has come about with the introduction of new agricultural technology. It transformed the economy of scarcity into an economy of plenty.
Rise in Production and Productivity. Green Revolution helped in removing continuing food shortages. HYVP was restricted to only five crops namely, wheat, rice, jowar, bajra and maize. Commercial crops were excluded from the ambit of the new strategy. Substantial increase in wheat production was noticed.

The wheat production increased from 11.1 million tonnes in the Third Plan to 93.9 million tonnes in 2011-12.
Rice production initially increased slowly and later at a fast pace. The production increased from 35.1 million tonnes in the Third Plan to 92.8 million tonnes in 2011-12.
The production of coarse cereals (jowar, bajra and maize) fell to 26.1 million tonnes in 1965-66 and then increased to 32.5 million tonnes in 2011-12.

Question 14. While subsidies encourage farmers to use new technology, they are a huge burden on govern¬ment finances. Discuss the usefulness of subsidies in the light of this face.
Answer. Subsidy is an economic benefit, direct or indirect, granted by a government to domestic producers of goods or services, often to strengthen their competitive position against foreign companies.
It helps farmers to buy HYV seeds, fertilizers and other inputs. The burden of granting subsidies falls on the government. The government has to bear the burden of financing subsidies.
There is scope for improving the resource use efficiency by reducing subsidies and aiming them better to small farmers and regions lagging behind.

Question 15. Why, despite the implementation of green revolution, 65 per cent of our population continued to be engaged in the agriculture sector till 1990?
Answer. The structural change in composition of GDP shows that India is on the path of sustained devel- opihent. But the occupational structure pattern shows that India is still underdeveloped. When nearly 60.8 per cent of the working force is engaged in agriculture where productivity is low and employment uncertain this would surely lead to low per capita income and widespread poverty for the rural masses which form about 72.2 per cent of India’s population. It also means that ex¬cessive pressure of population on land would be a hindrance in the way of productivity improve¬ment in agriculture sector.

Question 16. Though public sector is very essential for industries, many public sector undertakings incur huge losses and are a drain on the economy’s resources. Discuss the usefulness of public sector undertakings in the light of this fact.
Answer. Though many public sector undertakings are incurring huge losses, they are still very useful in the areas of strategic concerns and hazardous chemicals. Public sector undertaking are required for:
1. Creation of a Strong Industrial Base
2. Development of Infrastructure
3. Development of Backward Areas
4. To Mobilise Savings and Earn Foreign Exchange
5. To Prevent Concentration of Economic Power
6. To Promote Equality of Income and Wealth Distri-bution
7. To Provide Employment
8. To Promote Import Substitution.

Question 17. Explain how import substitution can protect domestic industry.
Answer. The import substituting industrialisation was the objective of second FYP (1956-61) till the Seventh FYP (till 1990). The Mahalanobis strategy of development was based on import substitution. The rationale of the import substitution strategy is based on infant industry argument. It helped to save foreign exchange by drastically reducing import of goods. The foreign exchange saved was to be used for the developmental imports such as capital goods, sophisticated technology, etc. It created a protected market and large demand for domestically produced goods.

Question 18. Why and how was private sector regulated under the IPR 1956?
Answer. Private sector was given minimum role in IPR 1956. New industry could start operation after it had obtained licence from the government. Licence was given after scrutiny by the government.

Question 19. Match the following:

Answer. 1. (C), 2. (D), 3. (B), 4. (E), 5. (A), 6. (F).

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Liberalisation, Privatisation and GlobalisationAn Appraisal NCERT Solutions for Class 11 Indian Econmonic Developtment

NCERT TEXTUAL QUESTIONS WITH ANSWERS

Question 1. Why were reforms introduced in India?
Answer. In 1991, economic reforms were introduced in India because 1991 was the year of crisis for the Indian economy. It is clear from the following facts:
(a) National income was growing at the rate of 0.8%.
(b) Inflation reached the height of 16.8%.
(c) Balance of payment crisis was to the extent of 10,000 crores.
(a) India was highly indebted country. It was paying 30,000 crores interest charges per year.
(e) Foreign exchanges reserves were only 1.8 billion dollars which were sufficient for three weeks.
(f) India sold large amount of gold to Bank of England.
(g) India applied for the loan from World Bank and IMF to the extent of 7 billion dollars.
(h) Fiscal deficit was more than 7.5%.
(i) Deficit financing was around 3%.
(j) Trade relation with Soviet block had broken down.
(k) Remmittances from non-residence Indians stopped due to war in Arab countries.
(l) Price of petroleum products was very high.

Question 2. How many countries are members of the WTO?
Answer. At present there are 149 countries which are members of WTO.

Question 3. What is the most important function of RBI?
Answer. There was a substantial shift in role of the RBI from ‘a regulator’ to ‘a facilitator’ of the financial sector. Earlier as a regulator, the RBI would itself fix interest rate structure for the commercial banks. After liberalisation in 1991, RBI as a facilitator would only facilitate free play of the market forces and leave it to the commercial banks to decide their interest rate structure. Thus, with liberalisation competition prevails rather than controls.

Question 4. How was RBI controlling the commercial banks?
Answer. Prior to 1991, banking institutions were subject to too much control by the RBI through high bank rate, high cash reserve ratio and statutory liquidity ratio.
Financial sector includes:
(a) banking and non-banking financial’institutions,
(b) stock exchange market, and
(c) foreign exchange market.
In India, financial sector is regulated and controlled by the RBI (Reserve Bank of India).
There was a substantial shift in role of the RBI from ‘a regulator’ to ‘a facilitator’ of the financial sector. Earlier as a regulator, the RBI would itself fix interest rate structure for the commercial banks. After liberalisation in 1991, RBI as a facilitator would only facilitate free play of the market forces and leave it to the commercial banks to decide their interest rate structure.

Question 5. What do you understand by devaluation of rupee?
Answer. Devaluation refers to lowering in the official value of a currrency with respect to gold or foreign currency. It results in costlier imports and cheaper exports.

Question 6. Distinguish between the following:
(i) Strategic and Minority sale
Answer. Government has been disinvesting by many methods. Two main methods are:
(a) Minority sale. In this method, equity is offered to investors through domestic public issue.
(b) Strategic sale. In this method, government offloads above 51 per cent in strategic sale.
(ii) Bilateral and Multi-lateral trade
Answer. Trade agreements involving more than two countries are referred to as multilateral trade agreements.
Trade agreements involving two countries are referred to as bilateral trade agreements.
(iii) Tariff and Non-tariff barriers
Answer. Tariff Barriers. Tariff barriers are imposed on imports to make them relatively costly as a measure to protect domestic production.
Non-Tariff Barriers. They are imposed on the amount of imports and exports.

Question 7. Why are tariffs imposed?
Answer. Tariffs are imposed on imports to make them relatively expensive. This will protect domestically produced goods.

Question 8. What is the meaning of quantitative restrictions?
Answer. Quantitative restrictions refers to non-tariff barriers imposed on the amount of imports and exports.

Question 9. Those public sector undertakings which are making profits should be privatised. Do you agree with this view? Why?
Answer. No, if profit making PSUs are privatised then there will be only loss making PSUs left. Government
needs the profit of the profit.making PSUs to modernise them, to make them, more competitive and more efficient.

Question 10. Do you think outsourcing is good for India? Why are developed countries opposing it?
Answer. Outsourcing is good for India because it provides employment to large number of unemployed Indians. Developed countries oppose it because :
(a) They-are not sure about the sincerity of Indian workers.
(b) It will narrow down the income disparity between the two countries.

Question 11. India has certain advantages which makes it a favourite outsourcing destination. What are these advantages?
Answer. India is a favourite outsourcing destination. The advantages that India has are:
(a) India can provide a ready supply of skilled people at relatively lower price.
(b) India has the advantage of time difference as it is located on the other side of the developed countries.

Question 12. Do you think the navratna pdlicy of the government helps in improving the performance of public sector undertakings in India? How?
Answer. The government has decided to give special treatment to some of the important profit making PSUs and they were given the status of navratnas. These navratnas were granted financial and operational autonomy in the working of the companies. These navratnas are:
1. Indian Oil Corporation Ltd. (IOCL)
2. Bharat Petroleum Corporation Ltd. (BPCL)
3. Hindustan Petroleum Corporation Ltd. (HPCL)
4. Oil and Natural Gas Corporation Ltd (ONGC)
5. Steel Authority of India Ltd. (SAIL)
6. Indian Petrochemicals Corporation Ltd. (IPCL)
7. Bharat Heavy Electricals Ltd. (BHEL) –
8. National Thermal Power Corporation (NTPC)
9. Mahanagar Telephone Nigam Limited (MTNL)
10. Gas Authority of India Limited (GAIL)
11. Videsh Sanchar Nigam Limited (VSNL)
The granting of navratna status resulted in better performance of these. companies. The ‘ government partly privatised these companies through disinvestment.

Question 13. What are the major factors responsible for the high growth of the service sector?
Answer. There has been high growth of the service sector in India. There is too much demand for services because :
(a) It is more profitable to contract services from developing countries.
(b) There is easy availability of skilled manpower at lower wage rate.

Question 14. Agriculture sector appears to be adversely affected by the reform process. Why?
Answer. There has been deceleration in agricultural growth. This deceleration is the root cause of the problem of rural distress that reached crisis in some parts of the country. Farmers find themselves into crippling debt due to low farm incomes combined with low prices of output and lack of credit at reasonable prices. This has led to widespread distress migration.
Economic reforms have not been able to benefit the agricultural sector because:
(a) Liberalisation has forced the small farmers to compete in a global market where prices of goods have fallen while removal of subsidies has led to increase in the cost of production. It has made farming more expensive.
(b) Various policy changes like reduction in import duties on agricultural products, removal of minimum support price and lifting of quantitative restrictions have increased the threat of international competition to the Indian farmers.
(c) The export-oriented growth has favoured increased production of cash crops rather than food grains. This has increased the prices of food grains.
(d) Public investment in agriculture sector especially in infrastructure which includes irrigation, power, roads, market linkages and research has been reduced in the reform period.

Question 15. Why has the industrial sector performed poorly in the reform period?
Answer. The post-reform period shows that industrial growth has slowed down. This was due to:
(a) Globalisation created conditions for free movement of goods and services from foreign countries. It adversely affected the local industries and employment in developing countries.
(b) Globalisation led to decrease in demand for domestic industrial products due to cheaper imports.
(c) There was inadequate investment in infrastructural facilities such as power supply.
(d) A development country like India still does not have the access to markets of developed countries due to high non-tariff barriers.

Question 16. Discuss economic reforms in India in the light of social justice and welfare.
Answer. Economic reforms have been criticised on the following grounds:
(a) Privatisation encourages growth-ofunonopoly power in the hands of big business houses. It results in greater inequalities of income and wealth.
(b) Globalisation has devastated local producers since they are unable to compete with cheap imports.
(c) Economic reforms have led to mounting workers unrest. Workers have protested against low wages, poor working conditions, autocratic management rule, long work days and fall in social benefits.
(d) These have made public employees worse off. Public employees are adversely effected by budget cuts, privatisation and massive loss of purchasing power.
(e) Small business class is adversely affected by fall of public subsidies, de-industrialisation and floods of cheap imports.
(f) During the globalisation phase, about half a billion people in South Asia have experienced a decline in their income. Data shows that it is the poor who have suffered most.
(g) Since the government is unable to help the victims of globalisation, the provisions of social safety net have been weakened.
(h) The global village appears deeply divided between the street of the haves and those of the havenots. The average person in Norway (which has highest human development) and the average person in countries such as Niger (which has lowest human development) certainly live in different human development districts of the global village.

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Current Challenges Facing Indian Economy  NCERT Solutions for Class 11 Indian Econmonic Developtment

NCERT TEXTUAL QUESTIONS WITH ANSWERS

Question 1. Define poverty.
Answer. Poverty in India has been defined as that situation in which an individual fails to earn income sufficient to buy him minimum means of subsistence.

Question 2. What is meant by ‘Food for Work’ programme?
Answer. National Food for Work Programme (NFWP). This programme was initially launched w.e.f. February 2001 for five months and was further extended. This programme aims at augmenting food security through wage employment in the drought affected rural areas in eight States, i.e., Gujarat, Chhattisgarh, Himachal Pradesh, Madhya Pradesh, Maharashtra, Orissa, Rajasthan and Uttaranchal. The centre makes available appropriate quantity of foodgrains free of cost to each of the drought affected States as an additionality under the programme. Wages by the State government can be paid partly in kind and partly in cash. The workers are paid the balance of wages in cash, such that they are assured of the notified minimum wages.

Question 3. State an example each of self-employment in rural and urban areas,
Answer. PMRY is a self-employment programme in rural areas.
SJSRY is a self-employment programme in urban areas.

Question 4. How can creation of income earning assets address the problem of poverty?
Answer. With the creation of income earning assets, people will have a way to earn their livelihood. It will help in removal of poverty.

Question 5. Briefly explain the three-dimensional attack on poverty adopted by the government.
Answer. A country is caught in a vicious trap once poverty is inbuilt in the system. The government has followed three-dimensional poverty removal programme. These dimensions are:
1. The rate of economic growth should be raised. Economic growth can be helpful in removing poverty by the trickle d»wn effect. It was felt that raised economic growth would benefit the underdeveloped region and the more backward sections of the society.
2. Various beneficiary-oriented programmes need to be strengthened. For this, local institutions have to be involved in these programmes. The activities should be organised on a co-operative basis. Major training programmes should be taken up to improve the skills of potential workers.
3. To provide minimum basic amenities. The provision of basic anenities should be made like water supply, sanitation, nutrition, etc. to the people.

Question 6. What programmes has the government adopted to help the elderly people and poor and destitute women?
Answer. (a) National Social Assistance Programme (NSAP). NSAP was introduced on 15 August, 1995 as a 100 per cent Centrally Sponsored Scheme for social assistance to poor households affected by old age, death of primary bread earner and maternity care. The programme has three components, i.e., N ational Old Age Pension Scheme (NOAPS), National Family Benefit Scheme (NFBS) and National Maternity Benefit Scheme (NMBS).
(b) Annapurna. This scheme came into effect from April 1, 2000 as a 100 per cent Centrally Sponsored Scheme. It aims at providing food security to meet the requirement of those senior citizens who though eligible for pensions under the National Old Age Pension Scheme, are not getting the same. Foodgrains are provided to the beneficiaries at subsidised rates of ? 2 per kg of wheat and ? 3 per kg of rice. The scheme is operational in states and 5 union territories. More than 6.08 lakh families have been identified and the benefits of the scheme are passing on to them.

Question 7. Is there any relationship between unemployment and poverty? Explain.
Answer. Unemployment means lack of living. It leads to hunger, gloom, pessimism, indebtedness, etc. They all are signs of poverty.

Question 8. What is the difference between relative and absolute poverty?
Answer.

Question 9. Suppose you are from a poor family and you wish to get help from the government to set up a petty shop. Under which scheme will you apply for assistance and why?
Answer. The assistance can be given by Aajeevika. In this scheme one can get financial help in the form of bank loans. Other Programmes which can provide help are:
(a) REGP (Rural Employment Generation Programme)
(b) PMRY (Pradhan Mantri Rctegar Yojana).

Question 10. Illustrate the difference between rural and urban poverty. Is it correct to say that poverty has shifted from rural to urban areas? Use the trends in poverty ratio to support your answer.
Answer. In the rural areas, poor people are those who are landless agricultural labourers, small and mar¬ginal farmers. In the urban areas, poor people are those who are unemployed, underemployed or employed in low productivity occupations with very low wages.
Rural-Urban Break-up of Poverty Following pattern emerges:
1. The decline in poverty was comparatively much steep in rural areas where the percentage
of people living below poverty line fell to 33.8 per cent (2009-10) from 41.8 per cent (2004-05).
2. In urban areas, percentage of people living below poverty line fell to 20.9 per cent (2009-10) from 25.7 per cent (2004-05).
3. The number of people living below poverty line was estimated at 354.7 million in 2009-10.

Question 11. Explain the concept of relative poverty with the help of the population below poverty line in some states of India.
Answer. Relative Poverty refers to poverty in relative terms. It refers to poverty of people in comparison to other people, regions or nations. It indicates that a group or class of people belonging to the lower income groups is poorer when compared to those belonging to higher income groups. Among the major states, percentage of people living below poverty line was 37.9 per cent in
Assam, 23.0 per cent in Gujarat, 20.1 per cent in Haryana, 23.6 per cent in Karnataka, 36.7 per cent in Madhya Pradesh, 24.8 per cent in Rajasthan and 26.7 per cent in West Bengal in 2009-10.

Question 12. Suppose you are a resident of a village, suggest a few measures to tackle the problem of poverty.
Answer. Some measures that can be taken are:
(a) Making people aware about benefits of sanitation.
(b) Telling people about various programmes of the government.
(c) Helping people to take loan and get self employed.
(d) Keeping a control on growth rate of population.
(e) Helping people to start small scale and cottage industries which would generate employment.

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Chapter Scheme NCERT Solutions for Class 11 Indian Econmonic Developtment

NCERT TEXTUAL QUESTIONS WITH ANSWERS

Question 1. What do you mean by rural development? Bring out the key issues in rural development.
Answer. Rural development is a comprehensive term which essentially focuses on action for the development of areas that are lagging behind in the overall development of the village economy.
Some of the areas which are in need of fresh initiatives for rural development are:
(a) Development of human resources like literacy, more specifically, female literacy, education and skill development.
(b) Development of human resources like health, addressing both sanitation and public health.
(c) Honest implementation of land reforms.
(d) Development of the productive resources in each locality.
(e) Infrastructure development like electricity, irrigation, credit, markseting, transport facilities including construction of village roads and feeder roads to nearby highways, facilities for agriculture research-and extension, and information dissemination.
(f) Special measures for alleviation of poverty and bringing about significant improvement in the living conditions of the weaker sections of the population.

Question 2. Discuss the importance of credit in rural development.
Answer. Farmers need money to buy additional land, implements and tools, fertilizers and seeds, paying off old debt, personal expenses like marriage, death, religious ceremonies, etc. Since the gestation period between crop sowing and realisation of income after sale of agricultural produce is very long, farmers need to take credit.

Question 3. Explain the role of micro-credit in meeting credit requirements of the poor.
Answer. SHGs (Self-Help Groups) and micro credit programmes promote thrift in small proportions by a minimum contribution from each member. From the pooled money, credit needs are fulfilled. The member have to repay the credit in small instalments at low rate of interest. The borrowings are mainly for consumption purposes.

Question 4. Explain the steps taken by the government in developing rural markets.
Answer. The government has taken various steps for improving agricultural marketing system. These are:
(a) Establishment of Regulated Markets. Government has formed regulated markets to remove most of the evils of an unorganised market system.
Functions of regulated markets are:
(i) Enforcement of standard weights.
(ii) Fixation of charges, fees, etc.
(iii) Settling of disputes among the operating parties in the market.
(iv) Prevention of unlawful deductions and control of wrong practices of middlemen.
(v) Providing reliable market information.
(b) Provision of Infrastructural Facilities. The government has taken measures to develop ; infrastructural facilities like roads, railways, warehouses, godowns, cold storages and processing units.
(c) Co-operative Market. Co-operative marketing is a measure to ensure a fair price to fanners. Member farmers sell their surplus to the co-operative society which substitutes collective bargaining in place of individual bargaining. It links rural credit farming marketing processes to the best advantage of the farmers.
(d) Important Instruments to Safeguard the Interests of Farmers. The Government has also developed some instruments to safeguard the interests of farmers. These instruments are:
(e) Fixation of Minimum Support Price (MSP)
(ii) Buffer Stock
(iii) Public Distribution System (PDS).

Question 5. Why is agricultural diversification essential for sustain-able livelihoods?
Answer. Diversification into non-farm activities is important because it will:
(a) reduce the risk from agriculture sector.
(b) provide sustainable livelihood options to people living in villages.
(c) provide ecological balance.

Question 6. Critically evaluate the role of the rural banking system in the process of rural development in India.
Answer. Since 1969, when the nationalisation of commercial banks took place, rural banking has expanded a great deal. Significant expansion of rural banking system played a positive role in:
(a) Raising farm and non-farm output by providing services and credit facilities to farmers.
(b) Providing long term loans with better repayment options. It, thus helped in eliminating moneylenders from the scene.
(c) Generating credit for self-employment schemes in rural areas.
(d) Achieving food security which is clear from the abundant buffer stocks of grains.
Limitations of rural banking are:
(a) The sources of institutional finance are inadequate to meet the requirements of agricultural credit. Farmers still depend on money-lenders for their credit needs.
(b) There exist regional inequalities in the distribution of institutional credit.
(e) Rural banking is suffering from the problems of large amount of overdues and default rate.
(d) Small and marginal farmers receive only a very small portion of the institutional credit. A large portion of institutional credit is taken away by the rich farmers.

Question 7. What do you mean by agricultural marketing?
Answer. Agricultural Marketing is defined as a process of marketing farm produce through wholesalers and stockists to ultimate consumers.

Question 8. Mention some obstacles that hinder the mechanism of agricultural marketing.
Answer. Defects of Agricultural Marketing are :
(a) Inadequate Warehouses
(b) Multiplicity of Middlemen
(c) Malpractices in Unregulated Markets
(d) Improper Measuring for Weighing, Grading and Standardisation
(e) Lack of Adequate Finance
(f) Inadequate means of Transport and Communication ”
(g) Inadequate Market Information.

Question 9. What are the alternative channels available for agricultural marketing? Give some examples.
Answer. In India, alternative marketing channels are emerging. Through these channels farmers directly
sell their produce to the consumers. This system increases farmers’, share in the price paid by the consumers. Important examples of such channels are: (a) Apani Mandi (Punjab, Haryana and Rajasthan), (b) Hadaspar Mandi (Pune); Rythu Bazars (Vegetable and fruit market in Andhra Pradesh) and (c) Uzhavar Sandies (Tamil Nadu), (d) Several national and international fast food chains and hotels are also entering into contracts with the farmers to supply them fresh vegetables and fruits.

Question 10. Explain the term ‘Golden Revolution’.
Answer. The period between 1991-2003 is called ‘Golden Revolution’ because during this period, the planned investment in horticulture became highly productive and the sector emerged as a sustainable livelihood option. India has emerged as a world leader in producing a variety of fruits like mangoes, bananas, coconuts, cashew nuts and a number of spices and is the second largest producer of fruits and vegetables.

Question 11. Explain four measures taken by the government to improve agricultural marketing.
Answer. The government has taken various steps for improving agricultural marketing system. These are:
(a) Establishment of Regulated Markets. Government has formed regulated markets to remove most of the evils of an unorganised market system. Functions of regulated markets are:
(i) Enforcement of standard weights.
(ii) Fixation of charges, fees, etc.
(iii) Settling of disputes among the operating parties in the market.
(iv) Prevention of uMawful deductions and control of wrong practices of middlemen.
(v) Providing reliable market information.
(b) Provision of Infrastructural Facilities. The government has taken measures to develop infrastructural facilities like roads, railways, warehouses, godowns, cold storages and processing units.
(c) Co-operative Market. Co-operative marketing is a measure to ensure a fair price to farmers. Member farmers sell their surplus to the co-operative society which substitutes collective bargaining in place of individual bargaining. It links rural credit farming marketing processes to the best advantage of the farmers.
(d) Important Instruments to Safeguard the Interests of Farmers. The Government has also developed some instruments to safeguard the interests of farmers. These instruments are:
(i) Fixation of Minimum Support Price (MSP)
(ii) Buffer Stock
(iii) Public Distribution System (PDS).

Question 12. Explain the role of non-farm employment in promoting rural diversification.
Answer. The non-farm sectors include agro-processing industries, food processing industries, leather industry, tourism, etc. Some other sectors which have the potential but lack infrastructure are traditional household-based industries like pottery, crafts, handlooms, etc.

Question 13. Bring out the importance of animal husbandry, fisheries and horticulture as a source of diver¬sification.
Answer. 1. Animal Husbandry
(a) In India, the farming community uses the mixed crop-livestock farming system—cattle, goats, fowl are the widely held species.
(b) This system provides increased stability in income, food security, transport, fuel and nutrition for the family without disrupting other food-producing activities.
(c) Today, livestock sector alone provides alternate livelihood options to over 70 million small and marginal farmers including landless labourers.
(d) Poultry accounts for the largest share. It is 42 per cent of total livestock in India.
(e) Milk production in the country has increased by more than four times between 1960-2002.
(f) Meat, eggs, wool and other by-products are also emerging as important productive sectors for diversification.
2. Fisheries
(a) The fishing community regards the water body as ‘mother’ or ‘provider’. The water bodies consist of sea, oceans, rivers, lakes, natural aquatic ponds, streams, etc.
(b) Presently, fish production from inland sources contributes about 49 per cent to the total fish production and the balance 51 per cent comes from the marine sector (sea and oceans). Today total fish production accounts for 1.4 per cent of the total GDP.
(c) Among states, Kerala, Gujarat, Maharashtra and Tamil Nadu are the major producers of marine products.
3. Horticulture
(a) Due to varying climate and soil conditions, India has adopted growing of diverse horticultural crops such as fruits, vegetables, tuber crops, flowers, medicinal and aromatic plants, spices and plantation crpps..
(b) These crops play an important role in providing food, nutrition and employment.
(c) India has emerged as a world leader in producing a variety of fruits like mangoes, bananas, coconuts, cashew, nuts and a number of spices and is the second largest producer of fruits and vegetables.
(d) Flower harvesting, nursery maintenance, hybrid seed production and tissue culture, propagation of fruits and flowers and food processing are highly profitable employment opportunities for rural women. It has been estimated that this sector provides employment to around 19 per cent of the total labour force.

Question 14. ‘Information technology plays a very significant role in achieving sustainable development and food security’—comment.
Answer. Information technology plays a very significant role in achieving sustainable development and food security in the following ways:
(a) It can act as a tool for releasing the creative potential and knowledge embedded in our poeple.
(b) Issues like weather forecast, crop treatment, fertilizers, pesticides, storage conditions, etc. can be well administered if expert opinion is made available to the farmers.
(c) The quality and quantity of crops can be increased manifold if the farmers are made aware of the latest equipments, technologies and resources.
(d) IT has ushered in a knowledge economy.
(e) It has potential of employment generation in rural areas.

Question 15. What is organic farming and how does it promote sustainable development?
Answer. Organic farming is a system of farming that maintains, enhances and restores the ecological balance.
Need for organic farming arises because:
(a) In the past, modem farming methods made excessive use of chemical fertilizers and pesticides. It led to soil, water and air pollution, loss of soil fertility and too much chemical contents in foodgrains.
(b) There is urgency to conserve the environment and eco-system and promote sustainable development.
(c) Organic farming is an inexpensive farming technology. It can be purchased by small and marginal farmers.

Question 16. Identify the benefits and limitations of organic farming. .
Answer. The advantages of organic farming are:
(a) Inexpensive Process. Organic agriculture offers a means to substitute costlier agricultural inputs (such as HYV seeds, chemical fertilizers, pesticides, etc.) with locally produced organic inputs that are cheaper and thereby generate more return on investment.
(b) Generates Income. It generates income through international exports as the demand for organically grown crops is on a rise.
(c) Healthier and Tastier Food. Organically grown food has more nutritional value than food grown with chemical farming. It, thus, provides us with healthy foods.
(d) Solves Unemployment Problem. Since organic farming requires more labour input than conventional farming, it will solve unemployment problem.
(e) Environment Friendly. The produce is pesticide-free and produced in an environmentally sustainable way.
Limitations of organic farming are:
(a) It has been observed that the yield from organic farming is much less than modern agricultural farming. Thus, goods produced organically command a higher price.
(b) Small and marginal farmers may not adapt to this type of farming due to lack of awareness and limited choice of alternate production in off-seasons.
(c) Organic produce may have a shorter shelf life.

Question 17. Enlist some problems faced by farmers during the initial years of organic farming.
Answer. 1. Organic farming requires:
(a) Organic Manure
(b) Bio-fertilizers
(c) Organic Pesticides
Although they are cheaper to qjatain, yet farmers find it difficult to get them.
2. The yield from organic farming is much less than modem agricultural farming.
3. The price of organic foods is high, so it is difficult to sell them.
4. Organic produce generally has a shorter shelf life.

The post Chapter Scheme NCERT Solutions for Class 11 Indian Econmonic Developtment appeared first on Learn CBSE.

NCERT Exemplar Problems Class 8 Mathematics Chapter 5 Understanding Quadrilaterals and Practical Geometry

Multiple Choice Questions
Question. 1 If three angles of a quadrilateral are each equal to 75°, then, the fourth angle is(a) 150° (b) 135°
(c) 45° (d) 75°
Solution.

Question. 2 For which of the following, diagonals bisect each other?
(a) Square (b) Kite
(c) Trapezium (d) Quadrilateral
Solution. (a) We know that, the diagonals of a square bisect each other but the diagonals of kite, trapezium and quadrilateral do not bisect each other.

Question. 3 In which of the following figures, all angles are equal?
(a) Rectangle (b) Kite
(c) Trapezium (d) Rhombus
Solution. (a) In a rectangle, all angles are equal, i.e. all equal to 90°.

Question. 4 For which of the following figures, diagonals are perpendicular to each other?
(a) Parallelogram (b) Kite
(c) Trapezium (d) Rectangle
Solution. (b) The diagonals of a kite are perpendicular to each other.

Question. 5 For which of the following figures, diagonals are equal?
(a) Trapezium (b) Rhombus
(c) Parallelogram (d) Rectangle
Solution. (d) By the property of a rectangle, we know that its diagonals are equal.

Question. 6 Which of the following figures satisfy the following properties?
All sides are congruent
All angles are right angles.
Opposite sides are parallel.

Solution. (c) We know that all the properties mentioned above are related to square and we can observe that figure R resembles a square.

Question. 7 Which of the following figures satisfy the following property?Has two pairs of congruent adjacent sides.

Solution. (c) We know that, a kite has two pairs of congruent adjacent sides and we can observe that figure R resembles a kite.

Question. 8 Which of the following figures satisfy the following property?
Only one pair of sides are parallel.

Solution. (a) We know that, in a trapezium, only one pair of sides are parallel and we can observe that figure P resembles a trapezium.

Question. 9 Which of the following figures do not satisfy any of the following properties?
All sides are equal.
All angles are right angles.
Opposite sides are parallel.

Solution. (a) On observing the above figures, we conclude that the figure P does not satisfy any of the given properties.

Question. 10 Which of the following properties describe a trapezium?
(a) A pair of opposite sides is parallel
(b) The diagonals bisect each other
(c) The diagonals are perpendicular to each other
(d) The diagonals are equal
Solution. (a) We know that, in a trapezium, a pair of opposite sides are parallel.

Question. 11 Which of the following is a propefay of a parallelogram?
(a) Opposite sides are parallel
(b) The diagonals bisect each other at right angles
(c) The diagonals are perpendicular to each other
(d) All angles are equal
Solution. (a) We,know that, in a parallelogram, opposite sides are parallel.

Question. 12 What is the maximum number of obtuse angles that a quadrilateral can have?
(a) 1 (b) 2
(c) 3 (d) 4
Solution. (c) We know that, the sum of all the angles of a quadrilateral is 360°.
Also, an obtuse angle is more than 90° and less than 180°.
Thus, all the angles of a quadrilateral cannot be obtuse.
Hence, almost 3 angles can be obtuse.

Question. 13 How many non-overlapping triangles can we make in a-n-gon (polygon having n sides), by joining the vertices?
(a)n-1 (b)n-2
(c) n – 3 (d) n – 4
Solution. (b) The number of non-overlapping triangles in a n-gon = n – 2, i.e. 2 less than the number of sides.

Question. 14 What is the sum of all the angles of a pentagon?
(a) 180° (b) 360° (c) 540° (d) 720°
Solution. (c) We know that, the sum of angles of a polygon is (n – 2) x 180°, where n is the number of sides of the polygon.
In pentagon, n = 5
Sum of the angles = (n – 2) x 180° = (5 – 2) x 180°
= 3 x 180°= 540°

Question. 15 What is the sum of all angles of a hexagon?
(a) 180° (b) 360° (c) 540° (d) 720°
Solution. (d) Sum of all angles of a n-gon is (n – 2) x 180°.
In hexagon, n = 6, therefore the required sum = (6 – 2) x 180° = 4 x 180° = 720°

Question. 16 If two adjacent angles of a parallelogram are (5x – 5) and (10x + 35), then the ratio of these angles is
(a) 1 : 3 (b) 2 : 3 (c) 1 : 4 (d) 1 : 2
Solution.

Question. 17 A quadrilateral whose all sides are equal, opposite angles are equal and
the diagonals bisect each other at-right angles is a .
(a) rhombus (b) parallelogram (c) square (d) rectangle
Solution. (a) We know that, in rhombus, all sides are equal, opposite angles are equal and diagonals bisect each other at right angles.

Question. 18 A quadrilateral whose opposite sides and all the angles are equal is a
(a) rectangle (b) parallelogram (c) square (d) rhombus
Solution. (a) We know that, in a rectangle, opposite sides and all the angles are equal.

Question. 19 A quadrilateral whose all sides, diagonals and angles are equal is a
(a) square (b) trapezium (c) rectangle (d) rhombus
Solution. (a) These are the properties of a square, i.e. in a square, all sides, diagonals and angles are equal.

Question. 20 How many diagonals does a hexagon have?
(a) 9 (b) 8 (c) 2 (d) 6
Solution.

Question. 21 If the adjacent sides of a parallelogram are equal, then parallelogram is a
(a) rectangle (b) trapezium (c) rhombus (d) square
Solution. (c)We know that, in a parallelogram, opposite sides are equal.
But according to the question, adjacent sides are also equal.
Thus, the parallelogram in which all the sides are equal is known as rhombus.

Question. 22 If the diagonals of a quadrilateral are equal and bisect each other, then the quadrilateral is a
(a) rhombus (b) rectangle (c) square (d) parallelogram
Solution. (b) Since, diagonals are equal and bisect each other, therefore it will be a rectangle.

Question. 23 The sum of all exterior angles of a triangle is
(a) 180° (b) 360° (c) 540° (d) 720°
Solution. (b) We know that the sum of exterior angles, taken in order of any polygon is 360° and triangle is also a polygon.
Hence, the sum of all exterior angles of a triangle is 360°.

Question. 24 Which of the following is an equiangular and equilateral polygon?
(a) Square (b) Rectangle (c) Rhombus (d) Right triangle
Solution. (a) In a square, all the sides and all the angles are equal.
Hence, square is an equiangular and equilateral polygon.

Question. 25 Which one has all the properties of a kite and a parallelogram?
(a) Trapezium (b) Rhombus (c) Rectangle (d) Parallelogram
Solution. (b) In a kite
Two pairs of equal sides.
Diagonals bisect at 90°.
One pair of opposite angles are equal.
In a parallelogram Opposite sides are equal.
Opposite angles are equal.
Diagonals bisect each other.
So, from the given options, all these properties are satisfied by rhombus.

Question. 26 The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. The smallest angle is
(a) 72° (b) 144° (c) 36° (d) 18°
Solution.

Question. 27 In the trapezium ABCD, the measure of \(\angle D\) is
(a) 55° (b) 115° (c)135° (d) 125°

Solution.

Question. 28 A quadrilateral has three acute angles. If each measures 80°, then the measure of the fourth angle is
(a) 150° (b) 120° (c) 105° (d) 140°
Solution.

Question. 29 The number of sides of a regular polygon where each exterior angle has a measure of 45° is
(a) 8 (b) 10 (c) 4 (d) 6
Solution.

Question. 30 In a parallelogram PQRS, if \(\angle P\) = 60°, then other three angles are
(a) 45°, 135°, 120° (b) 60°, 120°, 120°
(c) 60°, 135°, 135° (d) 45°, 135°, 135°
Solution.

Question. 31 If two adjacent angles of a parallelogram are in the ratio 2 : 3, then the measure of angles are
(a) 72°, 108° (b) 36°, 54° (c) 80°, 120° (d) 96°, 144°
Solution. (a) Let the angles be 2x and 3x.
Then, 2x + 3x = 180° [ adjacent angles of a parallelogram are supplementary]
=> 5x = 180°
=> x = 36°
Hence, the measures of angles are 2x = 2 x 36°= 72° and 3x = 3×36°= 108°

Question. 32 IfPQRS is a parallelogram then \(\angle P\) – \(\angle R\) is equal to
(a) 60° (b) 90° (c) 80° (d) 0°
Solution. (d) Since, in a parallelogram, opposite angles are equal. Therefore, \(\angle P\) – \(\angle R\) = 0, as \(\angle P\) and \(\angle R\) are opposite angles.

Question. 33 The sum of adjacent angles of a parallelogram is
(a) 180° (b) 120° (c) 360° (d) 90°
Solution. (a) By property of the parallelogram, we know that, the sum of adjacent angles of a parallelogram is 180°.

Question. 34 The angle between the two altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is 30°. The measure of the obtuse angle is
(a) 100° (b) 150° (c) 105° (d) 120°
Solution.

Question. 35 In the given figure, ABCD and BDCE are parallelograms with common base DC. If \(BC\bot BD\), then \(\angle BEC\) is equal to
(a) 60° (b) 30° (c) 150° (d) 120°

Solution.

Question. 36 Length of one of the diagonals of a rectangle whose sides are 10 cm and 24 cm is
(a) 25 cm (b) 20 cm (c) 26 cm (d) 3.5 cm
Solution.

Question. 37 If the adjacent angles of a parallelogram are equal, then the parallelogram is a (a) rectangle (b) trapezium (c) rhombus (d) None of these
Solution. (a) We know that, the adjacent angles of a parallelogram are supplementary, i.e. their sum equals 180° and given that both the angles are same. Therefore, each angle will be of measure 90°. .
Hence, the parallelogram is a rectangle.

Question. 38 Which of the following can be four interior angles of a quadrilateral?
(a) 140°, 40°, 20°, 160° (b) 270°, 150°, 30°, 20°
(c) 40°, 70°, 90°, 60°    (d) 110°, 40°, 30°, 180°
Solution. (a) We know that, the sum of interior angles of a quadrilateral is 360°.
Thus, the angles in option (a) can be four interior angles of a quadrilateral as their sum is 360°.

Question. 39 The sum of angles of a concave quadrilateral is
(a) more than 360° (b) less than 360°
(c) equal to 360° (d) twice of 360°
Solution. (c) We know that, the sum of interior angles of any polygon (convex or concave) having n sides is(n -2) x 180°.
.-.The sum of angles of a concave quadrilateral is (4 – 2) x 180°, i.e. 360°

Question. 40 Which of the following can never be the measure of exterior angle of a regular polygon? (a) 22° (b) 36° (c)45° (d) 30°
Solution. (a) Since, we know that, the sum of measures of exterior angles of a polygon is 360°, i.e. measure of each exterior angle =360°/n ,where n is the number of sides/angles.
Thus, measure of each exterior angle will always divide 360° completely.
Hence, 22° can never be the measure of exterior angle of a regular polygon.

Question. 41 In the figure, BEST is a rhombus, then the value of y – x is
(a) 40° (b) 50° (c) 20° (d) 10°

Solution.

Question. 42 The closed curve which is also a polygon, is

Solution. (a) Figure (a) is polygon as no two line segments intersect each other.

Question. 43 Which of the following is not true for an exterior angle of a regular polygon with n sides?

Solution. (d) We know that, (a) and (b) are the formulae to find the measure of each exterior angle, when number of sides and measure of an interior angle respectively are given and (c) is the formula to find number of sides of polygon when exterior angle is given.
Hence, the formula given in option (d) is not true for an exterior angle of a regular polygon with n sides.

Question. 44 PQRS is a square. PR and SQ intersect at 0. Then, \(\angle POQ\) is a (a) right angle (b) straight angle (c) reflex angle (d) complete angle
Solution.

Question. 45 Two adjacent angles of a parallelogram are in the ratio 1 : 5. Then, all the angles of the parallelogram are
(a) 30°, 150°, 30°, 150° (b) 85°, 95°, 85°, 95° .
(c) 45°, 135°, 45°, 135° (d) 30°, 180°, 30°, 180°
Solution. (a) Let the adjacent angles of a parallelogram be x and 5x, respectively.
Then, x + 5x = 180° [ adjacent angles of a parallelogram are supplementary] => 6x = 180°
=> x = 30°
The adjacent angles are 30° and 150°.
Hence, the angles are 30°, 150°, 30°, 150°

Question. 46 A parallelogram PQRS is constructed with sides QR = 6 cm, PQ = 4 cm and \(\angle PQR\) = 90°. Then, PQRS is a
(a) square (b) rectangle (c) rhombus  (d) trapezium
Solution. (b) We know that, if in a parallelogram one angle is of 90°, then all angles will be of 90° and a parallelogram with all angles equal to 90° is called a rectangle.

Question. 47 The angles P, Q, R and 5 of a quadrilateral are in the ratio  1:3 :7:9. Then, PQRS is a
(a) parallelogram  (b) trapezium with PQ \\ RS
(c) trapezium with  QR \\PS (d) kite
Solution.

Question. 48 PQRS is a trapezium in which PQ || SR and ZP = 130°, \(\angle Q\) = 110°. Then, \(\angle R\) is equal to.
(a) 70° (b) 50° (c)65° (d) 55°
Solution.

Question. 49 The number of sides of a regular polygon whose each interior angle is of 135° is (a) 6  (b) 7 (c) 8 (d) 9
Solution.

Question. 50 If a diagonal of a quadrilateral bisects both the angles, then it is a
(a) kite (b) parallelogram  (c) rhombus (d) rectangle
Solution. (c) If a diagonal of a quadrilateral bisects both the angles, then it is a rhombus.

Question. 51 To construct a unique parallelogram, the minimum number of measurements required is (a) 2 (b) 3 (c) 4 (d) 5
Solution. (b) We know that, in a parallelogram, opposite sides are equal and parallel. Also,
opposite angles are equal.
So, to construct a parallelogram uniquely, we require the measure of any two non-parallel sides and the measure of an angle.
Hence, the minimum number of measurements required to draw a unique parallelogram is 3.

Question. 52 To construct a unique rectangle, the minimum number of measurements required is (a) 4 (b) 3 (0 2 (d) 1
Solution. (c) Since, in a rectangle, opposite sides are equal and parallel, so we need the measurement of only two adjacent sides, i.e. length and breadth. Also, each angle measures 90°.
Hence, we require only two measurements to construct a unique rectangle.

Fill in the Blanks
In questions 53 to 91, fill in the blanks to make the statements true.
Question. 53 In quadrilateral HOPE, the pairs of opposite sides are————–.
Solution.

Question. 54 In quadrilateral ROPE, the pairs of adjacent angles are—————-.
Solution .

Question. 55 In quadrilateral WXYZ, the pairs of opposite angles are————–.
Solution.

Question . 56 The diagonals of the quadrilateral DEFG are———–and————–.
Solution.

Question. 57 The sum of all———— of a quadrilateral is 360°.
Solution. angles
We know that, the sum of all angles of a quadrilateral is 360°.

Question. 58 The measure of each exterior angle of a regular pentagon is————— .
Solution.

Question. 59 Sum of the angles of a hexagon is———————-.
Solution.

Question. 60 The measure of each exterior angle of a regular polygon of 18 sides is———.
Solution.

Question. 61 The number of sides of a regular polygon, where each exterior angle has a measure of 36°, is—————-.
Solution.

Question. 62

Solution. concave polygon
As one interior angle is of greater than 180°.

Question. 63 A quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure is—————–.
Solution. kite
By the property of a kite, we know that, it has two opposite angles of equal measure.

Question. 64 The measure of each angle of a regular pentagon is————–.
Solution.

Question. 65 The name of three-sided regular polygon is—————-.
Solution. equilateral triangle, as polygon is regular, i.e. length of each side is same.

Question. 66 The number of diagonals in a hexagon is—————-.
Solution.

Question. 67 A polygon is a simple closed curve made up of only————.
Solution. line segments ,
Since a simple closed curve made up of only line segments is called a polygon.

Question. 68 A regular polygon is a polygon whose all sides are equal and all———are equal.
Solution. angles
In a regular polygon, all sides are equal and all angles are equal.

Question. 69 The sum of interior angles of a polygon of n sides is———- right angles.
Solution.

Question. 70 The sum of all exterior angles of a polygon is————.
Solution. 360°
As the sum of all exterior angles of a polygon is 360°.

Question. 71 ————-is a regular quadrilateral.
Solution. Square
Since in square, all the sides are of equal length and all angles are equal.

Question. 72 A quadrilateral in which a pair of opposite sides is parallel is————-.
Solution. trapezium
We know that, in a trapezium, one pair of sides is parallel.

Question. 73 If all sides of a quadrilateral are equal, it is a————–.
Solution. rhombus or square
As in both the quadrilaterals all sides are of equal length.

Question. 74 In a rhombus, diagonals intersect at———– angles.
Solution. right
The diagonals of a rhombus intersect at right angles.

Question. 75 ———measurements can determine a quadrilateral uniquely.
Solution. 5
To construct a unique quadrilateral, we require 5 measurements, i.e. four sides and one angle or three sides and two included angles or two adjacent sides and three angles are given.

Question. 76 A quadrilateral can be constructed uniquely, if its three sides and———–angles are given.
Solution. two included
We cap determine a quadrilateral uniquely, if three sides and two included angles are given.

Question. 77 A rhombus is a parallelogram in which————sides are equal.
Solution. all
As length of each side is same in a rhombus.

Question. 78 The measure of——– angle of concave quadrilateral is more than 180°.
Solution. one
Concave polygon is a polygon in which at least one interior angle is more than 180°.

Question. 79 A diagonal of a quadrilateral is a line segment that joins two——– vertices of the quadrilateral.
Solution. opposite
Since the line segment connecting two opposite vertices is called diagonal.

Question. 80 The number of sides in a regular polygon having measure of an exterior angle as 72° is————— .
Solution. 5
We know that,the sum of exterior angles of any polygon is 360°.

Question. 81 If the diagonals of a quadrilateral bisect each other, it is a————.
Solution. parallelogram
Since in a parallelogram, the diagonals bisect each other.

Question. 82 The adjacent sides of a parallelogram are 5 cm and 9 cm. Its perimeter is—–.
Solution. 28 cm
Perimeter of a parallelogram = 2 (Sum of lengths of adjacent sides)
=2(5+ 9) = 2 x 14=28cm

Question. 83 A nonagon has————sides.
Solution. 9
Nonagon is a polygon which has 9 sides.

Question. 84 Diagonals of a rectangle are————.
Solution. equal
We know that, in a rectangle, both the diagonals are of equal length.

Question. 85 A polygon having 10 sides is known as————.
Solution. decagon
A polygon with 10 sides is called decagon.

Question. 86 A rectangle whose adjacent sides are equal becomes a ————.
Solution. square
If in a rectangle, adjacent sides are equal, then it is called a square.

Question. 87 If one diagonal of a rectangle is 6 cm long, length of the other diagonal is—–.
Solution. 6 cm
Since both the diagonals of a rectangle are equal. Therefore, length of other diagonal is also 6 cm.

Question. 88 Adjacent angles of a parallelogram are————.
Solution. supplementary
By property of a parallelogram, we know that, the adjacent angles of a parallelogram are supplementary.

Question. 89 If only one diagonal of a quadrilateral bisects the other, then the quadrilateral is known as————.
Solution. kite
This is a property of kite, i.e. only one diagonal bisects the other.

Question. 90 In trapezium ABCD with AB || CD, if \( \angle A\)= 100°, then \( \angle D\) =————.
Solution.

Question. 91 The polygon in which sum of all exterior angles is equal to the sum of interior angles is called————.
Solution. quadrilateral
We know that, the sum of exterior angles of a polygon is 360° and in a quadrilateral, sum of interior angles is also 360°. Therefore, a quadrilateral is a polygon in which the sum of both interior and exterior angles are equal.

True/False
In questions 92 to 131, state whether the statements are True or False.
Question. 92 All angles of a trapezium are equal.
Solution. False
As all angles of a trapezium are not equal.

Question. 93 All squares are rectangles.
Solution. True
Since squares possess all the properties of rectangles. Therefore, we can say that, all squares are rectangles but vice-versa is not true.

Question. 94 All kites are squares.
Solution. False
As kites do not satisfy all the properties of a square.
e.g. In square, all the angles are of 90° but in kite, it is not the case.

Question. 95 All rectangles are parallelograms.
Solution. True
Since rectangles satisfy all ”the”properties” of parallelograms. Therefore, we can say that, all rectangles are parallelograms but vice-versa is not true.

Question. 96 All rhombuses are square.
Solution. False
As in a rhombus, each angle is not a right angle, so rhombuses are not squares.

Question. 97 Sum of all the angles of a quadrilateral is 180°.
Solution. False
Since sum of all the angles of a quadrilateral is 360°.

Question. 98 A quadrilateral has two diagonals.
Solution. True
A quadrilateral has two diagonals.

Question. 99 Triangle is a polygon whose sum of exterior angles is double the sum of interior angles.
Solution. True
As the sum of interior angles of a triangle is 180° and the sum of exterior angles is 360°, i.e. double the sum of interior angles.

Question. 100

Solution. False
Because it is not a simple closed curve as it intersects with itself more than once.

Question. 101 A kite is not a convex quadrilateral.
Solution. False
A kite is a convex quadrilateral as the line segment joining any two opposite vertices inside it, lies completely inside it.

Question. 102 The sum of interior angles and the sum of exterior angles taken in an order are equal in case of quadrilaterals only.
Solution. True
Since the sum of interior angles as well as of exterior angles of a quadrilateral are 360°.

Question. 103 If the sum of interior angles is double the sum of exterior angles taken in an order of a polygon, then it is a hexagon.
Solution. True
Since the sum of exterior angles of a hexagon is 360° and the sum of interior angles of a hexagon is 720°, i.e. double the sum of exterior angles.

Question. 104 A polygon is regular, if all of its sides are equal.
Solution. False
By definition of a regular polygon, we know that, a polygon is regular, if all sides and all angles are equal.

Question. 105 Rectangle is a regular quadrilateral.
Solution. False
As its all sides are not equal.

Question. 106 If diagonals of a quadrilateral are equal, it must be a rectangle.
Solution. True
If diagonals are equal, then it is definitely a rectangle. –

Question. 107 If opposite angles of a quadrilateral are equal, it must be a parallelogram.
Solution. True
If opposite angles are equal, it has to be a parallelogram.

Question. 108 The interior angles of a triangle are in the ratio 1:2:3, then the ratio of its exterior angles is 3 : 2 : 1.
Solution.

Question. 109

Solution. False
As it has 6 sides, therefore it is a concave hexagon.

Question. 110 Diagonals of a rhombus are equal and perpendicular to each other.
Solution. False
As diagonals of a rhombus are perpendicular to each other but not equal.

Question. 111 Diagonals of a rectangle are equal.
Solution. True
The diagonals of a rectangle are equal.

Question. 112 Diagonals of rectangle bisect each other at right angles.
Solution. False
Diagonals of a rectangle does not bisect each other.

Question. 113 Every kite is a parallelogram.
Solution. False
Kite is not a parallelogram as its opposite sides are not equal and parallel.

Question. 114 Every trapezium is a parallelogram.
Solution. False
Since in a trapezium, only one pair of sides is parallel.

Question. 115 Every parallelogram is a rectangle.
Solution. False
As in a parallelogram, all angles are not right angles, while in a rectangle, all angles are equal and are right angles.

Question. 116 Every trapezium is a rectangle.
Solution. False
Since in a rectangle, opposite sides are equal and parallel but in a trapezium, it is not so.

Question. 117 Every rectangle is a trapezium.
Solution. True
As a rectangle satisfies all the properties of a trapezium. So, we can say that, every rectangle is a trapezium but vice-versa is not true.

Question. 118 Every square is a rhombus.
Solution. True
As a square possesses all the properties of a rhombus. So, we can say that, every square is a rhombus but vice-versa is not true.

Question. 119 Every square is a parallelogram.
Solution. True
Every square is also a parallelogram as it has all the properties of a parallelogram but vice-versa is not true.

Question. 120 Every square is a trapezium.
Solution. True
As a square has all the properties of a trapezium. So, we can say that, every square is a trapezium but vice-versa is not true.

Question. 121 Every rhombus is a trapezium.
Solution. True
Since a rhombus satisfies all the properties of a trapezium. So, we can say that, every rhombus is a trapezium but vice-versa is not true.

Question. 122 A quadrilateral can be drawn if only measures of four sides are given.
Solution. False
As we require at least five measurements to determine a quadrilateral uniquely.

Question. 123 A quadrilateral can have all four angles as obtuse.
Solution. False
If all angles will be obtuse, then their sum will exceed 360°. This is not possible in case of a quadrilateral.

Question. 124 A quadrilateral can be drawn, if all four sides and one diagonal is known.
Solution. True
A quadrilateral can be constructed uniquely, if four sides and one diagonal is known.

Question. 125 A quadrilateral can be drawn, when all the four angles and one side is given.
Solution. False
We cannot draw a unique-quadrilateral, if four angles and one side is known.

Question. 126 A quadrilateral can be drawn, if all four sides and one angle is known.
Solution. True
A quadrilateral can be drawn, if all four sides and one angle is known.

Question. 127 A quadrilateral can be drawn, if three sides and two diagonals are given.
Solution. True
A quadrilateral can be drawn, if three sides and two diagonals are given.

Question. 128 If diagonals of a quadrilateral bisect each other, it must be a parallelogram.
Solution. True
It is the property of a parallelogram.

Question. 129 A quadrilateral can be constructed uniquely, if three angles and any two included sides are given.
Solution. True
We can construct a unique quadrilateral with given three angles given and two included sides.

Question. 130 A parallelogram can be constructed uniquely, if both diagonals and the angle between them is given.
Solution. True
We can draw a unique parallelogram, if both diagonals and the angle between them is given.

Question. 131 A rhombus can be constructed uniquely, if both diagonals are given.
Solution. True
A rhombus can be constructed uniquely, if both diagonals are given.

Question. 132 The diagonals of a rhombus are 8 cm and 15 cm. Find its side.
Solution.

Question. 133 Two adjacent angles of a parallelogram are in the ratio 1 : 3. Find its angles.
Solution. Let the adjacent angles of a parallelogram be x and 8c.
Then, we have x + (3 x) = 180° [adjacent angles of parallelogram are supplementary]
=> 4 x = 180°
=> x = 45°
Thus, the angles are 45°, 135°.
Hence, the angles are 45°, 135, 45°, 135°. [ opposite angles in a parallelogram are equal]

Question. 134 Of the four quadrilaterals – square, rectangle, rhombus and trapezium-one is somewhat different from the others because of its design. Find it and give justification.
Solution. In square, rectangle and rhombus, opposite sides are parallel and equal. Also, opposite angles are equal, i.e. they all are parallelograms.
But in trapezium, there is only one pair of parallel sides, i.e. it is not a parallelogram. Therefore, trapezium has different design.

Question. 135 In a rectangle ABCD, AB = 25 cm and BC = 15 cm. In what ratio, does the bisector of \(\angle C\) divide AB?
Solution.

Question. 136 PQRS is a rectangle. The perpendicular ST from S on PR divides \(\angle S\) in the ratio 2 : 3. Find \(\angle TPQ\).
Solution.

Question. 137 A photo frame is in the shape of a quadrilateral, with one diagonal longer than the other. Is it a rectangle? Why or why not?
Solution. No, it cannot be a rectangle, as in rectangle, both the diagonals are of equal lengths.

Question. 138 The adjacent angles of a parallelogram are (2x – 4)° and (3x – 1)°. Find the measures of all angles of the parallelogram.
Solution. Since, the adjacent angles of a parallelogram are supplementary.
(2 x – 4)° + (3* – 1)° = 180°

Question. 139 The point of intersection of diagonals of a quadrilateral divides one diagonal in the ratio 1: 2. Can it be a parallelogram? Why or why not?
Solution. No, it can never be a parallelogram, as the diagonals of a parallelogram intersect each other in the ratio 1 : 1.

Question. 140 The ratio between exterior angle and interior angle of a regular polygon is 1 : 5. Find the number of sides of the polygon.
Solution.

Question. 141 Two sticks each of length 5 cm are crossing each other such that they bisect each other. What shape is formed by joining their end points? Give reason.
Solution. Sticks can be taken as the diagonals of a quadrilateral.
Now, since they are bisecting each other, therefore the shape formed by joining their end points will be a parallelogram.
Hence, it may be a rectangle or a square depending on the angle between the sticks.

Question. 142 Two sticks each of length 7 cm are crossing each other such that they bisect each other at right angles. What shape is formed by joining their end points? Give reason.
Solution. Sticks can be treated as the diagonals of a quadrilateral.
Now, since the diagonals (sticks) are bisecting each other at right angles, therefore the shape formed by joining their end points will be a rhombus.

Question. 143 A playground in the town is in the form of a kite. The perimeter is 106 m. If one of its sides is 23 m, what are the lengths of other three sides?
Solution. Let the length of other non-consecutive side be x cm.
Then, we have, perimeter of playground = 23 + 23+ x + x
=> 106 = 2 (23+ x)
=>46 + 2x = 106 2x = 106 – 46
=>2x = 60
=>x = 30 m
Hence, the lengths of other three sides are 23m, 30m and 30m. As a kite has two pairs of equal consecutive sides.

Question. 144 In rectangle READ , find \(\angle EAR\), \(\angle RAD\) and \(\angle ROD\).

Solution.

Question. 145 In rectangle PAIR, find \(\angle ARI\), ZRMI and \(\angle PMA\).

Solution.

Question. 146 In parallelogram ABCD, find \(\angle B\), \(\angle C\) and \(\angle D\).

Solution.

Question. 147 In parallelogram PQRS, 0 is the mid-point of SQ. Find \(\angle S\), \(\angle R\), PQ, QR and diagonal PR.

Solution.

Question. 148 In rhombus BEAM, find \(\angle AME\) and \(\angle AEM\).

Solution.

Question. 149 In parallelogram FIST, find \(\angle SFT\), \(\angle OST\) and \(\angle STO\).

Solution.

Question. 150 In the given parallelogram YOUR, \(\angle RUO\)= 120° and 0Y is extended to points, such that \(\angle SRY\) = 50°. Find \(\angle YSR\).

Solution.

Question.151 In kite WEAR, \(\angle WEA\) = 70° and \(\angle ARW\) = 80°. Find the remaining two angles.

Solution.

Question.152

Solution.

Question.153 In parallelogram LOST, SNLOL and \( SM\bot LT\). Find \(\angle STM\), \(\angle SON\) and \(\angle NSM\).

Solution.

Question. 154 In trapezium HARE, EP and RP are bisectors of \(\angle E\) and \(\angle R\), respectively. Find \(\angle HAR\) and \(\angle EHA\).

Solution.

Question. 155 In parallelogram MODE, the bisectors of \(\angle M\) and \(\angle O\) meet at Q. Find the measure of \(\angle MQO\).
Solution.

Question. 156 A playground is in the form of a rectangle ATEF. Two players are standing at the points F and B, where EF =EB. Find the values of x and y.

Solution.

Question. 157 In the following figure of a ship, ABDH and CEFG are two parallelograms. Find the value of x.

Solution.

Question. 158 A rangoli has been drawn on the floor of a house. ABCD and PQRS both are in the shape of a rhombus. Find the radius of semi-circle drawn on each side of rhombus ABCD.

Solution.

Question. 159 ABCDE is a regular pentagon. The bisector of angle A meets the sides CD at M. Find \(\angle AMC\)

Solution.

Question. 160 Quadrilateral EFGH is a rectangle in which J is the point of intersection of the diagonals. Find the value of x, if JF = 8x + 4 and EG = 24 x – 8.
Solution.

Question. 161 Find the values of x and y in the following parallelogram.

Solution.

Question. 162 Find the values of x and y in the following kite.

Solution.

Question. 163 Find the value of x in the trapezium ABCD given below.

Solution.

Question. 164 Two angles of a quadrilateral are each of measure 75° and the other two angles are equal. What is the measure of these two angles? Name the possible figures so formed.
Solution.

Question. 165 In a quadrilateral PQRS, \(\angle P\) = 50°, \(\angle Q\) = 50°, \(\angle R\) = 60°. Find \(\angle S\). Is this quadrilateral convex or concave?
Solution.

Question. 166 Both the pairs of opposite angles of a quadrilateral are equal and supplementary. Find the measure of each angle.
Solution.

Question. 167 Find the measure of each angle of a regular octagon.
Solution.

Question. 168 Find the measure of an exterior angle of a regular pentagon and an exterior angle of a regular decagon. What is the ratio between these two angles?
Solution.

Question. 169 In the figure, find the value of x.

Solution.

Question. 170 Three angles of a quadrilateral are equal. Fourth angle is of measure 120°. What is the measure of equal angles?
Solution.

Question. 171 In a quadrilateral HOPE, PS and ES are bisectors of \(\angle P\) and \(\angle E\) respectively. Give reason.
Solution. Data insufficient.

Question. 172 ABCD is a parallelogram. Find the values of x, y and z.

Solution.

Question. 173 Diagonals of a quadrilateral are perpendicular to each other. Is such a quadrilateral always a rhombus? Give a figure to justify your answer.
Solution.

Question. 174 ABCD is a trapezium such that AB || CD, \(\angle A\): \(\angle D\) = 2:1, \(\angle B\) : \(\angle C\) = 7:5. Find the angles of the trapezium.
Solution.

Question. 175 A line / is parallel to Line m and a-transversal p intersects them at X, Y respectively. Bisectors of interior angles at X and Y intersect at P and Q. Is PXQY a rectangle? Give reason.
Solution.

Question. 176 ABCD is a parallelogram. The bisector of angle A intersects CD at X and bisector of angle C intersects AB at Y. Is AXCY a parallelogram? Give reason.
Solution.

Question. 177 A diagonal of a parallelogram bisects an angle. Will it also bisect the other angle? Give reason.
Solution. Consider a parallelogram ABCD.
Given, \(\angle 1\) = \(\angle 2\)

Question. 178 The angle between the two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 45°. Find the angles of the parallelogram.
Solution. Let ABCD be a parallelogram, where BE and BF are the perpendiculars through the vertex B to the sides DC and AD, respectively.

Question. 179 ABCD is a rhombus such that the perpendicular bisector of AB passes through D. Find the angles of the rhombus.[Hint Join BD. Then, AABD is equilateral.]
Solution. Let ABCD be a rhombus in which DE is perpendicular bisector of AB.

Question. 180 ABCD is a parallelogram. Point P and Q are taken on the sides AB and AD, respectively and 4he parallelogram PRQA is formed. If \(\angle C\)= 45°, find \(\angle R\).
Solution.

Question. 181 In parallelogram ABCD, the angle bisector of \(\angle A\) bisects BC. Will angle bisector of B also bisect AD? Give reason.
Solution. Given, ABCD is a parallelogram, bisector of \(\angle A\), bisects BC at F, i.e. \(\angle 1\) = \(\angle 2\),CF = FB Draw FE || BA.

Question. 182 A regular pentagon ABCDE and a square ABFG are formed on opposite sides of AB. Find \(\angle BCF\)?
Solution.

Question. 183 Find maximum number of acute angles which a convex quadrilateral, a pentagon and a hexagon can have. Observe the pattern and generalise the result for any polygon.
Solution. If an angle is acute, then the corresponding exterior angle is greater than 90°. Now, suppose a convex polygon has four or more acute angles. Since, the polygon is convex, all the exterior angles are positive, so the sum of the exterior angle is at least the sum of the interior angles. Now, supplementary of the four acute angles, which is greater than 4 x 90° = 360°
However, this is impossible. Since, the sum of exterior angle of a polygon must equal to 360° and cannot be greater than it. It follows that the maximum number of acute angle in convex polygon is 3.

Question. 184 In the following figure, FD || BC || AE and AC || ED. Find the value of x.

Solution.

Question. 185 In the following figure, AB || DC and AD = BC. Find the value of x.

Solution.

Question. 186 Construct a trapezium ABCD in which AB || DC, \(\angle A\) = 105°, AD = 3 cm, AB = 4 cm and CD = 8 cm.
Solution.

Question. 187 Construct a parallelogram ABCD in which AB =4 cm, BC = 5cm and \(\angle B\) = 60°.
Solution.

Question. 188 Construct a rhombus whose side is 5 cm and one angle is of 60°
Solution.

Question. 189 Construct a rectangle whose one side is 3 cm and a diagonal is equal to 5 cm.
Solution.

Question. 190 Construct a square of side 4 cm.
Solution.

Question. 191 Construct a rhombus CLUE in which CL = 7.5 cm and LE = 6 cm.
Solution.

Question. 192 Construct a quadrilateral BEAR in which BE = 6 cm, EA = 7 cm, RB = RE = 5 cm and BA = 9 cm. Measure its fourth side.
Solution.

Question. 193 Construct a parallelogram POUR in which PO = 5.5 cm, OU = 7.2 cm and \(\angle O\) = 70°.
Solution.

Question. 194 Draw a circle of radius 3 cm and draw its diameter and label it as AC. Construct its perpendicular bisector and let it intersect the circle at B and D. What type of quadrilateral is ABCD? Justify your answer.
Solution.

Question. 195 Construct a parallelogram HOME with HO = 6 cm, HE = 4 cm and OE = 3 cm.
Solution.

Question. 196 Is it possible to construct a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 5.4 cm, DA = 5.9 cm and diagonal AC = 8 cm? If not, why?
Solution. No,
Given measures are AS = 3 cm, SC = 4 cm,CD = 5.4 cm,
DA = 59cmand AC = 8cm
Here, we observe that AS + SC = 3 + 4 = 7 cm and AC = 8 cm
i.e. the sum of two sides of a triangle is less than the third side, which is absurd.
Hence, we cannot construct such a quadrilateral.

Question. 197 Is it possible to construct a quadrilateral ROAM in which RO = 4 cm, OA = 5 cm, \(\angle O\) = 120°,\(\angle R\) = 105° and \(\angle A\) = 135°? If not, why?
Solution.

Question. 198 Construct a square in which each diagonal is 5 cm long.
Solution.

Question. 199 Construct a quadrilateral NEWS in which NE = 7 cm, EW = 6 cm, \(\angle N\) = 60°, \(\angle E\)= 110° and \(\angle S\) = 85°
Solution.

Question. 200 Construct a parallelogram when one of its side is 4 cm and its two diagonals are 5.6 cm and 7 cm. Measure the other side.
Solution.

Question. 201 Find the measure of each angle of a regular polygon of 20 sides?
Solution.

Question. 202 Construct a trapezium RISK in which RI || KS, RI = 7 cm, IS = 5 cm, RK = 6.5 cm and \(\angle I\) = 60°.
Solution.

Question. 203 Construct a trapezium ABCD, where AB|| CD, AD = BC = 3.2 cm, AB = 6.4 cm and CD = 9.6 cm. Measure \(\angle B\) and \(\angle A\)

[Hint Difference of two parallel sides gives an equilateral triangle.]
Solution.

The post NCERT Exemplar Problems Class 8 Mathematics Understanding Quadrilaterals and Practical Geometry appeared first on Learn CBSE.

NCERT Exemplar Problems Class 8 Mathematics Chapter 3 Square-Square Root and Cube-Cube Root

Multiple Choice Questions (MCQs)

Question1  196 is the square of
(a) 11                  (b) 12
(c) 14                  (d) 16
Solution.
(c) Square of 11 = 11 x 11 = 121
Square of 12 = 12 x 12 = 144
Square of 14 = 14 x 14 = 196
Clearly, 196 is the square of 14

Question 2 Which of the following is a square of an even number?
(a) 144 (b) 169
(c) 441 (d) 625
Solution.

Thus, 144 is a square of an even number.
Alternate Method
We know that, square of an even number is always an even number. Hence, 169, 441 and 625 are not even numbers. So, only 144 is an even number, which is the square of 12.

Question 3  A number ending in 9 will have the unit’s place of its square as
(a) 3                           (b) 9
(c) 1                            (d) 6
Solution.

Question 4 Which of the following will have 4 at the unit’s place?
(a) 14²                 (b) 62²                 (c) 27²             (d)35²
Solution.

Question 5  How many natural numbers lie between 5² and 6²?
(a) 9 (b) 10 (c)11 (d) 12
Solution. (b) The natural numbers lying between 5² and 6², i.e. between 25 and 36 are 26, 27, 28, 29, 30, 31,32, 33, 34 and 35.
Hence, 10 natural numbers lie between 5² and 6².

Question 6 Which of the following cannot be a perfect square?
(a) 841  (b) 529  (c) 198  (d) All of these
Solution.(c) We know that, a number ending with digits 2, 3, 7 or 8 can never be a perfect square. So, 198 cannot be written in the form of a perfect square.

Question 7 The one’s digit of the cube of 23 is
(a) 6 (b) 7 (c) 3 (d) 9
Solution. (b) We know that, the cubes of the numbers ending with digits 3 and 7, have 7 and 3 at one’s digit, respectively.
So, the one’s digit of the cube of 23 is 7.

Question 8 A square board has an area of 144 sq units. How long is each side of the board?
(a) 11 units  (b) 12 units  (c) 13 units  (d) 14 units
Solution.

Question 9

Solution.

Question 10  If one member of a Pythagorean triplet is 2m, then the other two members are

Solution.

Question 11 The sum of successive odd numbers 1, 3, 5, 7, 9, 11, 13 and 15 is
(a) 61   (b)   64   (c) 49   (d) 36
Solution. (b) We know that, the sum of first n odd natural numbers is n².
Given odd numbers are 1,3, 5, 7, 9,11,13 and 15.
So, number of odd numbers, n = 8
The sum of given odd numbers =n² = (8)² = 64

Question 12 The sum of first n odd natural numbers is
(a) 2n +1 (b)     n²  (c)     n² –1    (d) n² +1
Solution.

Question 13 Which of the following numbers is a perfect cube?
(a) 243   (b) 216   (c) 392 (d) 8640
Solution.(b) For option (a) We have, 243
Resolving 243 into prime factors, we have
243= 3 x 3 x 3 x 3 x 3
Grouping the factors in triplets of equal factors, we get
243 = (3 x 3 x 3) x 3 x 3
Clearly, in grouping, the factors in triplets of equal factors, we are left with two factors 3 x 3.
Therefore, 243 is not a perfect cube.
For option (b) We have, 216 Resolving 216 into prime factqrs, we have
216 = 2  x 2 x  2 x 3 x 3 x 3
Grouping the factors in triplets of equal factors, we get 216 = (2 x 2 x 2) x (3 x 3 x 3)
Clearly, in grouping, the factors of triplets of equal factors, no factor is left over.
So, 216 is a perfect cube.
For option (c) We have, 392
Resolving 392 into prime factors, we get
392 = 2 x 2 x 2 x 7 x 7
Grouping the factors in triplets of equal factors, we get
392 = (2 x 2 x 2) x 7 x 7
Clearly, in grouping, the factors in triplets of equal factors, we are left with two factors 7 x 7.
Therefore, 392 is not a perfect cube.
For option (d) We have, 8640
Resolving 8640 into prime factors, we get
8640=2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5
Grouping the factors in triplets of equal factors, we get
8640 = (2 x 2 x 2) x (2 x 2 x 2) x (3 x 3 x 3) x 5
Clearly, in grouping, the factors in triplets of equal factors, we are left with one factor 5. Therefore, 8640 in not a perfect cube.
After solving, it is clear that option (b) is correct.

Question 14 The hypotenuse of a right angled triangle with its legs of lengths 3x  x  4x is
(a) 5X                                   (b )7x                                 (c) 16x                              (d) 25x
Solution.

Question 15  The next two numbers in the number pattern 1, 4, 9,16, 25,… are
(a) 35, 48 (b) 36, 49 (c) 36, 48 (d) 35, 49
Solution. (b) We have, 1,4, 9,16, 25, ….
The number pattern can be written as (1)², (2)², (3)², (4)², (5)²
Hence, the next two numbers are (6)² and (7)², i.e. 36 and 49.

Question 16  Which among 43²   , 67² , 52² , 59² would end with digit 1?
(a) 43²           (b)67²           (c)52²          (d)59²
Solution.

Question 17  A perfect square can never have the following digit in its one’s place.
(a) 1                                  (b) 8                             (c) 0                                    (d) 6
Solution.
(b) We know that, a number ending with digits 2, 3, 7 or 8 can never be a perfect square. Clearly, a perfect square can never have the digit 8 in its one’s place.

Question 18 Which of the following numbers is not a perfect cube?
(a) 216                   (b) 567                   (c) 125              (d) 343
Solution.
(b) 216=6 x 6 x 6, 567 = 3 x 3 x 3 x 3 x 7
125 = 5 x 5 x 5, 343 = 7 x 7 x 7
Clearly, 567 is not a perfect cube, because in grouping, the factors in triplets of equal factors, we are left with two factors 3 x 7.

Question 19

Solution.

Question 20

Solution.

Question 21  A perfect square number having n digits, where n is even, will have square root with

Solution. (b) A perfect square number having n digits, where n is even, will have square root with n/2 digit.

Question 22

solution.

Question 23

Solution.

Question 24

Solution.

Fill in the Blanks
In questions 25 to 48, fill in the blanks to make the statements true.

Question 25  There are________perfect squares between 1 and 100.
Solution.8
There are 8 perfect squares between 1 and 100, i.e. 4, 9,16, 25, 36, 49, 64 and 81.

Question 26  There are________ perfect cubes between 1 and 1000.
Solution.8
There are 8 perfect cubes between 1 and 1000, i.e. 8, 27,64,125, 216, 343 and 729.

Question 27 The unit’s digit in the square of 1294 is________
Solution. 6
We know that, the unit’s digit of the square of a number having digit .at unit’s place as 4 or 6 is 6.
Hence, the units digit in the square of 1294 is 6 as 4 x 4 = 16.

Question 28  The square of 500 will have zeroes.
Solution.  four
The square of 500 = (500)²
= 500 x 500 = 250000
Hence, the square of 500 will have four zeroes.

Question 29  There are natural numbers between n² and (n + l)²
Solution.

Question 30 The square root of 24025 will have________digits.
Solution.

Question 31 The square of 5.5 is________
Solution. 30.25
Square of 5.5= (5.5)² = 55 x 5.5= 30.25

Question 32  The square root of 5.3 x 5.3 is________
Solution.

Question 33  The cube of 100 will havfe________zeroes.
Solution. 6
Cubeof100 = 100³
= 100x100x100 = 1000000

Question 34  1m² =________ cm².
Solution.

Question 351m³ =________ cm³.
Solution.

Question 36 One’s digit in the cube of 38 is________
Solution.

Question 37 The square of 0.7 is________
Solution.0.49
Square of 0.7 = (0.7)² = 07 x 07 = 0.49

Question 38  The sum of first six odd natural numbers is________
Solution.

Question 39  The digit at the one’s place of 572 is________
Solution.

Question 40  The sides of a right angled triangle whose hypotenuse is 17cm, are________and________
Solution.

As, hypotenuse of right angled triangle is 17 cm.

Question 41

Solution.

Question 42 (1.2)³=________
Solution.

Question 43 The cube of an odd number is always an________number.
Solution.odd
We know that, the cubes of all odd natural numbers are odd.

Question 44  The cube root of a number x is denoted by________
Solution.

Question 45  The least number by which 125 be multiplied to make it a perfect square, is________
Solution.

Question 46 The least number by which 72 be multiplied to make it a perfect cube, is________
Solution. 3
Resolving 72 into prime factors, we get
72=2 x 2 x 2 x 3 x 3
Grouping the factors in triplets of equal factors, we get
72 = (2 x 2 x 2) x 3 x 3
We find that 2 occurs as a prime factor of 72 thrice, but 3 occurs as a prime factor only twice. Thus, if we multiply 72 by 3, 3 will also occurs as a prime factor thrice and the product will be 2 x 2 x 2 x 3 x 3 x 3, which is a perfect cube.
Hence, the least number, which should be multiplied with 72 to get perfect cube, is 3.

Question 47  The least number by which 72 be divided to make it a perfect cube, is________
Solution. 9
Resolving 72 into prime factors, we get
72=2 x 2 x 2 x 3 x 3
Grouping the factors in triplets of equal factors, we get
72 = (2 x 2 x 2) x 3 x 3
Clearly, if we divide 72 by 3 x 3, the quotient would be 2 x 2 x 2, which is a perfect cube. Hence, the least number by which 72 be divided to make it, a perfect cube, is 9.

Question 48 Cube of a number ending in 7 will end in the digit________
Solution 3
We know that, the cubes of the numbers ending in digits 3 or 7 ends in digits 7 or 3, respectively.
i.e 7 x 7 x 7 = 343
Hence, the cube of a number ending in 7 will end in the digit 3.

True/False
In questions 49 to 86, state whether the statements are True or False.

Question 49  The square of 86 will have 6 at the unit’s place.
Solution True
We know that, the unit’s digit of the square of a number having digit at unit’s place as 4 or 6 is 6.

Question 50 The sum of two perfect squares is a perfect square.
Solution False
e.g. 16 and 25 are the perfect squares, but 16 + 25 = 41 is not a perfect square.

Question 51 The product of twtfperfect squares is a perfect square.
Solution True
e.g. If 4 and 25 are the perfect square, then 4 x 25 = 100 is also a perfect square.
Clearly, the product of two perfect squares is a perfect square.

Question 52  There is no square number between 50 and 60.
Solution True
Numbers between 50 and 60 are 51,52, 53, 54, 55, 56, 57, 58 and 59.
We observed that there is no square number between 50 and 60.

Question 53 The square root of 1521 is 31.
Solution Falsie %
As, the square of 31 = (31)² = 31 x 31 = 961

Question 54 Each prime factor appears 3 times in its cube.
Solution True
If a3 is the cube and m is one of the prime factors of a. Then, m appears three times in a3.

Question 55 The square of 2.8 is 78.4.
Solution False
The square of 2.8 = (2.8)² = 2.8×2.8 = 7.84

Question 56 The cube of 0.4 is 0.064.
Solution True
Cube of 0.4 = (0.4)² = 0.4 x 0.4 x 0.4 = 0.064

Question 57 The square root of 0.9 is 0.3.
Solution False
As, the square of 0.3 = (0.3)² = 0.3 x 0.3 =0.09

Question 58  The square of every natural number is always greater than the number itself.
Solution False
1 is a natural number and square of 1 is not greater than 1.

Question 59  The cube root of 8000 is 200.
Solution

Question60 There are five perfect cubes between 1 and 100.
Solution False
There are eight perfect cubes between 1 and 100, i.e. 8,27,64,125,216,343,512 and 729.

Question 61 There are 200 natural numbers between 100² and 101².
Solution.

Question 62 The sum of first n odd natural numbers is n².
Solution.

Question 63  1000 is a perfect square.
Solution False
1000 = 2 x 2 x 2 x 5 x 5 x 5 = 2 ² x 5²x 2 x 5 Clearly, it is not a perfect square, because it has two unpaired factors 2 and 5.

Question 64  A perfect square can have 8 as its unit’s digit.
Solution False
A perfect square can never have 8 as its unit’s digit.

Question65

Solution

Question 66  All numbers of a Pythagorean triplet are odd.
Solution False
3, 4 and 5 are the numbers of Pythagorean triplet as 5² = 4 ² + 3 ² where, 4 is not an odd number.

Question 67  For an integer a, a³ is always greater than a².
Solution

Qustion68

Solution

Question 69  Let x and y be natural numbers. If x divides y, then x³ divides y³.
Solution.

Question 70 If a² ends in 5, then a³ ends in 25:
Solution.

Question 71 If a² ends in 9, thena³ ends in 7.
Solution

Question72

Solution.

Question 73  Square root of a number x is denoted by 4x.
Solution True
Square root of a number x is denoted by 4x.

Question 74 A number having 7 at its one’s place will have 3 at the unit’s place of its square.
Solution False
Square of 7 = 7 x 7 = 49
Square of 17 = 17 x 17 = 289
Square of 27 = 27 x 27 = 729
and so on.

Question 75 A number having 7 at its one’s place will have 3 at the one’s place of its cube.
Solution True
Cube of 7 = 7 x 7 x 7 =343
Cube of 17 = 17 x 17 x 17=4913
Cube of 27 = 27 x 27 x 27 = 19683
and so on.

Question 76 The cube of a one-digit number cannot be a two-digit number.
Solution

Question 77  Cube of an even number is odd.
Solution. False
We know that, the cube of an even number is always an even number,
e.g. 2 is an even number. Then, 2³ = 2 x 2 x 2 = 8
Clearly, 8 is also an even number.

Question 78 Cube of an odd number is even.
Solution. False
We know that, the cube of an odd number is always an odd number,
e.g. 3 is an odd number. Then, 33 = 3 x 3 x 3 = 27
Clearly, 27 is not an even number.

Question 79 Cube of an even number is even.
Solution. True
We know that, the cube of an even number is always an even number,
e.g. 4 is an even number. Then, 43 = 4 x 4 x 4 = 64
Clearly, 64 is also an even number.

Question 80 Cube of an odd number is odd.
Solution. True
We know that, the cube of an odd number is always an odd number,
e.g. 9 is an odd number.
Then,93 =9 x 9 x 9 = 729
Clearly, 729 is also an odd number.

Question 81  999 is a perfect cube.
Solution.

Question 82  363 x 81 is a perfect cube.
Solution.

Question 83 Cube roots of 8 are + 2 and – 2 .
Sol. False
Cube root of 8 is 2 only and cube root of – 8 is – 2.

Question 84

Solution.

Question 85 There is no cube root of a negative integer.
Solution.

Question 86 Square of a number is positive, so the cube of positive.
Solution.

Question 87  Write the first five square numbers.
Solution. First five square numbers are 1²,2², 3², 4² and 5², i.e. 1, 4, 9,16and 25.

Question 88  Write cubes of first three multiples of 3.
Solution. Since, the first three multiples of 3 are 3, 6 and 9.
Hence, the cubes of first three multiples of 3 are (3)³, (6)³ and (9)³, i.e. 27, 216 and 729.

Question 89  Show that 500 is not a perfect square.
Solution.

Question 90  Express 81 as the sum of first nine consecutive odd numbers.
Solution. 81= (9)² =1+3+ 5+ 7 + 9+ 11 + 13+ 15+ 17 = Sum of first nine consecutive odd numbers

Question 91 Using prime factorisation, find which of the following are perfect squares.
(a) 484                                     (b) 11250
(c) 841                                     (d) 729 .
Solution.

So, 484 is a perfect square.
(b) Prime factors of 11250 = 2 x (3 x 3) x (5 x 5) x (5 x 5)
As grouping, 2 has no pair.

So, 11250 is not a perfect square,
(c) Prime factors of 841 = (29 x 29)

As grouping, there is no unpaired factor left over. So, 841 is a perfect square.
(d) Prime factors of 729 = (3 x 3) x (3 x 3) x (3 x 3)
As grouping, there is no unpaired factor left over.

So, 729 is a perfect square.

Question 92  Using prime factorisatioji, find which of the following are perfect cubes,
(a) 128 (b) 343 (c) 729 (d) 1331
Solution.(a) We have, 128 = 2 x 2 x 2 x 2 x 2 x 2 x 2
Since, 2 remains after grouping in triplets.
So, 128 is not a perfect cube.
(b) We have, 343 = 7 x 7 x 7
Since, the prime factors appear in triplets.
So, 343 is a perfect cube.
(c) We have, 729 = 3 x 3 x 3 x 3 x 3 x3
Since, the prime factors appear in triplets.
So, 729 is a perfect cube.
(d) We have, 1331 =11x11x11
Since, the prime factors appear in triplets.
So, 1331 is a perfect cube.

Question 93 Using distributive law, find the squares of (a) 101 (b) 72
Sol. (a) We have, 101² = 101 x 101
= 101(100+ 1)= 10100+ 101 = 10201
(b) We have, 72² = 72 x 72 = 72 x (70 + 2)
= 5040+ 144= 5184

Question 94  Can a right angled triangle with sides 6cm, 10cm and 8cm be formed? Give reason.
Solution.

Question 95 Write the Pythagorean triplet whose one of the numbers is 4.
Solution.

Question 96  Using prime factorisation, find the square roots of (a) 11025 (b) 4761
Solution.

Question 97 Using prime factorisation, find the cube roots of
(a) 512
(b) 2197
Solution.

Question 98 Is 176 a perfect square? If not;- find the smallest number by which it should be multiplied to get a perfect square.
Solution.

Question 99 Is 9720 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube.

Solution.Prime factors of 9720 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x5
The prime factors 3 and 5 do not appear in group of triplets.
So, 9720 is not a perfect cube.
If we divide the number by 3 x 3 x 5, then the prime factorisation of the quotient will not contain 3 x 3 x 5 = 45.

Question 100 Write two Pythagorean triplets, each having one of the numbers as 5.
Sol.

Question 101  By what smallest number should 216 be divided, so that the quotient
is’ a perfect square? Also, find the square root of the quotient.
Solution.

Question 102 By what smallest number should 3600 be multiplied, so that the quotient is a perfect cube. Also, find the cube root of the quotient.
Solution. Prime factors of 3600 = 2x2x2x2x3x3x5x5
Grouping the factors into triplets of equal factors, we get

Question 103  Find the square root of the following by long division method.
(a) 1369 (b) 5625
Solution.

Question 104  Find the square root of the following by long division method. : (a) 27.04 (b) 1.44
Solution.

Question 105  What is the least number, that should be subtracted from 1385 to get a perfect square? Also, find the square root of the perfect square.
Solution.

Question 106  What is the least number that should be added to 6200 to make it a perfect square?
Solution.

Question 107  Find the least number of four digits that is a perfect square.
Solution.

Question 108  Find the greatest^umber of three digits that is a perfect square.
Solution.

Question 109  Find the least square, number, which is exactly divisible by 3, 4, 5, 6 and 8.
Solution.

Question 110 Find the length of the side of a square, if the length of its diagonal is 10 cm.
Solution.

Question 111  A decimal number is multiplied by itself. If the product is 51.84, then find the number.
Solution.

Question 112  Find the decimal fraction, which when multiplied by itself, gives 84.64.
Solution.

Question 113  A farmer wants to plough his square field of side 150m. How much area will he have to plough?
Solution.

Question 114  What will be the number of unit squares on each side of a square graph paper, if the total number of unit squares is 256?
Solution.

Question 115  If one side of a cube is 15m in Length, then find its volume.
Solution.

Question 116  The dimensions of a rectangular field are 80m and 18m. Find the length of its diagonal.
Solution.

Question 117 Find the area of a square field, if its perimeter is 96 m.
Solution.

Question 118 Find the length of each side of a cube, if its volume is 512 cm3.
Sol.

Question 119 Three numbers are in the ratio 1:2:3 and the sum of their cubes is 4500. Find the numbers.
Solution.

Question 120  How many square metres of carpet will be required for a square room of side 6.5m to be carpeted?
Solution.

Question 121 Find the side of a square, whose area is equal to the area of a rectangle with sides 6.4m and 2.5m.
Solution.

Question 122 Difference of two perfect cubes is” 189. If the cube root of the smaller of the two numbers is 3, then find the cube root of the larger number.
Solution.

Question 123  Find the number of plants in each row, if 1024 plants are arranged, so
that number of plants in a row is the same as the number of rows.
Solution.

Question 124  A hall has a capacity of 2704 seats. If the number of rows is equal to the number of seats in each row, then find the number of seats in each row.
Solution.

Question 125  A General wishes to draw up his 7500 soldiers in the form of a square. After arranging, he found out that some of them are left out. How many soldiers were left out?
Solution.

Question 126 8649 students were sitting in a lecture room in such a manner that there were as many students in the row as there were rows in the lecture room. How many students were there in each row of the lecture room?
Solution.

Question 127 Rahul walks 12m North from his house and turns West to walk 35m to reach his friend’s house. While returning, he walks diagonally from his friend’s house to reach back to his house. What distance did he walk, while returning?
Solution.

Question 128  A 5.5m long ladder is leaned against a wall. The ladder reaches the wall to a height of 4.4m. Find^the distance between the wall and the foot of the ladder.
Solution.

Question 129  A king wanted to reward his advisor, a wiseman of the kingdom. So, he asked the wiseman to name his own reward. The wiseman thanked the king, but said that he would ask only for some gold coins each day for a month. The coins were to be counted out in a pattern of one coin for the first day, 3 coins for the second day, 5 coins for the third day and so on for 30 days. Without making calculations, find how many coins will the advisor get in that month?
Solution.

Question 130  Find three numbers in the ratio 2 : 3 : 5, the sum of whose squares is 608.
Solution.

Question 131 Find the smallest square number divisible by each of the numbers 8, 9 and 10.
Solution.

Question 132

Solution.

Question 133  Find the square root of 324 by the method of repeated subtraction.
Solution.

Question 134 Three numbers are in the ratio 2 : 3 : 4. The sum of their cubes is 0.334125. Find the numbers.
Solution.

Question 135

Solution.

Question 136 

Solution.

Question137

Solution.

Question 138
A perfect square number has four digits, none of which is zero. The- digits from left to right have valfles, that are even, even, odd, even. Find the number.
Solution.
Suppose abed is a perfect square.
where, a = even number
b = even number
c = odd number
d = even number
Hence, 8836 is one of the number which satisfies the given condition.

Question 139  Put three different numbers in the circles, so that when you add the numbers at the end of each line, you always get a perfect square.

Solution.

Question 140 The perimeters of two squares are 40m and 96m, respectively. Find the perimeter of another square equal in area to the sum of the first two squares.
Solution.

Question 141  A three-digit perfect square is such that, if it is viewed upside down, the number seen is also a perfect square. What is the number?
[Hint The digits 1, 0 and 8 stay the same when viewed upside down, whereas 9 becomes 6 and 6 becomes 9]
Solution. Three-digit perfect squares are 196 and 961, which looks same when viewed upside down.

Question 142 13 and 31 is a strange pair of numbers, such that their squares 169 and 961 are also mirror of each other. Can yqu find two other such pairs?
Solution.

The post NCERT Exemplar Problems Class 8 Mathematics Square-Square Root and Cube-Cube Root appeared first on Learn CBSE.

Human Capital Formation in India NCERT Solutions for Class 11 Indian Economic Development

NCERT TEXTUAL QUESTIONS WITH ANSWERS

question 1.What are the two major sources of human capital in a country?
Answer.Two main sources of human capital are investment in education and health.

Question 2.What are the indicators of educational achievement in a country?
Answer.Educational attainment is measured by primary education, youth literacy and adult literacy.

Question 3.Why do we observe regional differences in educational attainment in India?
Answer.Regional differences in educational attainment in India is due to :

1.  inequality of income
2.  expenditure by the government in education facilities.

Question 4.Bring out the differences between human capital and human development.
Answer.Difference between Human Capital and Human Development

Question 5.How is human development a broader term as compared to human capital?
Answer.

1. Human capital is a narrow concept which treats human beings as a means to achieve an end which is higher productivity, failing which the investment is not considered to be productive.
2.  Human development is a broader concept which considers human beings as ends in themselves. Human welfare can be achieved through investments in education and health. It considers welfare—a right of every individual irrespective of their contribution to labour productivity. Every individual has right to be literate and lead a healthy life.

Question 6.What factors contribute to human capital formation?
Answer.Sources of Human Capital Formation :

1.  Expenditure on Education
2.  Training
3.  Expenditure on Health
4.  Migration
5.  Expenditure on Information.

Question 7.Mention two government organisations each that regulate the health and education sectors.
Answer.In India, the ministries of education at the Centre and State level, departments of education and
various organisations such as National Council of Educational Research and Training (NCERT),
University Grants Commission (UGC) and All India Council of Technical Education (AICTE) regulate the education sector. Similarly, the ministries of health at the Union and State level, departments of health and various organisations like Indian Council for Medical Research (ICMR) regulate the health sector.

Question 8. Education is considered an important input for the development of a nation. How?
or
Examine the role of education in the economic development of a nation.
Answer. Expenditure on education is an important source of capital formation. Education is an important source of human capital formation, because:

1.  It generates technical skills and creates a manpower which is suited for improving labour productivity. It, thus, results in sustained economic development.
2.  It tends to bring down birth rate which, in turn, brings decline in population growth rate. It makes more resources available per person.
3.  It results in social benefits since it spreads to others who may not be skilled. Thus, investment in education leads to higher returns in future.

Question 9. Discuss the following’as a sources of human capital formation
(a) Health infrastructure
(b) Expenditure on migration.
Answer.

1. Health Infrastructure. Health is another important source of human capital formation. Preventive medicine (vaccination), curative medicine (medical intervention during illness), social medicine (spread of health literacy) and provision of clean drinking water and good sanitation are the various forms of health expenditure. Health expenditure directly increases the supply of healthy labour force and is, thus, a source of human capital formation.
2. Migration. People sometimes migrate from one place to the other in search of better job. It includes
   migration of people from rural areas to urban areas in India and migration of technical personnel from India to qther countries of the world. Migration in both these cases involves cost of transport, higher cost of living in the migrated places and psychic costs of living in a strange socio-cultural set-up. The enhanced earnings in the new place outweigh the costs of migration. Expenditure on migration is also a source of capital formation.

Question 10. Establish the need for acquiring information relating to health and education expenditure for the effective utilisation of human resources.
Answer. People need to have information on the cost and benefit of investment in health and education. When people know the benefits of their investment in these two areas, they make more expenditure. The result is more human capital formation.

Question 11. How does investment in human capital contribute to growth?
Answer. Role of Human Capital Formation in Economic Growth:

1. Raises Production .
2.  Raises Efficiency and Productivity
3.  Brings Positive Changes in Outlook and Attitudes
4.  Improves Quality of Life
5.  Raises Life Expectancy
6. Raises Social Justice.

Question 12. ‘There is a downward trend in inequality world-wide with a rise in the average education levels.Comment.
Answer. This is true, because education makes everyone equal and they earn similar salaries. It reduces inequalities of income world wide.

Question 13. Explain how investment in education stimulates economic growth. (or)
Explain the role of education in the development of a country.
Answer. Education is an important source of human capital formation. Investment in education stimulates economic development in the following ways:

1.  Raises production. Knowledgeable and skilled workers can make better use of resources at their disposal. It will increase production in the economy. An educated and trained person can apply his knowledge and skill at farm, factory and office to increase production.
2.  Raises efficiency and productivity. Investment in education increases efficiency and productivity, and hence yields higher income to the people.
3.  Brings positive changes in outlook and attitudes. Knowledgeable and skilled people have modem outlook and attitudes, that they make rational choice in respect of places and jobs.
4.  Improves quality of life. Education improves quality of life as it provides better job, high income and improves health. It results in better standard of living.

Question 14. Bring out the need forjm-the-j ob-training for a person.
Answer. Technical training adds to the capacity of the people to produce more. Firms given on-the-job- training to enhance the productive skills of the workers so as to enable them to absorb new technologies and modem ideas. It can be given in two forms:

1.  The workers may be trained in the firm itself under the assistance of a senior and experienced worker.
2.  The workers may be sent off the firm campus for the training.

Question 15. Trace the relationship between human capital and economic growth.
Answer. Human capital formation raises the process of economic growth and economic growth raises the process of human capital formation. There is a cause and effect relationship between human capital and economic growth. It is shown in the figure.

Question 16. Discuss the need for promoting women’s education in India.
Answer. Women Education Council has been set up to provide technical education to the women. It has
set up many women polytechnics. It is essential to promote women’s education in India to:

1.  improve women’s economic independence and their social status.
2.  make a favourable impact on fertility rate and health care of women and children.

Question 17. Argue in favour of the need for different forms of government intervention in education and health sectors.
Answer. Government intervention in education and health sectors is necessary because of the following reasons:

1.  Education and health care services create both private as well as social benefits. Both private and public institutions are needed to provide these services and government must keep its control on them.
2.  Expenditure on education and health institutes are important for the growth of a nation. The private providers of education and health services need to be regulated by the government.

Question 18. What are the main problems of human capital formation in India?
Answer. Main problems of human capital formation in India are:

1. Rising Population. Rapidly rising population adversely affects the quality of human capital formation in developing countries. It reduces per capita availability of existing facilities. A large population requires huge investment in education and health. This diverts the scarce money to production of human capital at the cost of physical capital.
2. Long Term Process. The process of human development is a long term policy because skill formation takes time. The process which produces skilled manpower is thus slow.
3.  High Regional and Gender Inequality. Regional and gender inequality lowers the human development levels.
4. Brain Drain. Migration of highly skilled labour termed as “Brain Drain” adversely affects the economic development.
5.  Insufficient on-the-job-training in agriculture. Agriculture sector is neglected where the workers are not given on-the-job training to absorb emerging new technologies.
6.  High Poverty Levels. A large proportion of the population lives below poverty line and do not have access to basic health and educational facilities. A large section of society cannot afford to get higher education or expensive medical treatment for major disease.

Question 19. In your view, is it essential for the government to regulate the fee structure in education and health care institutions? If so, why?
Answer. Yes, government intervention is necessary in regulating the fee structure in education and health care institutions:

1. to maintain uniformity
2. to have accountability
3.  to help poorer people.

The post Human Capital Formation in India NCERT Solutions for Class 11 Indian Economic Development appeared first on Learn CBSE.

Employment-Growth, Informalisation and Related Issues NCERT Solutions for Class 11 Indian Economic Development

NCERT TEXTUAL QUESTIONS WITH ANSWERS

Question 1.Who is a worker?
Answer.A worker is an individual who is doing some productive employment to earn a living.

Question 2.Define worker-population ratio.
Answer.Workforce Participation Rate (or ratio)

Participation ratio is defined as the percentage of total population which is actually participating in productive activity. It is also called workers-population ratio. It indicates the employment situation of the country. A high ratio means that more proportion of population is actively contributing to the production of goods and services of a country.

Question 3.Are the following workers — a beggar, a thief, a smuggler, a gambler? Why?
Answer.No, they are not workers because they, are not doing any productive activity.

Question 4.Find the odd man out (i) owner of a saloon with more than 10 employees (ii) a cobbler
(iii) a cashier in Mother Dairy (iv) a tuition master (v) transport operator (vi) construction worker.
Answer.Owner of a saloon.

Question 5.The newly emerging jobs are found mostly in the sector (service/manufacturing).
Answer.Service.

Question 6.An establishment with four hired workers is known as (formal/informal) sector establishment.
Answer.Informal.

Question 7.Raj is going to school. When he is not in school, you will find him working in his farm. Can you consider him as a worker? Why?
Answer.Raj is disguisedly unemployed.

Question 8.Compared to urban women, mSre rural women are found working. Why?
Answer.Participation rate for women is higher in rural areas compared with urban areas. It is because in rural areas, poverty forces women to seek employment. Without education, women in rural areas find only less productive jobs and get low wages.
In urban areas, men are able to earn high incomes. So they discourage female members from taking up jobs.

Question 9.Meena is a housewife. Besides taking care of household chores, she works in the cloth shop which is owned and operated by her husband. Can she be considered as a worker? Why?
Answer.Meena is a self-employed worker. She is working in her husband’s cloth shop. She will not get salary.

Question 10.Find the odd man out (i) rickshaw puller who works under a rickshaw owner (ii) mason (iii) mechanic shop worker (iv) shoeshine boy.
Answer.Shoeshine boy.

Question 11.The following table shows distribution of workforce in India for the year 1972-73. Analyse it and give reasons for the nature of workforce distribution. You will notice that the data is pertaining to the situation in India 30 years ago.

Answer. In 1972-73, out of total workforce of 234 million, 195 million was in rural areas and 39 million in urban areas. It shows 83% workforce lived in rural areas. Gender differences were also observed. In rural areas, males accounted for 125 million workforce and women 70 million of workforce. In urban areas, 32 million males formed the workforce whereas women workforce was only 7 million. In the country only 77 million female workers were there as compared to 157 million male workers. In other words, 32% of female workers were there and 68% male workers were there in the country in 1972-73. The data shows:
(a) pre dominance of agriculture.
(b) more male workers both in urban and rural areas.
(c) less female workers in both rural and urban areas. Also, female workers were much lesser in urban areas.

Question 12. The following table shows the population and worker population ratio for India in 1999-2000. Can you estimate the workforce (urban and total) for India?

Answer. Estimated number of workers (in crores) for urban =\(\frac { 28.52 }{ 100 }\) x 33.7 = 9.61 crores
Total workforce = 30.12 + 9.61 = 39.73 crores

Question 13. Why are regular salaried employees more in urban areas than in rural areas?
Answer. In urban areas, a considerable section is able to study in various educational institutions. Urban people have a variety of employment opportunities. They are able to look for an appropriate job to suit their qualifications and skills.J3ut in rural areas, people cannot stay at home as they are economically poor.

Question 14. Why are less women found in regular salaried employment?
Answer. Female workers give preference to self-employment than to hired employment. It is because women, both in rural and urban areas, are less mobile and thus, prefer to engage themselves in self-employment.

Question 15. Analyse the recent trends in sectoral distribution of workforce in India.
Answer. l.The data in occupational structure is as follows (for the year 1999-2000):
(a) Industry wise the distribution is:
(i) 37.1% of workforce is engaged in primary sector.
(ii) 18.7% of workforce is engaged in secondary sector.
(iii) 44.2% of workforce is engaged in tertiary sector.
(b) Area wise the data is:
(i) In rural areas:
77% of workforce is in primary sector.
11% of workforce is in secondary sector.
12% of workforce is in tertiary sector.
(ii) In urban areas:
10% of workforce is in primary sector.
31% of workforce is in secondary sector.
59% of workforce is in tertiary sector.
2. The data reveals that:
(a) Economic backwardness in the country as 60% of workforce is engaged in agricultural activities. A large proportion of population depend on agriculture for their livelihood.
(b) In urban area, tertiary sector account for 59% of workforce. It shows development and growth in the tertiary sector and the fact that this sector is able to generate sustainable employment and provide livelihood to 59% of the workforce.
3. It can be concluded that in the urban areas, tertiary sector is the main source of livelihood for majority of workforce.

Question 16. Compared to the 1970s, ’there has hardly been any change in the distribution of workforce across various industries. Comment.
Answer. It is true that no much change is observed in the distribution of workforce across various industries. It is because the plans did not emphasise the need for development of:
(a) non-agricultural rural employment industries.
(b) small scale, village and cottage industries.

Question 17. Do you think that in the last 50 years, employment generated in the country is commensurate with the growth of GDP in India? How?
Answer. Jobless growth is defined as a situation in which there is an overall acceleration in the growth rate of GDP in the economy which is not accompanied by a commensurate expansion in employment opportunities.This means that in an economy, without generating additional employment we have been able to produce more goods and services. Since the starting of economic reforms in 1991, our economy is experiencing a gap between GDP growth rate and employment growth rate that is, jobless growth.

Question 18. Is it necessary to generate employment in the formal sector rather than in the informal sector? Why?
Answer. With economic reforms in 1991, there has been significant rise in informalisation of workers. Since informal workers face uncertainties of making of living, it is surprising that such a high percentage of total workforce prefer to be employed in the informal sector. All necessary steps should be taken to generate employment in the formal sector, which is only 7% at present.

Question 19. Victor is able to get work only for two hours in a day. Rest of the day, he is looking for work. Is hie unemployed? Why? What kind of jobs could persons like Victor be doing?
Answer. No. he is employed because Victor has work for 2 hours daily for which he gets paid. He is a casual worker.

Question 20. You are residing in a village. If you are asked to advice the village panchayat, what kinds of activities would you suggest for the improvement of your village which would also generate employment.
Answer. Digging of wells, fencing, building roads and houses, etc.

Question 21. Who is a casual wage labourer?
Answer. Those people who are not hired by their employers on a regular/permanent basis and do not get social security benefits are said to be casual workers. Example: construction workers.

Question 22. How will you know whether a worker is working in the informal sector?
Answer. Informal Sector:
(a) It is an unorganised sector of an economy which includes all those private sector enterprises which employ less than 10 workers. Example: agriculture labourers, farmers, owners of small enterprises, etc.
(b) The workers of this sector are called informal workers.
(c) The workers are not entitled to social security benefits.
(d) The workers cannot form trade union and are not protected by labour laws.

The post Employment-Growth, Informalisation and Related Issues NCERT Solutions for Class 11 Indian Economic Development appeared first on Learn CBSE.

Infrastructure NCERT Solutions for Class 11 Indian Economic Development

NCERT TEXTUAL QUESTIONS WITH ANSWERS

Question 1. Explain the term ‘infrastructure’.
Answer. Infrastructure refers to the basic supporting structure which is built to provide different kinds of services in an economy. Infrastructural installations do not directly produce goods but help in promoting production activities in an economy. Examples of infrastructure are: transport, communication, banking, power etc.

Question 2. Explain the two categories into which infrastructure is divided. How are both interdependent?
Answer. There are two types of infrastructure: (a) economic infrastructure, (b) social infrastructure.
Economic infrastructure directly supports the economic system from inside. Examples are energy, transport and communication. Social infrastructure indirectly supports the economic system from outside. Examples are health, education and housing.
Economic and social infrastructure are complementary to each other. Economic infrastructure improves the qualityof economic resources and raises the production, but it cannot be possible until population is literate to use them efficiently. Thus, both of them are needed for the growth and development of the country.

Question 3. How do infrastructure facilities boost production?
Answer. The prosperity of a country depends directly upon the development of agricultural and industrial production. Agricultural production requires power, credit, transport facilities, etc.; the deficiency of which leads to fall in productivity. Industrial production requires machinery and equipment, energy, banking and insurance facilities, marketing facilities, transport services which include railways, roads and shipping and communication facilities etc. All these facilities help in raising agricultural and industrial productivity.

Question 4. Infrastructure contributes to the economic development of a country. Do you agree? Explain.
Answer. Infrastructure contributes to the economic development of a country and it is an important determinant of its growth and development. It raises productivity, induces investment in different areas of economic activity, raises size of the market, facilitates outsourcing and employment. Thus, it is an essential support system for the economic development of the country.

Question 5. What is the state of rural infrastructure in India?
Answer. A majority of people live in rural areas. The state of rural infrastructure in India is as follows:

1.  Rural women are still using bio-fuels such as crop residues, dung and fuel wood to meet their energy requirement.
2.  They walk long distances to fetch fuel, water and other basic needs.
3.  The census 2001 shows that in rural India only 56 per cent households have an electricity connection and 43 per cent still use kerosene. About 90 per cent of the rural households use bio-fuels for cooking.
4.  Tap water availability is limited to only 24 per cent of rural households. About 76 per cent of the population drinks water from open sources such as wells, tanks, ponds, lakes, rivers, canals, etc.
5.  Another study conducted by the National Sample Survey Organisation noted that by 1996, access to improved sanitation in rural areas was only 6 per cent.

Question 6. What is the significance of ‘energy’? Differentiate between commercial and non-commercial sources of energy.
Answer. Energy is a critical aspect of development process of a nation. It is essential for industries, agriculture and related areas like transportation of finished goods. It is also used for domestic purposes like cooking, lighting, heating, etc.
Difference between Commercial and Non-commercial Sources of Energy

Question 7. What are the three basic sources of generating power?
Answer. Sources of generating power are:

1.  water—it gives hydroelectricity.
2. oil, gas, coal—they give thermal electricity.
3.  radioactive elements like uranium, plutonium—they give atomic power or nuclear power.

Question 8. What do you mean by transmission and distribution losses? How can they be reduced?
Answer. Transmission and Distribution (T&D) losses refer to theft of power which has not been controlled.
Nation’s average loss is 23%.
T&D losses can be reduced by having:

1.  Appropriate size of conductors
2. Proper load management
3.  Meter supply
4.  Privatisation of distribution work
5.  Introduction of energy audits. Some steps have already been initiated in this direction.

Question 9. What are the various non-commercial sources of energy?
Answer. Vegetable wastes, firewood and dried dung.

Question 10. Justify that energy crisis can be overcome with the use of renewable sources of energy.
Answer. There is energy crises in the country. The demand for all commercial fuels is more than its supply.
Government is encouraging the use of hydel and wind energy.
Bio-gas generation programmes have been boosted up. For a tropical country like India, where sun is an abundant source, solar energy should be given highest priority.

Question 11. How has the consumption pattern of energy changed over the years?
Answer. Pattern of energy consumption in India is as follows:

1. In India, different sources of energy are converted into a common unit ‘million tonne of oil equivalent’ (MTOE).
2. At present, commercial energy consumption is 65 per cent of total energy consumed in India.
3.  Goal has the largest share of 55 per cent, followed by oil at 31 per cent, natural gas at 11 per cent and hydro energy at 3 per cent.
4.  Non-commercial energy sources account for over 30 per cent of the total energy consumption.
5.  There is import dependence on crude and petroleum products, which is likely to grow to more than 100 per cent in the near future.
6.  Atomic energy is an important source of electric power. At present nuclear/atomic energy accounts for only 2.4 per cent of total primary energy consumption.

Question 12. How are the rates of consumption of energy and economic growth connected?
Answer. Energy is a critical aspect of development process of a nation. It is essential for industries, agriculture and related areas like transportation of finished goods. It is also used for domestic purposes like cooking, lighting, heating, etc. With economic growth, consumption of energy will rise.

Question 13. What problems are being faced by the power sector in India?
Answer. Emerging Challenges in the Power Sector:

1.  Insufficient Installed Capacity
2.  Underutilisation of Capacity
3.  Losses Incurred by SEBs
4.  Uncertain Role of Private Players
5.  Public Unrest
6.  Shortage of Raw Materials
7.  Unable to Cover up the Transmission and Distribution (T&D) Losses
8.  Operational Inefficiency
9. Incomplete Electrification
10.  Need to Conserve Energy.

Question 14. Discuss the reforms which have been initiated recently to meet the energy crisis in India.
Answer. The reforms to meet energy crisis in India:

1.  Improved Plant Load Factor. The Ministry of Power has launched the ‘Partnership in Excellence’ programme. In this 26 thermal stations (with PLF less than 60%) have Been taken up for improving the efficiency.
2.  Encourage Private Sector Participation. In order to overcome the problems of power sector, the government announced a policy in 1991 which allowed private sector participation in power generation and distribution schemes. It is important to resolve the problems arid difficulties and frame policies which can ensure effective participation of private sector in this sector.
3.  Promote the Use of CFLs to Conserve Energy. A new and advanced lighting technology called the Compact Fluorescent Lamp (CFL) is a more efficient alternative to domestic energy consumption. According to the Bureau of Energy Efficiency (BEE), the Compact Fluorescent Lamps (CFLs) consume 80 per cent less power as compared to ordinary bulbs.

Question 15. What are the main characteristics of health of the people of our country?
Answer. The main characteristics of health of people of our country:

1.  Decline in death rate to 8 per thousand in 2001.
2.  Reduction in infant mortality rate to 7 per thousand in 2001.
3.  Rise in life expectancy to 64 years in 2001.
4. Control over deadly diseases like cholera, smallpox, malaria, polio and leprosy.
5.  Fall in child mortality rate to 23 per thousand in 2001.

Question 16. What is a ‘global burden of disease’?
Answer. Global Burden of Diseases (GBD) is an indicator used by experts to gauge the number of people dying prematurely, due to particular diseases as well as the number of years spent by them in a state of disability owing to the disease.

Question 17. Discuss the main drawbacks of our health care system.
Answer. Emerging Challenges in the Health:

1. High GBD
2.  Poor State of Primary Health Centres
3. Regional Bias—Urban-Rural Divide
4.  Income Bias—Poor-Rich Divide
5. Gender Bias—Poor Health of Women.
6.  Communicable diseases
7.  Poor Provision
8.  Privatisation

Question 18. How has women’s health become a matter of great concern?
Answer. Gender Bias—Poor Health of Women:

1.  There is growing incidence of female foeticide in the country. Close to 3,00,000 girls under the age of 15 are not only married but have already borne children at least once.
2.  More than 50 per cent of married women between the age group of 15 and 49 suffer from anaemia caused by iron deficiency. It has contributed to 19 per cent of maternal deaths.

Question 19. Describe the meaning of public health. Discuss the major public health measures undertaken by the state in recent years to control diseases.
Answer. Public health refers to the health status of all the people of the country.
Some measures undertaken by the state in recent years to control diseases are:

1.  Success in the long-term battle against diseases depends on education and efficient health infrastructure. It is, therefore, critical to create awareness on health and hygiene systems.
2.  The role of telecom and IT sectors cannot be neglected in this process.
3.  The effectiveness of health care programmes also rests on primary centres. Efforts should be made to make PHCs more efficient.
4. Encouragement should be given to private-public partnership. They can effectively ensure reliability, quality and affordability of both drugs and medical care.

Question 20. List out the six systems of Indian medicine.
Answer. AYUSH means:
A : Ayurveda
Y : Yoga and Naturopathy
U : Unani
S : Siddha H : Homoeopathy.

Question 21. How can we increase the effectiveness of health care programmes?
Answer. Health is a vital public good and a basic human right. All citizens can get better health facilities if public health services are decentralised. Some measures that should be taken are:

1.  Success in the long-term battle against diseases depends on education and efficient health infra-structure. It is, therefore, critical to create awareness on health and hygiene systems.
2.  The role of telecom and IT sectors cannot be neglected in this process.
3.  The effectiveness of health care programmes also rests on primary centres. Efforts should be tnade to make PHCs more efficient.
4.  Encouragement should be given to private-public partnership. They can effectively ensure
   reliability, quality and affordability of both drugs and medical care. .

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Environment Sustainable Development NCERT Solutions for Class 11 Indian Economic Development

NCERT TEXTUAL QUESTIONS WITH ANSWERS

Question 1. What is meant by environment?
Answer. Environment is defined as the total planetary inheritance and the totality of all resources. It includes all the biotic and abiotic factors that influence each other. Biotic elements are all living elements — the birds, ainimals and plants, forests, fisheries, etc. Abiotic elements are like air, water, land, rocks, sunlight, etc.

Question 2. What happens when the rate of resource extraction exceeds that of their regeneration?
Answer. Environment includes sun, soil, water and air which are essential ingredients for the sustenance of human life. The carrying capacity of the environment implies that the resource extraction is not above the rate of regeneration of the resources and the waste generated are within the assimilating capacity of the environment. Carrying capacity of the environment helps to sustain life. Absence of carryingjcapacity of environment means absence of life.

Question 3. Classify the following into renewable and non-renewable resources (i) trees (ii) fish
(iii) petroleum (iv) coal (v) iron-ore (vi) water.
Answer. Trees and fish are renewable resources.
Petroleum, coal, iron-ore and water are non-renewable resources.

Question 4.Two major environmental issues facing the world today are and .
Answer.Global warming and Ozone depletion.

Question 5.How do the following factors contribute to the environmental crisis in India? What problem do they pose for the government?

1.  Rising population
2.  Air pollution
3.  Water contamination
4. Affluent consumption standards.
5.  Illiteracy
6.  Industrialisation
7.  Urbanisation
8.  Reduction of forest coverage
9.  Poaching
10.  Global warming.

Answer.

1.  The high rate of growth of population adversely affects the environment. It certainly leads to soil and water pollution.
2. India is one of the ten most industrialised nations of the world. It has led to unplanned
   urbanisation, pollution and the risk of accidents. The CPCB (Central Pollution Control Board) has identified 17 categories of industries which are significant pollutors.
3.  Many states in India are on the edge of famine. Whatever water is available, it is polluted or contaminated. It causes diseases like diarrhoea and hepatitis.
4.  With affluent consumption standards, people Use more air conditioners. CFCs are used as cooling agents in air condition which leads to ozone depletion.
5.  Illiteracy and ignorance about the use of non-renewable resources, alternative energy sources, lead to environmental crisis.
6.  With rise in national income or economic activity, there is rise in industrialisation and urbanisation. This raises pollution of air, water and noise. There are accidents, shortage of water, housing problems, etc. In other words, with rise in national income there is ecological degradation which reduces welfare of the people.
7.  Whenever there is large migration of population from rural to urban areas, it leads to fast growth of slum areas. There is excess of load on the existing infrastructural facilities. It causes environmental degradation and ill health.
8.  The per capita forestland in the country is only 0.08 hectare. There is an excess felling of about 15 million cubic metre forests over the permissible limit. Indiscriminate felling of trees has led to destruction of forest cover.
   Once forests haye been cut down, essential nutrients are washed out of the soil all-together. This leads to soil erosion. It leads to disastrous flooding since there is no soil to soak up the rain.
9.  Poaching leads to extinction of wildlife.
   The long-term results of global warming are:
   (a) Melting of polar ice caps with a resulting rise in the sea level and coastal flooding.
   (b) Disruption of drinking water supplies as snow melts.
   (c) Extinction of species.
   (d) Frequent tropical storms and tropical diseases.

Question 6. What are the functions of the environment?
Answer. The environment performs^four vital functions:

1. Environment Supplies Resources. Resources include both renewable and non-renewable re¬sources. Renewable resources are those which can be used without the possibility of the resource becoming depleted or exhausted. In other words, a continuous supply of the resource remains available. Examples of renewable resources are trees in the forest and fish in the ocean. Non-renew¬able resources are those which get exhausted with extraction and use. Example, fossil fuels.
2.  Environment Sustains Life. Environment includes sun, soil, water and air which are essential ingredients for the sustenance of human life. The carrying capacity of the environment implies that the resource extraction is not above the rate of regeneration of the resources and the waste generated are within the assimilating capacity of the environment. Carrying capacity of the environment helps to sustain life. Absence of carrying capacity of environments means absence of life.
3.  Environment Assimilates Waste. Production and consumption activities generate waste. This occur mostly in the form of garbage. Environment absorbs garbage.
4.  Environment Enhances Quality of Life. Environment includes oceans, mountains, deserts, etc. Man enjoys these surroundings, adding to the quality of life.

Question 7. Identify six factors contributing to land degradation in India.
Answer. Some of the factors responsible for land degradation are:

1. Loss of vegetation occuring due to deforestation
2.  Unsustainable fuel wood and fodder extraction .
3.  Shifting cultivation
4. Encroachment into forest lands
5. Forest fires and over grazing
6. Non-adoption of adequate soil conservation measures.

Question 8. Explain how the opportunity costs of negative environmental impact are high.
Answer. Opportunity cost is the cost of alternative opportunity given up. The country has to pay huge amount for damages done to human health. The health cost due to degraded environmental quality have resulted in diseases like asthma, cholera, etc. Huge expenditure is incurred in treat¬ing the diseases.

Question 9. Outline the steps involved in attaining sustainable development in India.
Answer. Steps and Strategies to Achieve Sustainable Development in India:

1.  Use of Non-Conventional Sources of Energy
2.  LPG, Gobar Gas in Rural Areas
3.  CNG in Urban Areas
4.  Wind Power
5. Solar Power through Photovoltaic Cells
6. Mini-Hydel Plants
7.  Traditional Knowledge and Practices
8.  Biocomposting
9.  Biopest Control.

Question 10. India has abundant natural r&ources—substantiate the statement.
Answer. India has rich quality of natural resources in plenty. It is clear from the following points:

1.  India has rich quality of soil, hundreds of rivers and tributaries, lush green forests, abundant mineral deposits under the land surface, vast stretch of the Indian Ocean, mountain ranges, etc.
2.  The black soil of the Deccan Plateau is particularly suitable for cultivation of cotton. It has lead to concentration of textile industries in this region.
3.  The Indo-Gangetic plains — spread from the Arabian Sea to the Bay of Bengal — are one of the most fertile, intensively cultivated and densely populated regions in the world.
4.  India’s forests provide green cover for a majority of its population and natural cover for its
   wildlife.
5.  Large deposits of iron-ore, coal and natural gas are found in the country. India alone accounts for nearly 20 per cent of the world’s total iron-ore reserves.
6. Bauxite, copper, chromate, diamonds, gold, lead, lignite, manganese, zinc, uranium, etc. are also available in different parts of the country.

Question 11. Is environmental crisis a recent phenomenon? If so, why?
Answer. Yes, because India is suffering from population explosion. .

1.  India has approximately 20 per cent of livestock population on a mere 2.5 per cent of the world’s geographical area. The high density of population and livestock and the competing
   uses of land for forestry, agriculture, pastures, human settlements and industries exert an enormous pressure on the country’s finite land resources.
2.  The per capita forestland in the country is only 0.08 hectare. There is an excess felling of about 15 million cubic metre forests over the permissible limit. Indiscriminate felling of trees has led to destruction of forest cover.

Question 12. Give two instances of:
(a) Overuse of environmental resources
(b) Misuse of environmental resources.
Answer.

1. There is massive overuse and misuse of environmental resources. Examples of overuse of environmental resources are deforestation and land degradation.
2.  Example of misuse of environmental resources are ozone depletion and global warming.

Question 13. (a) State any four pressing environmental concerns of India.
(b) Correction for environmental damages involves opportunity costs — explain.
Answer. (a) Pressing environmental concerns of India:

1.  Global Warming. Global warming is a gradual increase in the average temperature of the earth’s lower atmosphere as a result of the increase in greenhouse gases due to industrialisation in recent times.
2.  Ozone Depletion. The depletion of ozone layer has been caused by high levels of chlorine and bromine compounds in the stratosphere. It causes skin cancer, and lowers the production of acquatic organisms.
3.  Environmental Crisis. The rising population of the developing countries and the affluent • , consumption and production standards of the developed world have put a great stress on the environment in terms of its functions of supplying resources and assimilating waste.
4.  Massive Overuse and Misuse of Environmental Resources. There is massive overuse and misuse of environmental resources which results in deforestation, land degradation, ozone depletion and global warming. .

(b) The correction of environmental damages involve huge opportunity cost. It is the cost of alternative opportunity given up. The country has to pay huge amount for damages done to human health. The helath cost due to degraded environmental quality have resulted in diseases like asthma, cholera, etc. Huge expenditure is incurred on treating the diseases.

Question 14. Explain the supply-demand reversal of environmental resources.
Answer. Supply Demand Reversal of Environmental Resources: –
The demand for resources for both production and consumption has gone beyond the rate of regeneration of the resources increasing the pressure on the absorptive capacity of the environment. This reversal of the supply-demand relationship with demand for resources exceeding the supply has led to degeneration of the environment.

Question 15. Account for the current environmental crisis.
Answer.

1. Land Degradation
2.  Biodiversity Loss
3.  Air Pollution
4.  Management of Fresh Water and Solid Waste.

Question 16. (a) Highlight any two serious adverse environmental consequences of development in India.
(b) India’s environmental problems pose a dichotomy — they are poverty induced and, at the same time, due to affluence in living standards—is this true?
Answer. (a)

1.  Biodiversity Loss
   (i) India has approximately 20 per cent of livestock population on a mere 2.5 per cent of the world’s geographical area. The high density of population and livestock and the competing uses of land for forestry, agriculture, pastures, human settlements and industries exert an enormous pressure on the country’s finite land resources.
   (ii) The per capita forestland in the country is only 0.08 hectare. There is an excess felling of about 15 million cubic metre forests over the permissible limit. Indiscriminate felling of trees has led to destruction of forest cover.
2.  Air Pollution
   (i) In India, air pollution is widespread in urban areas where vehicles are the major contributors. Vehicular emissions are of particular concern since these are ground level sources and, thus, have the maximum impact on the general population. The number of motor vehicles has increased from about 3 lakh in 1951 to 67 crores in 2003.
   (ii) India is one of the ten most industrialised nations of the world. It has led to unplanned urbanisation, pollution and the risk of accidents.

(b) Dichotomy of the Threat to India’s Environment
The developmental activities in India have resulted in pressure on its finite natural resources, besides .creating impacts on human health and well-being. The threat to India’s environment poses a dichotomy—threat of poverty-induced environmental degradation and, at the same time, threat of pollution from affluence and a rapidly growing industrial sector. Air pollution, water contamination, soil erosion, deforestation and wildlife extinction are some of the most pressing environmental concerns of India.

Question 17. What is sustainable development?
Answer. Sustainable Development implies meeting the basic needs of everyone and extending to all the opportunity to satisfy their aspirations for better life, without compromising on the needs of future.

Question 18. Keeping in view your locality, describe any four strategies of sustainable development.
Answer. Four strategies of sustainable development in my locality can be:

1. Solar energy should be put up.
2.  People should use less air conditioners.
3.  People should use herbal cosmetics.
4.  People should not use polythene bags, instead they must use bags made of paper.

Question 19. Explain the relevance of intergenerational equity in the definition of sustainable development.
Answer. The Brundtland Commission emphasises on protecting the future generations. This is in line with the argument of the environmentalists who emphasise that we have a moral obligation to hand over the planet earth in good order to the future generations, i.e., the present generation should give better environment to the future generations, no less than what we have inherited.
According to the United Nations Conference on Environment and Development (UNCED) sustained development is, “Development that meets the needs of the present generation without compromising the ability of the future generation to meet their own needs.”

The post Environment Sustainable Development NCERT Solutions for Class 11 Indian Economic Development appeared first on Learn CBSE.

Comparative Development Experience of India with its Neighbours NCERT Solutions for Class 11 Indian Economic Development

NCERT TEXTUAL QUESTIONS WITH ANSWERS

Question 1. Mention some examples of regional and economic groupings.
Answer. Every country aims to strengthen its own domestic territory. The nations are forming regional and global economic groupings such as:

1. SAARC. It has 8 countries of South Asia.
2.  EU has 25 independent states based on European Communities.
3.  ASEAN. It has 5 countries of South East Asia.
4.  G-8 (Group of Eight). It has 8 countries.
5.  G-20 (Group of Twenty). It consists of 19 world’s largest economies.

Question 2. What are the various means by which countries are trying to strengthen their own domestic economies?
Answer. Countries are trying to strengthen their own domestic economies by:

1.  forming regional apd global economic groupings like SAARC, EU, ASEAN, G-8, G-20, etc.
2.  By having economic reforms.

Question 3. What similar development strategies have India and Pakistan followed for their respective developmental paths?
Answer. Similar developmental strategies of India and Pakistan are:

1.  India has the largest democracy of the world. Pakistan has authoritarian militarist political power structure.
2.  Both India and Pakistan followed a mixed economy approach. Both countries created a large public sector and planned to raise public expenditure on social development.

Question 4. Explain the Great Leap Forward campaign of China as initiated in 1958.
Answer. Communist China or the People’s Republic of China, as it is formally known, came into being in 1949. There is only one party, i.e., the Communist Party of China that holds the power there. All the sectors of economy including various enterprises and all land owned by individuals was brought under governmental control. A programme called ‘The Great Leap Forward’ was launched in 1958. Its aim was to industrialise the country on a large scale and in as short a time as possible. For this, people were eyeji encouraged to set up industries in their backyards. In villages, village Communes or cooperatives were set up. Communes means collective cultivation of land. Around 26000 communes covered almost all the farm population in 1958.
The Great Leap Forward programme faced many problems. These were:

1.  In the earlier phase, a severe drought occurred in China and it killed some 3 crore people.
2.  Soviet Russia was a comrade to communist China, but they had border dispute. As a result, Russia withdrew its professionals who had been helping China in its industrialisation bid.

Question 5. China’s rapid industrial growth can be traced back to its reforms in 1978. Do you agree? Elucidate.
Answer. Starting 1978, several reforms were introduced in phases in China. First, agriculture, foreign trade and investment sectors were taken up. Commune lands were divided into small plots. These were allotted to individual households for cultivation.
The reforms were expanded to industrial sector. Private firms were allowed to set up manufacturing units. Also, local collectives or cooperatives could produce goods. This meant competition between the newly sanctioned private sector and the old state-owned enterprises.
This kind of reform in China brought in the necessity of dual pricing. This meant the farmers and industrial units were to buy and sell fixed quantities of raw material and products on the basis of prices fixed by the government. As production increased, the material transacted through the open market also rose in quantity. Special Economic Zones (SEZs) were set up in China to attract foreign investors.

Question 6. Describe the path of developmental initiatives taken by Pakistan for its economic development.
Answer. The developmental initiatives taken by Pakistan were:

1.  In the late 1950s and 1960s, Pakistan introduced a variety of regulated policy framework (for import substitution industrialisation). The policy combined tariff protection for manufacturing of consumer goods together with direct import controls on competing imports.
2.  The introduction of Green Revolutioned led to mechanisation of agriculture. It finally led to a rise in the production of foodgrains. This changed the agrarian structure dramatically.
3.  In the 1970s, nationalisation of capital good industries took place.
4. In 1988, structural reforms were introduced. The thrust areas were denationalisation and en¬couragement to private sector.
5.  Pakistan received financial support from western nations and remittances from emigrants to the Middle East. It helped in raising economic growth of the country.

Question 7. What is the important implication of ‘one child norm’ in China?
Answer. One-child norm introduced in China in the late 1970s is the major reason for low population growth. It is stated that this measure led to a decline in the sex ratio, that is, the proportion of females per 1000 males.

Question 8. Mention the salient demographic indicators of China, Pakistan and India.
Answer. We shall compare some demographic indicators of India, China and Pakistan.

1. The population of Pakistan is very small and accounts for roughly about one-tenth of China or India.
2.  Though China is the largest nation geographically among the three, its density is the lowest.
3.  The population growth is highest in Pakistan followed by India and China. One-child norm introduced in China in the late 1970s is the major reason for low population growth. They also state that this measure led to a decline in the sex ratio, that is, the proportion of females per 1000 males.
4.  The sex ratio is low and biased against females in all the three countries. There is strong son- preference prevailing in 11 these countries.
5.  The fertility rate is low in China and very high in Pakistan.
6. Urbanisation is high in both Pakistan and China with India having 28 per cent of its people living in urban areas.

Question 9. Compare and contrast India and China’s sectoral contribution towards GDP. What does it in¬dicate?
Answer. Sectoral Distribution of Output and Employment:

1.  Agriculture Sector. China has more proportion of urban people than India. In China in the year 2009, with 54 per cent of its workforce engaged in agriculture, its contribution to GDP is 10 per cent. In India’s contribution of agriculture to GDP is at 17 per cent.
2.  Industry and Service Sectors. In both India and China, the industry and service sectors have less proportion of workforce but contribute more in terms of output. In China, manufacturing contributes the highest to GDP at 46 per cent whereas in India it is the service sector which contributes the highest. Thus, China’s growth is mainly contributed by the manufacturing sector and India’s growth by service sector.

Question 10. Mention the various indicators of human development.
Answer. Parameters of human development are:

1.  HDI— (a) Value—higher the better.
   (b) Rank—lower the better.
2.  Life expectancy—higher the better.
3. Adult literacy rate—higher the better.
4.  GDP per capita (PPP US $)—higher the better –
5.  Percentage of population below poverty line (on $1 a day)—lower the better.
6. Infant mortality rate (per 1000 live births)—lower the better.
7.  Maternal mortality rate (per 100,000 live births)—lower the better.
8.  Percentage of population having access to improved sanitation—higher the better.
9.  Percentage of population having access to improved water source—higher the better.
10.  Percentage of population which is undernourished (% of total) – lower the better.

Question 11. Define the liberty indicator. Give some examples of liberty indicators.
Answer. Liberty indicator has actually been added as a measure of ‘the extent of democratic participation
in social and political decision-making’ but it has not been given any extra weight. Some of the
examples of liberty indicators are : literacy rate, women participation in politics, etc.

Question 12. Evaluate the various factors that led to the rapid growth in economic development in China.
Answer. Reforms were initiated jn China in 1978. China did not have any compulsion to introduce reforms.
1. Pre-Reform Period : Failures
(a) There was slow pace of growth and lack of modernisation in the Chinese economy under the Maoist rule.
(b) It was felt that Maoist vision of economic development which was based on decentralisation, self-sufficiency and shunning of foreign technology, goods and capital, had failed.
(c) Despite extensive land reforms, collectivisation, the Great Leap Forward and other initiatives, the per capita grain output in 1978 was the same as it was in the mid-1950s.
Pre-Reform Period: Success
(a) There was existence of infrastructure in the areas of education and health.
(b) There were land reform.
(c) There was decentralised planning and existence of small enterprises.
(d) There was extension of basic health services in rural areas.
(e) Through the commune system, there was more equitable distribution of foodgrains.
2. Post-Reform Period (after 1978): Success
(a) In agriculture, by handing over plots of land to individuals for cultivation, it brought prosperity to a vast number of poor people.
(b) It created conditions for the subsequent phenomenal growth in rural industries and built up a strong support base for more reforms.
(c) More reforms included the gradual liberalisation of prices, fiscal decentralisation, increased autonomy for state owned enterprises (SOEs), the introduction of a diversified banking system, the development of stock markets, the rapid growth of the non-state sector, and the opening to foreign trade and investment.
(d) The restructuring of the economy and resulting efficiency gains have contributed to a more than ten-fold increase in GDP since 1978. Measured on a Purchasing Power Parity (PPP) basis, China in 2005 stood as the second largest economy in the world after the US.
(e) China’s economic growth as measured in terms of GDP on an average is 10.9% per year. In economic size, China is surpassed today only by the US, Japan, Germany and France.
(f) If its present growth trend continues, China is likely to be the world’s largest economic power by any measure by the year 2025.
Comparative Development Experience of India with its Neighbours 11 .IS
(g) China had success when it enforced one-child norm in 1979. The low population growth of China can be attributed to this one factor.
Thus, China’s structural reforms introduced in 1978 in a phased manner offer various lessons from its success story.

Question 13. Group the following features pertaining to the economies of India, China and Pakistan under three heads.

1. One-child norm
2. Low fertility rate
3. High degree of urbanisation
4. Mixed economy
5. Very high fertility rate
6. Large population
7. High density of population
8. Growth due to inanufacturing sector
9. Growth due to service sector

Answer.

1. China
2. China
3.  Pakistan and China
4.  India and Pakistan
5. Pakistan
6.  India and China
7.  India
8.  China
9.  India.

Question 14. Give reasons for the slow growth and re-emergence of poverty in Pakistan.
Answer. Reforms were initiated in Pakistan in 1988.
1. Pre-Reform Period : Failure
(a) The proportion of poor in 1960s was more than 40 per cent.
(b) The economy started to stagnate, suffering from the drop in remittances from the Middle East.
(c) A growth rate of over 5% in the 1980s could not be sustained and the budget deficit increased steadily.
(d) At times foreign exchange reserves were as low as 2 weeks of imports.
2. Post-Reform Period (after 1988): Failure
The reform process led to worsening of all the economic indicators.
(a) The growth rate of GDP and its sectoral constituents have fallen in the 1990s.
(b) The proportion of poor declined to 25 per cent in 1980s and started rising again in 1990s. The reasons for the slow-down of growth and re-emergence of poverty in Pakistan’s economy are:
(i) Agricultural growth and food supply situation were based not on an institutionalised process of technical change but on good harvest. When there was a good harvest, the economy was in a good condition; when it was not, the economic indicators showed stagnation or negative trends.
(ii) Fall in foreign exchange earnings coming from remittances from Pakistani workers in the Middle East and the exports of highly volatile agricultural products.
(iii) There was also growing dependence on foreign loans on the one hand and increasing difficulty in paying back the loans on the other.

Question 15. Compare and contrast the development of India, China and Pakistan with respect to some
salient human development indicators.
Answer. It is clear that:

1. China is moving ahead of India .and Pakistan. This is true for many indicators—income indicator such as GDP per capita, or proportion of population below poverty line or health indicators such as mortality rates, access to sanitation, literacy, life expectancy or malnourishment.
2. Pakistan is ahead of India in reducing proportion of people below the poverty line and also its performance in education, sanitation and access to water is better than that of India. Both China and Pakistan are in similar position with respect to the proportion of people below the international poverty rate of $1 a day, whereas the proportion is almost two times higher for India.
3. In China, for one lakh births, only 38 women die whereas in India it is 230 and in Pakistan it is 260.
4. India and Pakistan are ahead of China in providing improved water sources.

Question 16. Comment on the growth rate trends witnessed in China and India in the last two decades.
Answer. Growth of Gross Domestic Product (%), 1980-2009 In 1980s, China had remarkable growth rate of 10.3% when India was finding it difficult to maintain a growth rate of even 5%. After two decades, there was a marginal improvement in India’s and China’s growth rate.

Question 17. Fill in the blanks:

1.  First Five Year Plan of commenced in the year 1956. (Pakistan/China)
2.  Maternal mortality rate is high iri (China/Pakistan)
3. Proportion of people below poverty line is more in (India/Pakistan)
4.  Reforms in were introduced in 1978. (China/Pakistan).

Answer. (1) Pakistan, (2) Pakistan, (3) India, (4) China.

The post Comparative Development Experience of India with its Neighbours NCERT Solutions for Class 11 Indian Economic Development appeared first on Learn CBSE.

NCERT Exemplar Problems Class 8 Mathematics  Chapter 4 Linear Equations in One Variable

Multiple Choice Questions
Question. 1 The solution of which of the following equations is neither a fraction nor an integer?
(a) -3x + 2=5x + 2 (b)4x-18=2 (c)4x + 7 = x + 2 (d)5x-8 = x +4
Solution. For option (c)

Question. 2 The solution of the equation ax + b = 0 is

Solution.

Question. 3 If 8x – 3 = 25 + 17x, then x is
(a) a fraction (b) an integer
(c) a rational number (d) Cannot be solved
Solution. (c) Given, 8x-3 = 25+17x

Question. 4 The shifting of a number from one side of an equation to other is called
(a) transposition (b) distributivity
(c) commutativity (d) associativity .
Solution. (a) The shifting of a number from one side of an equation to other side is called transposition.
e.g. x +a = 0is the equation, x = -a
Here, number ‘a’ shifts from left hand side to right hand side.

Question. 5 If \(\frac { 5x }{ 3 }\)-4 =\(\frac { 2x }{ 5 }\) , then the numerical value of 2x – 7 is
(a)\(\frac { 19 }{ 13 }\) (b)\(\frac { -13 }{ 19 }\)
(c)0 (d)\(\frac { 13 }{ 19 }\)
Solution.(b)

Question. 6 The value of x, for which the expressions 3x – 4 and 2x + 1 become equal, is
(a) -3 (b) 0
(c) 5 x (d) 1
Solution. (c) Given expressions 3x – 4 and 2x + 1 are equal.
Then, 3x-4 = 2x + 1
3x- 2x = 1 + 4 [transposing 2x to LHS and -4 to RHS]
x = 5
Hence, the value of x is 5.

Question. 7 If a and b are positive integers, then the solution of the equation ax = b has to be always
(a) positive (b) negative (c) one (d) zero
Solution. (a) If ax = b, then x = \(\frac { b }{ a }\)
Since, a and b are positive integers. So,\(\frac { b }{ a }\) is also positive integer, Hence, the solution of the given equation has to be always positive.

Question. 8 Linear equation in one variable has
(a) only one variable with any power
(b) only one term with a variable
(c) only one variable with power 1
(d) only constant term
Solution. (c) Linear equation in one variable has only one variable with power 1.
e.g. 3x + 1 = 0,2y – 3 = 7 and z + 9 = – 2 are the linear equations in one variable.

Question. 9 Which of the following is a linear expression?
(a) \({ x }^{ 2 }\) +1 (b) y + \({ y }^{ 2 }\)
(c) 4 (d) 1 + z
Solution. (d) We know that, the algebraic expression in one variable having the highest power of the variable as 1, is known as the linear expression.
Here, 1 + z is the only linear expression, as the power of the variable z is 1.

Question.10 A linear equation in one variable has
(a) only one solution (b) two solutions
(c) more than two solutions (d) no solution
Solution. (a) A linear equation in one variable has only one solution.
e.g. Solution of the linear equation ax + b = 0 is unique, i.e. x = \(\frac { -b }{ a }\)

Question. 11 The value of S in \(\frac { 1 }{ 3 }\) + S = \(\frac { 2 }{ 5 }\) is
(a)\(\frac { 4 }{ 5 }\) (b)\(\frac { 1 }{ 15 }\)
(c)10 (d)0
Solution.(b) Given, \(\frac { 1 }{ 3 }\) + S = \(\frac { 2 }{ 5 }\)

Question.12 If –\(\frac { 4 }{ 3 }\) y = –\(\frac { 3 }{ 4 }\) then y is equal to
(a)\(-{ \left[ \frac { 3 }{ 4 } \right] }^{ 2 }\) (b)\(-{ \left[ \frac { 4 }{ 3 } \right] }^{ 2 }\)
(c)\({ \left[ \frac { 3 }{ 4 } \right] }^{ 2 }\) (d)\({ \left[ \frac { 4 }{ 3 } \right] }^{ 2 }\)
Solution.

Question. 13 The digit in the ten’s place of a two-digit number is 3 more than the digit in the unit’s place. Let the digit at unit’s place be b. Then, the number is
(a) 11b+30 (b) 10b+ 30
(c) 11 b + 3 (d) 10b + 3
Solution. (a) Let digit at unit’s place be b.
Then, digit at ten’s place = (3 + b)
Number = 10 (3 + b) + b – 30 + 10b + b = 11b + 30

Question. 14 Arpita’s present age is thrice of Shilpa. If Shilpa’s age three years ago was x, then Arpita’s present age is
(a) 3 (x – 3) (b)3x + 3
(c) 3x – 9 (d) 3(x + 3)
Solution. (d) Given, Shilpa’s age three years ago = x
Then, Shilpa’s present age = (x + 3)
Arpita’s present age = 3 x Shilpa’s present age = 3 (x + 3)

Question. 15 The sum of three consecutive multiples of 7 is 357. Find the smallest multiple.(a) 112 (b) 126 (c) 119 (d) 116
Solution.

Fill in the Blanks
In questions 16 to 32, fill in the blanks to make each statement true.
Question. 16 In a linear equation, the——— power of the variable appearing in the equation is one.
Solution. highest
e.g. x + 3 = O and x + 2 = 4 are the linear equations.

Question. 17 The solution of the equation 3x – 4 = 1 – 2x is————- .
Solution.

Question. 18 The solution of the equation 2y = 5y-\(\frac { 18 }{ 5 }\) is————.
Solution.

Question. 19 Any value of the variable, which makes both sides of an equation equal, is known as a———–of the equation.
Solution. e.g. x + 2 = 3 => x = 3-2 = 1 [transposing 2 to RHS]
Hence, x = 1 satisfies the equation and it is a solution of the equation.

Question. 20 9x – ……………….. = – 21 has the solution (- 2).
Solution. 3
Let 9x-m= -21 has the solution (-2).

Question. 21 Three consecutive numbers whose sum is 12 are——–,————-and———.
Solution.

Question. 22 The share of A when Rs 25 are divided between A and B, so that A gets Rs 8 more than B, is——–.
Solution.

Question. 23 A term of an equation can be transposed to the other side by changing its—-.
Solution. sign
e.g. x + a = 0 is a linear equation. .
=> x = -a
Hence, the term of an equation can be transposed to the other side by changing its sign.

Question. 24 On subtracting 8 from x, the result is 2. The value of x is——–.
Solution.

Question. 25 \( \frac { x }{ 5 }\) + 30 = 18 has the solution as——–.
Solution.

Question. 26 When a number is divided by 8, the result is -3. The number is——–.
Solution.

Question. 27 When 9 is subtracted from the product of p and 4, the result is 11. The value of p is—-.
Solution.

Question. 28 If \( \frac { 2 }{ 5 }\) x-2=5-\( \frac { 3 }{ 5 }\) x,then x=——-.
Solution.

Question. 29 After 18 years, Swarnim will be 4 times as old as he is now. His present age is——–.
Solution.

Question. 30 Convert the statement ‘adding 15 to 4 times x is 39’ into an equation.
Solution. 4x+ 15=39
To convert the given statement into an equation, first x is multiplied by 4 and then 15 is added to get the result 39. i.e. 4x + 15=39

Question. 31 The denominator of a rational number is greater than the numerator by 10. If the numerator is increased by 1 and the denominator is decreased by 1, then expression for new denominator is——.
Solution.

Question. 32 The sum of two consecutive multiples of 10 is 210. The smaller multiple is——-.
Solution.

True/False
In questions 33 to 48, state whether the statements are True or False.
Question. 33  3 years ago, the age of boy was y years. His age 2 years ago was (y — 2) years.
Solution. False
Given, 3 yr ago, age of boy = y yr
Then, present age of boy = (y + 3)yr
2 yr ago, age of boy = y + 3-2 = (y + 1)yr

Question. 34 Shikha’s present age is p years. Reemu’s present age is 4 times the present age of Shikha. After 5 years, Reemu’s age will be 15p years.
Solution. False
Given, Shikha’s present age = pyr
Then, Reemu’s present age = 4 x (Shikha’s present age) = 4pyr After 5 yr, Reemu’s age = (4p+5)yr

Question. 35 In a 2-digit number, the unit’s place digit is x. If the sum of digits be 9, then the number is (10x – 9).
Solution. False
Given, unit’s digit = x
and sum of digits = 9
Ten’s digit = 9 – x
Hence, the number = 10 (9 -x)+x = 90 -10x + x = 90 – 9x

Question. 36 Sum of the ages of Anju and her mother is 65 years. If Anju’s present age is y years, then her mother’s age before 5 years is (60 – y) years.
Solution. True
Given, Anju’s present age = y yr
Then, Anju’s mother age = (65 – y)yr
Before 5 yr, Anju’s mother age = 65 – y – 5 = (60 – y)yr

Question. 37 The number of boys and girls in a class are in the ratio 5 : 4. If the number of boys is 9 more than the number of girls, then number of boys is 9.
Solution. False
Let the number of boys be 5x and the number of girls be 4x.
According to the question, – 5x – 4x = 9 => x = 9
Hence, number of boys = 5 x 9 = 45

Question. 38 A and B are together 90 years old. Five years ago, A was thrice as old as B was. Hence, the ages of A and B five years back would be (x – 5) years and (85 – x) years, respectively.
Solution. True
Let the age of A be x yr.
Then, age of S = (90 – x) yr
Five years ago, the age of A = (x- 5) yr
The age of B= 90-x-5 = (85-x)yr
Hence, the ages of A and 8 five years back would be (x – 5) yr and (85 – x) yr, respectively.

Question. 39 Two different equations can never have the same answer.
Solution. False
Two different equations may have the same answer.
e.g.2x + 1 = 2 and 2x – 5 = – 4 are the two linear equations whose solution is \(\frac { 1 }{ 2 }\)

Question. 40 In the equation 3x – 3 = 9, transposing – 3 to RHS, we get 3x = 9.
Solution. False
Given, 3x – 3 = 9
=> 3x = 9 + 3 [transposing -3 to RHS]
=> 3x = 12

Question. 41 In the equation 2x = 4 – x, transposing – x to LHS, we get x = 4.
Solution. False
Given, 2x = 4-x
=> 2x + x = 4 [transposing -x to LHS]
=> 3x = 4

Question. 42

Solution.

Question. 43

Solution.

Question. 44 If 6x = 18, then 18x = 54.
Solution.

Question. 45 If \(\frac { x }{ 11 } \) , then x=\(\frac { 11 }{ 15 } \).
Solution.

Question. 46 If x is an even number, then the next even number is 2(x +1).
Solution. False
Given, x is an even number. Then, the next even number is (x + 2).

Question. 47 If the sum of two consecutive numbers is 93 and one of them is x, then the other number is 93 – x.
Solution. True
Given, one of the consecutive number = x
Then, the next consecutive number = x + 1

Question. 48 Two numbers differ by 40. When each number is increased by 8, the bigger becomes thrice the lesser number. If one number is x, then the other number is (40 – x).
Solution.

In Questions 49 to 78, solve the following.
Question. 49 \(\frac { 3x-8 }{ 2x } =1\).
Solution.

Question. 50 \(\frac { 5x }{ 2x-1 } =2\).
Solution.

Question. 51 \(\frac { 2x-3 }{ 4x+5 } =\frac { 1 }{ 3 }\) .
Solution.

Question. 52 \(\frac { 8}{ x } =\frac { 5 }{ x-1 }\) .
Solution.

Question. 53 \(\frac { 5(1-x)+3(1+x) }{ 1-2x } =8 \) .
Solution.

Question. 54 \(\frac { 0.2x+5 }{ 3.5x-3 } =\frac { 2 }{ 5 }\)
Solution.

Question. 55 \( \frac { y-(4-3y) }{ 2y-(3y+4y) } =\frac { 1 }{ 5 }\)
Solution.

Question. 56 \(\frac { x }{ 5 } =\frac { x-1 }{ 6 }\)
Solution.

Question. 57 0.4(3x-1)=0.5x +1
Solution.

Question. 58 8x-7-3x=6x-2x-3
Solution.

Question. 59 10x-5-7x=5x+15-8
Solution.

Question. 60 4t-3-(3t+1)=5t-4
Solution.

Question. 61 5(x-1)-2(x+8)=0
Solution.

Question. 62 \(\frac { x }{ 2 } -\frac { 1 }{ 4 } \left( x-\frac { 1 }{ 3 } \right) =\frac { 1 }{ 6 } \left( x+1 \right) +\frac { 1 }{ 12 }\)
Solution.

Question. 63 \(\frac { 1 }{ 2 } \left( x+1 \right) +\frac { 1 }{ 3 } \left( x-1 \right) =\frac { 5 }{ 12 } \left( x-2 \right)\)
Solution.

Question. 64 \(\frac { x+1 }{ 4 } =\frac { x-2 }{ 3 }\)
Solution.

Question. 65 \(\frac { 2x-1 }{ 5 } =\frac { 3x+1 }{ 3 }\)
Solution. Given \(\frac { 2x-1 }{ 5 } =\frac { 3x+1 }{ 3 }\)

Question. 66 1-(x-2)-[(x-3)-(x-1)]=0
Solution.

Question. 67 \(3x-\frac { x-2 }{ 3 } =4-\frac { x-1 }{ 4 }\)
Solution.

Question. 68 \( \frac { 3t+5 }{ 4 } -1=\frac { 4t-3 }{ 5 }\)
Solution.

Question. 69 \( \frac { 2y-3 }{ 4 } -\frac { 3y-5 }{ 2 } =y+\frac { 3 }{ 4 }\)
Solution.

Question. 70 0.25(4x-5)=0.75x +8
Solution.

Question. 71 \(\frac { 9-3y }{ 1-9y } =\frac { 8 }{ 5 }\)
Solution.

Question. 72 \( \frac { 3x+2 }{ 2x-3 } =-\frac { 3 }{ 4 }\)
Solution.

Question. 73 \( \frac { 5x+1 }{ 2x } =-\frac { 1 }{ 3 }\)
Solution.

Question. 74 \(\frac { 3t-2 }{ 3 } +\frac { 2t+3 }{ 2 } =t+\frac { 7 }{ 6 }\)
Solution.

Question. 75 \( m-\frac { m-1 }{ 2 } =1-\frac { m-2 }{ 3 }\)
Solution. Given \( m-\frac { m-1 }{ 2 } =1-\frac { m-2 }{ 3 }\)

Question. 76 4 (3p + 2) – 5 (6p – 1) = 2 (p – 8) – 6 (7p – 4)
Solution.

Question. 77 3(5x-2)+2(9x-11)=4(8x-7)-111
Solution.

Question. 78 0.16 (5x-2)=0.4x +7
Solution.

Question. 79 Radha takes some flowers in a basket and visits three temples one-by-one. At each temple, she offers one half of the flowers from the basket. If she is left with 3 flowers at the end, then find the number of flowers she had in the beginning.
Solution.

Question. 80 Rs 13500 are to be distributed among Salma, Kiran and Jenifer in such a way that Salma gets Rs 1000 more than Kiran and Jenifer gets Rs 500 more than Kiran. Find the money received by Jenifer.
Solution.

Question. 81 The volume of water in a tank is twice of that in the other. If we draw out 25 litres from the first and add it to the other, the volumes of the water in each tank will be the same. Find the volumes of water in each tank.
Solution.

Question. 82 Anushka and Aarushi are friends. They have equal amount of money in their pockets. Anushka gave 1/3 of her money to Aarushi as her birthday gift. Then, Aarushi gave a party at a restaurant and cleared the bill by paying half of the total money with her. If the remaining money in Aarushi’s pocket is Rs 1600, then find the sum gifted by Anushka.
Solution.

Question. 83 Kaustubh had 60 flowers. He offered some flowers in temple and found that the ratio of the number of remaining flowers to that of flowers in the beginning is 3 : 5. Find the number of flowers offered by him in the temple.
Solution.

Question. 84 The sum of three consecutive even natural numbers is 48. Find the greatest of these numbers.
Solution.

Question. 85 The sum of three consecutive odd natural numbers is 69. Find the prime number out of these numbers.
Solution.

Question. 86 The sum of three consecutive numbers is 156. Find the number which is a multiple of 13 out of these numbers.
Solution.

Question. 87 Find a number whose fifth part increased by 30 is equal to its fourth part decreased by 30.
Solution.

Question. 88 Divide 54 into two parts, such that one part is 2/7 of the other.
Solution.

Question. 89 Sum of the digits of a two-digit number is 11. The given number is less than the number obtained by interchanging the digits by 9. Find the number.
Solution.

Question. 90 Two equal sides of a triangle are each 4 m less than three times the third side. Find the dimensions of the triangle, if its perimeter is 55 m.
Solution.

Question. 91 After 12 years, Kanwar shall be 3 times as old as he was 4 years ago. Find his present age.
Solution.

Question. 92 Anima left one-half of her property to her daughter, one-third to her son and donated the rest to an educational institute. If the donation was worth Rs 100000, how much money did Anima have?
Solution.

Question. 93 If 1/2 is subtracted from a number and the difference is multiplied by 4, the result is 5. What is the number?
Solution.

Question. 94 The sum of four consecutive integers is 266. What are the integers?
Solution.

Question. 95 Hamid has three boxes of different fruits. Box A weighs \(2\frac { 1 }{ 2 }\) kg more than box B and Box C weighs \(10\frac { 1 }{ 4 }\)kg more than box B. The total weight of the three boxes is \(48\frac { 3 }{ 4 }\) kg. How many kilograms does box A weigh?
Solution.

Question. 96 The perimeter of a rectangle is 240 cm. If its length is increased by 10% and its breadth is decreased by 20%, then we get the same perimeter. Find the length and breadth of the rectangle.
Solution.