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NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2

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NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2

Get Free NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 PDF in Hindi and English Medium. Sets Class 12 Maths NCERT Solutions are extremely helpful while doing your homework. Three Dimensional Geometry Exercise 11.2 Class 12 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 11 Class 12 Three Dimensional Geometry Ex 11.2 provided in NCERT Textbook.

Free download NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2

Ex 11.2 Class 12 Maths Question 1.
Show that the three lines with direction cosines:
\frac { 12 }{ 13 } ,\frac { -3 }{ 13 } ,\frac { -4 }{ 13 } ,\frac { 4 }{ 13 } ,\frac { 12 }{ 13 } ,\frac { 3 }{ 13 } ,\frac { 3 }{ 13 } ,\frac { -4 }{ 13 } ,\frac { 12 }{ 13 }
are mutually perpendicular.
Solution:
Let the lines be L1,L2 and L3.
∴ For lines L1 and L2
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 1
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 1.1

Ex 11.2 Class 12 Maths Question 2.
Show that the line through the points (1,-1,2) (3,4, -2) is perpendicular to the line through the points (0,3,2) and (3,5,6).
Solution:
Let A, B be the points (1, -1, 2), (3, 4, -2) respectively Direction ratios of AB are 2,5, -4
Let C, D be the points (0, 3, 2) and (3, 5, 6) respectively Direction ratios of CD are 3, 2,4 AB is Perpendicular to CD if
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 2

Ex 11.2 Class 12 Maths Question 3.
Show that the line through the points (4,7,8) (2,3,4) is parallel to the line through the points (-1,-2,1) and (1,2,5).
Solution:
Let the points be A(4,7,8), B (2,3,4), C (-1,-2,1) andD(1,2,5).
Now direction ratios of AB are
tiwari academy class 12 maths Chapter 11 Three Dimensional Geometry 3

Ex 11.2 Class 12 Maths Question 4.
Find the equation of the line which passes through the point (1,2,3) and is parallel to the vector 3\hat { i } +2\hat { j } -2\hat { k }
Solution:
Equation of the line passing through the point
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 4

Ex 11.2 Class 12 Maths Question 5.
Find the equation of the line in vector and in cartesian form that passes through the point with position vector 2\hat { i } -\hat { j } +4\hat { k } and is in the direction \hat { i } +2\hat { j } -\hat { k } .
Solution:
The vector equation of a line passing through a point with position vector \overrightarrow { a } and parallel to the
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 5
tiwari academy class 12 maths Chapter 11 Three Dimensional Geometry 5.1

Ex 11.2 Class 12 Maths Question 6.
Find the cartesian equation of the line which passes through the point (-2,4, -5) and parallel to the line is given by \frac { x+3 }{ 3 } =\frac { y-4 }{ 5 } =\frac { z+8 }{ 6 }
Solution:
The cartesian equation of the line passing through the point (-2,4, -5) and parallel to the
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 6

Ex 11.2 Class 12 Maths Question 7.
The cartesian equation of a line is
\frac { x-5 }{ 3 } =\frac { y+4 }{ 7 } =\frac { z-6 }{ 2 }
write its vector form.
Solution:
The cartesian equation of the line is
\frac { x-5 }{ 3 } =\frac { y+4 }{ 7 } =\frac { z-6 }{ 2 }
Clearly (i) passes through the point (5, – 4, 6) and has 3,7,2 as its direction ratios.
=> Line (i) passes through the point A with
tiwari academy class 12 maths Chapter 11 Three Dimensional Geometry 7

Ex 11.2 Class 12 Maths Question 8.
Find the vector and the cartesian equations of the lines that passes through the origin and (5,-2,3).
Solution:
The line passes through point
\therefore \overrightarrow { a } =\overrightarrow { 0 }
Direction ratios of the line passing through the
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 8
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 8.1

Ex 11.2 Class 12 Maths Question 9.
Find the vector and cartesian equations of the line that passes through the points (3, -2, -5), (3,-2,6).
Solution:
The PQ passes through the point P(3, -2, -5)
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 9

Ex 11.2 Class 12 Maths Question 10.
Find the angle between the following pair of lines
(i) \overrightarrow { r } =2\hat { i } -5\hat { j } +\hat { k } +\lambda (3\hat { i } +2\hat { j } +6\hat { k } )
and\quad \overrightarrow { r } =7\hat { i } -6\hat { j } +\mu (\hat { i } +2\hat { j } +2\hat { k } )
(ii) \overrightarrow { r } =3\hat { i } +\hat { j } -2\hat { k } +\lambda (\hat { i } -\hat { j } -2\hat { k } )
\overrightarrow { r } =2\hat { i } -\hat { j } -56\hat { k } +\mu (3\hat { i } -5\hat { j } -4\hat { k } )
Solution:
(i) Let θ be the angle between the given lines.
The given lines are parallel to the vectors
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 10
tiwari academy class 12 maths Chapter 11 Three Dimensional Geometry 10.1

Ex 11.2 Class 12 Maths Question 11.
Find the angle between the following pair of lines
(i) \frac { x-2 }{ 2 } =\frac { y-1 }{ 5 } =\frac { z+3 }{ -3 } and\frac { x+2 }{ -1 } =\frac { y-4 }{ 8 } =\frac { z-5 }{ 4 }
(ii) \frac { x }{ 2 } =\frac { y }{ 2 } =\frac { z }{ 1 } and\frac { x-5 }{ 4 } =\frac { y-2 }{ 1 } =\frac { z-3 }{ 8 }
Solution:
Given
(i) \frac { x-2 }{ 2 } =\frac { y-1 }{ 5 } =\frac { z+3 }{ -3 } and\frac { x+2 }{ -1 } =\frac { y-4 }{ 8 } =\frac { z-5 }{ 4 }
(ii) \frac { x }{ 2 } =\frac { y }{ 2 } =\frac { z }{ 1 } and\frac { x-5 }{ 4 } =\frac { y-2 }{ 1 } =\frac { z-3 }{ 8 }
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 11

Ex 11.2 Class 12 Maths Question 12.
Find the values of p so that the lines
\frac { 1-x }{ 3 } =\frac { 7y-14 }{ 2p } =\frac { z-3 }{ 2 } and\frac { 7-7x }{ 3p } =\frac { y-5 }{ 1 } =\frac { 6-z }{ 5 }
are at right angles
Solution:
The given equation are not in the standard form
The equation of given lines is
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 12

Ex 11.2 Class 12 Maths Question 13.
Show that the lines \frac { x-5 }{ 7 } =\frac { y+2 }{ -5 } =\frac { z }{ 1 } and\frac { x }{ 1 } =\frac { y }{ 2 } =\frac { z }{ 3 } are perpendicular to each other
Solution:
Given lines
\frac { x-5 }{ 7 } =\frac { y+2 }{ -5 } =\frac { z }{ 1 } …(i)
\frac { x }{ 1 } =\frac { y }{ 2 } =\frac { z }{ 3 } …(ii)
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 13

Ex 11.2 Class 12 Maths Question 14.
Find the shortest distance between the lines
\overrightarrow { r } =(\hat { i } +2\hat { j } +\hat { k } )+\lambda (\hat { i } -\hat { j } +\hat { k } ) and
\overrightarrow { r } =(2\hat { i } -\hat { j } -\hat { k } )+\mu (2\hat { i } +\hat { j } +2\hat { k } )
Solution:
The shortest distance between the lines
tiwari academy class 12 maths Chapter 11 Three Dimensional Geometry 14
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 14.1

Ex 11.2 Class 12 Maths Question 15.
Find the shortest distance between the lines
\frac { x+1 }{ 7 } =\frac { y+1 }{ -6 } =\frac { z+1 }{ 1 } and\frac { x-3 }{ 1 } =\frac { y-5 }{ -2 } =\frac { z-7 }{ 1 }
Solution:
Shortest distance between the lines
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 15

Ex 11.2 Class 12 Maths Question 16.
Find the distance between die lines whose vector equations are:
\overrightarrow { r } =(\hat { i } +2\hat { j } +3\hat { k) } +\lambda (\hat { i } -3\hat { j } +2\hat { k } ) and
\overrightarrow { r } =(4\hat { i } +5\hat { j } +6\hat { k) } +\mu (2\hat { i } +3\hat { j } +\hat { k } )
Solution:
Comparing the given equations with
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 16
tiwari academy class 12 maths Chapter 11 Three Dimensional Geometry 16.1

Ex 11.2 Class 12 Maths Question 17.
Find the shortest distance between the lines whose vector equations are
\overrightarrow { r } =(1-t)\hat { i } +(t-2)\hat { j } +(3-2t)\hat { k } and
\overrightarrow { r } =(s+1)\hat { i } +(2s-1)\hat { j } -(2s+1)\hat { k }
Solution:
Comparing these equation with
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 17

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NCERT Solutions for Class 12 Maths Exercise 11.2 of Three Dimensional Geometry
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NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.3

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NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.3

Get Free NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.3 PDF in Hindi and English Medium. Sets Class 12 Maths NCERT Solutions are extremely helpful while doing your homework. Three Dimensional Geometry Exercise 11.3 Class 12 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 11 Class 12 Three Dimensional Geometry Ex 11.3 provided in NCERT Textbook.

Free download NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.3 PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.3

Ex 11.3 Class 12 Maths Question 1.
In each of the following cases, determine the direction cosines of the normal to the plane and the distance from the origin.
(a) z = 2
(b) x+y+z = 1
(c) 2x + 3y – z = 5
(d) 5y+8 = 0
Solution:
(a) Direction ratios of the normal to the plane are 0,0,1
=> a = 0, b = 0, c = 1
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 1
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 1.1

Ex 11.3 Class 12 Maths Question 2.
Find the vector equation of a plane which is at a distance of 7 units from the origin and normal to the vector 3\hat { i } +5\hat { j } -6\hat { k }
Solution:
tiwari academy class 12 maths Chapter 11 Three Dimensional Geometry 2

Ex 11.3 Class 12 Maths Question 3.
Find the Cartesian equation of the following planes.
(a) \overrightarrow { r } \cdot (\hat { i } +\hat { j } -\hat { k) } =2
(b) \overrightarrow { r } \cdot (\hat { 2i } +3\hat { j } -4\hat { k) } =1
(c) \overrightarrow { r } \cdot [(s-2t)\hat { i } +(3-t)\hat { j } +(2s+t)\hat { k) } =15
Solution:
(a) \overrightarrow { r } is the position vector of any arbitrary point P (x, y, z) on the plane.
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 3
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 3.1

Ex 11.3 Class 12 Maths Question 4.
In the following cases find the coordinates of the foot of perpendicular drawn from the origin
(a) 2x + 3y + 4z – 12 = 0
(b) 3y + 4z – 6 = 0
(c) x + y + z = 1
(d) 5y + 8 = 0
Solution:
(a) Let N (x1, y1, z1) be the foot of the perpendicular from the origin to the plane 2x+3y+4z-12 = 0
∴ Direction ratios of the normal are 2, 3, 4.
Also the direction ratios of ON are (x1,y1,z1)
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 4
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 4.1

Ex 11.3 Class 12 Maths Question 5.
Find the vector and cartesian equation of the planes
(a) that passes through the point (1,0, -2) and the normal to the plane is \hat { i } +\hat { j } -\hat { k }
(b) that passes through the point (1,4,6) and the normal vector to the plane is \hat { i } -2\hat { j } +\hat { k }
Solution:
(a) Normal to the plane is i + j – k and passes through (1,0,-2)
tiwari academy class 12 maths Chapter 11 Three Dimensional Geometry 5
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 5.1

Ex 11.3 Class 12 Maths Question 6.
Find the equations of the planes that passes through three points
(a) (1,1,-1) (6,4,-5), (-4, -2,3)
(b) (1,1,0), (1,2,1), (-2,2,-1)
Solution:
(a) The plane passes through the points (1,1,-1) (6,4,-5), (-4,-2,3)
Let the equation of the plane passing through(1,1,-1)be
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 6

Ex 11.3 Class 12 Maths Question 7.
Find the intercepts cut off by the plane 2x+y-z = 5.
Solution:
Equation of the plane is 2x + y- z = 5 x y z
Dividing by 5: \Rightarrow \frac { x }{ \frac { 5 }{ 2 } } +\frac { y }{ 5 } -\frac { z }{ -5 } =1
∴ The intercepts on the axes OX, OY, OZ are \frac { 5 }{ 2 }, 5, -5 respectively

Ex 11.3 Class 12 Maths Question 8.
Find the equation of the plane with intercept 3 on the y- axis and parallel to ZOX plane.
Solution:
Any plane parallel to ZOX plane is y=b where b is the intercept on y-axis.
∴ b = 3.
Hence equation of the required plane is y = 3.

Ex 11.3 Class 12 Maths Question 9.
Find the equation of the plane through the intersection of the planes 3x – y + 2z – 4 = 0 and x + y + z – 2 = 0 and the point (2,2,1).
Solution:
Given planes are:
3x – y + 2z – 4 = 0 and x + y + z – 2 = 0
Any plane through their intersection is
3x – y + 2z – 4 + λ(x + y + z – 2) = 0
point (2,2,1) lies on it,
∴3 x 2 – 2 + 2 x 1 – 4 +λ(2+2+1-2)=0
=>λ = \frac { -2 }{ 3 }
Now required equation is 7x – 5y + 4z – 8 = 0

Ex 11.3 Class 12 Maths Question 10.
Find the vector equation of the plane passing through the intersection of the planes \overrightarrow { r } \cdot \left( 2\hat { i } +2\hat { j } -3\hat { k } \right) =7,\overrightarrow { r } \cdot \left( 2\hat { i } +5\hat { j } +3\hat { k } \right) =9 and through the point (2,1,3).
Solution:
Equation of the plane passing through the line of intersection of the planes
tiwari academy class 12 maths Chapter 11 Three Dimensional Geometry 10

Ex 11.3 Class 12 Maths Question 11.
Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x – y + z = 0.
Solution:
Given planes are
x + y + z – 1 = 0 …(i)
2x + 3y + 4z – 5 = 0 …(ii)
x – y + z = 0 ….(iii)
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 11
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 11.1

Ex 11.3 Class 12 Maths Question 12.
Find the angle between the planes whose vector equations are \overrightarrow { r } \cdot \left( 2\hat { i } +2\hat { j } -3\hat { k } \right) =5,\overrightarrow { r } \cdot \left( 3\hat { i } -3\hat { j } +5\hat { k } \right) =3
Solution:
The angle θ between the given planes is
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 12

Ex 11.3 Class 12 Maths Question 13.
In the following determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angle between them.
(a) 7x + 5y + 6z + 30 = 0 and 3x – y – 10z + 4 = 0
(b) 2x + y + 3z – 2 = 0 and x – 2y + 5 = 0
(c) 2x – 2y + 4z + 5 = 0 and 3x – 3y + 6z – 1 = 0
(d) 2x – y + 3z – 1 = 0 and 2x – y + 3z + 3 = 0
(e) 4x + 8y + z – 8 = 0 and y + z – 4 = 0.
Solution:
(a) Direction ratios of the normal of the planes 7x + 5y + 6z + 30 = 0 are 7,5,6
Direction ratios of the normal of the plane 3x – y – 10z + 4 = 0 are 3,-1,-10
The plane 7x + 5y + 6z + 30 = 0 …(i)
3x – y – 10z + y = 0 …(ii)
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 13
tiwari academy class 12 maths Chapter 11 Three Dimensional Geometry 13.1

Ex 11.3 Class 12 Maths Question 14.
In the following cases, find the distance of each of the given points from the corresponding given plane.
Point           Plane
(a) (0, 0,0) 3x – 4y + 12z = 3
(b) (3,-2,1) 2x – y + 2z + 3 = 0.
(c) (2,3,-5) x + 2y – 2z = 9
(d) (-6,0,0) 2x – 3y + 6z – 2 = 0
Solution:
(a) Given plane: 3x – 4y + 12z – 3 = 0
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 14
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry 14.1

NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Hindi Medium Ex 11.3

NCERT Solutions for Class 12 Maths Exercise 11.3 of Three Dimensional Geometry

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NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming Ex 12.2

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NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming Ex 12.2

Get Free NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming Ex 12.2 PDF in Hindi and English Medium. Sets Class 12 Maths NCERT Solutions are extremely helpful while doing your homework. Linear Programming Exercise 12.2 Class 12 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 12 Class 12 Linear Programming Ex 12.2 provided in NCERT Textbook.

Free download NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming Ex 12.2 PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming Ex 12.2

Ex 12.2 Class 12 Maths Question 1.
Reshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs 60/kg and Food Q costs Rs 80/kg. Food P contains 3 units/ kg of Vitamin A and 5 units/ kg of Vitamin B while food Q contains 4 units/kg of Vitamin A and 2 units/kg of vitamin B. Determine the minimum cost of the mixture.
Solution:
Let x kg of food P and y kg of food Q are mixed,
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 1
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 1.1
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 1.2
byjus class 12 maths Chapter 12 Linear Programming 1.3

Ex 12.2 Class 12 Maths Question 2.
One kind of cake requires 200 g of flour and 25g of fat, and another kind of cake requires 100 g of flour and 50 g of fat Find the maximum number of cakes which can be made from 5 kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients, used in making the cakes.
Solution:
Let number of cakes made of first kind are x and that of second kind is y.
∴ maximize Z = x + y
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 2
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 2.1

Ex 12.2 Class 12 Maths Question 3.
A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time.
(i) What number of rackets and bats must be made if the factory is to work at full capacity?
(ii) If the profit on a racket and on a bat is Rs 20 and Rs 10 respectively, find the maximum profit of the factory when it works at full capacity. .
Solution:
Let x tennis rackets and y cricket bats are produced in one day in the factory.
byjus class 12 maths Chapter 12 Linear Programming 3
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 3.1
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 3.2
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Ex 12.2 Class 12 Maths Question 4.
A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs 17.50 per package on nuts and Rs 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours
Solution:
Let x nuts and y bolts are produced.
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 4
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 4.1
byjus class 12 maths Chapter 12 Linear Programming 4.2

Ex 12.2 Class 12 Maths Question 5.
A factory manufactures two types of screws, A and B, Each type of screw requires the use of two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6 minutes on hand operated machines to manufacture a package of screws A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screws A at a profit of Rs 7 and screws B at a profit of Rs 10. Assuming that he can sell all the screws he manufactures, how many packages of each type should the factory owner produce in a day in order to maximise his profit? Determine the maximum profit.
Solution:
Let the manufacturer produces x packages of screws A and y packages of screw B, then time taken by x packages of screw A and y packages of screw B on automatic machine = (4x + 6y) minutes.
And hand operated machine = (6x + 3y) minutes
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 5
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 5.1

Ex 12.2 Class 12 Maths Question 6.
A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/ cutting machine and a sprayer. It takes 2 hours on grinding/ cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp, while it takes 1 hour on the grinding/ cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is Rs 5 and that from a shade is Rs 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit?
Solution:
Let the manufacturer produces x pedestal lamps and y wooden shades; then the time taken by x pedestal lamps and y wooden shades on grinding/ cutting machines = (2x + y) hours and time taken by x pedestal lamps and y shades on the sprayer = (3x + 2y) hours.
Since grinding/ cutting machine is available for at the most 12 hours, 2x + y ≤ 12 and sprayer is available for at the most 20 hours.
We have: 3x + 2y ≤ 20.
Profit from the sale of x lamps and y shades.
Z = 5x + 3y
So, our problem is to maximize Z = 5x + 3y subject to constraints 3x + 2y ≤ 20,2x + y ≤ 12, x, y ≥ 0.
Consider 3x + 2y ≤ 20
Let 3x + 2y = 20
y=\frac { 20-3x }{ 2 }
byjus class 12 maths Chapter 12 Linear Programming 6
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 6.1

Ex 12.2 Class 12 Maths Question 7.
A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4 hours for assembling. The profit is Rs 5 each for type A and Rs 6 each for type B souvenirs. How many souvenirs of each type should be company manufacture in order to maximise the profit?
Solution:
Let the company manufactures x souvenirs of type A and y souvenirs of type B, then time taken for cutting x souvenirs of type A and y souvenirs of type A and y souvenirs of type B = (5x + 8y) minutes.
Since 3 hours 20 minutes i.e 200 minutes are available for cutting, so we should have 5x + 8y ≤ 200
Also as 4 hours i.e., 240 minutes are available for assembling, so we have 10x + 8y ≤ 240 i. e., 5x + 4y ≤ 120
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 7
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 7.1

Ex 12.2 Class 12 Maths Question 8.
A merchant plans to sell two types of personal computers – a desktop model and a portable model that will cost Rs 25000 and Rs 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which die merchant should stock to get maximum profit if he does not want to invest more than Rs 70 lakhs and if his profit on the desktop model is Rs 4500 and on portable model is Rs 5000.
Solution:
Let there be x desktop and y portable computers. Total monthly demand of computer does not exceed 250. => x+y ≤ 250, cost of 1 desktop computer if Rs 25000 and 1 portable computer is Rs 40000
∴ cost of x desktop and y portable computer = Rs (25000 x+40000 y)
Maximum investment = Rs 70 lakhs = Rs 70,00,000
=> 25000 x+40000 y≤ 7000000 or 5x+8y ≤ 1400
profit on 1 desktop computer is Rs 4500 and on 1 portable is Rs 5000, total profit,
Z = 4500 x+5000 y
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 8
byjus class 12 maths Chapter 12 Linear Programming 8.1

Ex 12.2 Class 12 Maths Question 9.
A diet is to contain at least 80 units of vitamin A and 100 units of minerals. Two foods Ft and F2 are available. Food F1 costs Rs 4 per unit food and F2 costs Rs 6 per unit.One unit of food F2 contains 3 units of vitamin A and 4 units of minerals. One unit of food F2 contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem. Find the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.
Solution:
Let there be x units of food F1 and y units of food F2.
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 9
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 9.1
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 9.2
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 9.3

Ex 12.2 Class 12 Maths Question 10.
There are two types of fertilisers F1, and F2. F1 consists of 10% nitrogen and 6% phosphoric acid and F2 consists of 5% nitrogen and 10% phosphoric acid. After testing the soil conditions, a fanner finds that she needs atleast 14 kg of nitrogen and 14 kg of phsophoric acid for her crop. If F2 costs Rs 6/kg and F2 costs Rs 5/ kg, determine how much of each type of fertiliser should be used so that nutrient requirements are met at a minimum cost What is the minimum cost?
Solution:
Let x kg of festiliser and y kg of fertilised F2. be required.
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 10
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 10.1
byjus class 12 maths Chapter 12 Linear Programming 10.2
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming 10.3

Ex 12.2 Class 12 Maths Question 11.
The corner points of the feasible region determined by the following system of linear inequalities:
2x+y≤10,x+3y≤15, x,y≥0 are (0,0),(5,0), (3,4) and (0,5).
Let Z=px+qy, where p, q > 0. Condition on p and q so that the maximum of Z occurs at both (3,4) and (0,5) is
(a) p=q
(b) p=2q
(c) p=3q
(d) q=3p
Solution:
Maximum value of Z = px + qy occurs at (3,4) and (0,5),
At (3,4), Z = px + qy = 3p + 4q
At (0,5), Z = 0 + q . 5 = 5q
Both are the maximum values
=> 3p + 4q = 5q or q = 3p
Option (d) is correct.

NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming Hindi Medium Ex 12.2

NCERT Solutions for Class 12 Maths Exercise 12.2 of Linear Programming
NCERT Solutions for Class 12 Maths Exercise 12.2 of Linear Programming in PDF
NCERT Solutions for Class 12 Maths Exercise 12.2
NCERT Solutions for Class 12 Maths Exercise 12.2 in PDF
NCERT Solutions for Class 12 Maths Exercise 12.2 for up board
NCERT Solutions for Class 12 Maths Exercise 12.2 in Hindi medium
NCERT Solutions for Class 12 Maths Exercise 12.2 for 2019-20
NCERT Solutions for Class 12 Maths Exercise 12.2 updated
ex. 12.2 class 12
12 Maths exercise 12.2
12 Maths exercise 12.2 all questions
ex 12.2 solutions
Class 12 Maths Exercise 12.2 of Linear Programming
Class 12 Maths Exercise 12.2 in PDF
NCERT Solutions for Class 12 Maths Exercise 12.2 Questions 1, 2, 3, 4, 5, 6
NCERT Solutions for class 12 Maths Chapter 8 Exercise 12.2 for intermediate up board
NCERT Solutions for class 12 Maths Chapter 8 Exercise 12.2 for final year +2
NCERT Solutions for class 12 Maths Chapter 8 Exercise 12.2 inter second year
NCERT Solutions for class 12 Maths Chapter 8 Exercise 12.2 all question answers

HC Verma Concepts of Physics NCERT Solutions Homepage RD Sharma Solutions

 

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Call of Duty Mobile launching on October 1: PUBG MOBILE rival to feature new game modes

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Call of Duty Mobile launching on October 1: PUBG MOBILE rival to feature new game modes

Call of Duty Mobile is releasing on Android and iOS on October 1. The game will feature all popular Call of Duty playing modes from the PC versions.

PUBG MOBILE Call of Duty Mobile launching on October 1

HIGHLIGHTS

  • Call of Duty Mobile launching on October 1 across the globe.
  • The game will be available on both Android and iOS platforms.
  • Call of Duty Mobile will have many gameplay modes from the PC versions.

Earlier this year, Tencent Games released another online shooter title called Call of Duty Mobile for Android devices. The game was released in a closed beta for selected participants and it brought all the popular Call of Duty game modes from the PC versions in the past. We tried it out during the closed beta and it came close to displacing PUBG Mobile as the ultimate mobile shooter game you can play. However, once the beta was pulled off, many have been left wondering when the stable version will hit the servers. Well now, we have an answer.

The official page for Call of Duty Mobile has announced that the stable version of the game will be live from October 1. And the game will be available for both Android and iOS platform this time. The game is developed by Tencent’s Timi Studio and similar to the beta, it will be free-to-play for everyone.

For those in the unknown, the Call of Duty series is one of the most popular battle games from Activision. The mobile version aims to bring similar gameplay style to players around the globe along with all the classic Call of Duty gameplay modes and maps.

“We are delivering the definitive, first-person action experience on mobile with signature Call of Duty gameplay in the palms of your hands,” said Chris Plummer, VP, Mobile at Activision. “We are bringing together some of the best the franchise has to offer, including Modern Warfare maps like Crash and Crossfire, Black Ops maps like Nuketown and Hijacked, and many more, into one epic title.

The battle royale mode will be similar to the Classic mode matches in PUBG MOBILE, allowing 100 players at a time to battle it out in an open map. Similar to PUBG Mobile, Call of Duty Mobile can let you play in various modes like solo, duo and quad-player competitions. The maps will include battles across land, sea and air, with players able to rely on vehicles such as an ATV, helicopter and raft. Players can even choose first or third-person modes. And in typical Call of Duty style, the players can choose between any one of the six classes.

The Call of Duty Mobile will be a change for those players who have been playing PUBG MOBILE for long. In our short time with the beta, we found that Call of Duty Mobile fared better in many ways than PUBG MOBILE, especially with regards to gameplay style, graphics and more. In fact, PUBG MOBILE lifted off the PVP mode from COD Mobile’s Team Deathmatch mode.

Articles on PUBG Mobile

Call of Duty Mobile: Here’s how you can download it on your Android and iOS smartphone

Call of Duty Mobile

Activision’s Call of Duty Mobile is out now on Android and iOS in a closed beta. Closed beta restricts the distribution of the game but there is a way to install and play it on your phone right now.

HIGHLIGHTS

  • Call of Duty Mobile is now available in beta for Android and iOS users.
  • The game offers classic Call of Duty gameplay modes from the PC version and a new Battle Royale Mode.
  • Call of Duty Mobile will be a direct competitor to PUBG MOBILE.

For a long time, PUBG MOBILE has been sitting as the dominant game in the mobile world, increasingly gathering more popularity as the days pass by. Many other games have tried to steal PUBG of its limelight but the popular battle royale online fighter has maintained itself at the top of the charts. However, that hasn’t stopped other studios from trying and Activision is the latest one with its renowned Call of Duty series for Android and iOS.

Call of Duty Mobile is the latest title under Tencent’s umbrella and has been introduced as a new game that offers the thrills of the PC versions of the game while also dipping its foot in the viral battle royale mode. I even played it for a while and it seems like a breath of fresh air after being into PUBG for so long. The graphics are great and the gameplay does offer a variety of options. While it’s too early to say, it seems that Call of Duty Mobile could be the next big thing in the world of mobile games.

If you have been tempted to try it out, the game is available to the world in a closed beta form. However, Activision has been taking the registration for the game for almost a month now and those who were the early ones now have a chance to download it and try out the beta. If you didn’t register for the beta, here’s how you can do that from your Android and iOS device.

Call of Duty Mobile Guide: Everything you need to know about its class system

Call of Duty Mobile Guide

Call of Duty Mobile offers the class system from its PC counterpart to players. If you haven’t played Call of Duty before, here’s a brief guide to the class system and how you can take advantage of it.

HIGHLIGHTS

  • Call of Duty Mobile offers anew class-based system while playing as a team.
  • Those who play as clowns get a very special power – summon zombies.
  • As a Medic, the player is essentially the one responsible for looking after the team members.

It has been a few weeks since Call of Duty rolled out for the mobile platforms. And at the very least, the game competes with PUBG MOBILE in terms of player involvement. In fact, we did a comparison with PUBG MOBILE a few days ago and found that the Activision’s Call of Duty Mobile is ahead of PUBG MOBILE in certain areas, especially gameplay and graphics. However, like PUBG MOBILE, Call of Duty Mobile requires the player to understand some of its features to enjoy the game.

In essence, for you to play Call of Duty Mobile like an ace, you need to have a basic idea about the franchise and how its previous games used to work. And if you are like me who hasn’t played Call of Duty ever, then it must be a struggle to get along with the game, especially with the class system. Unlike PUBG MOBILE, Call of Duty Mobile requires you to choose a class while playing in the multiplayer mode.

If this class system is confusing to you, then here’s a brief explanation that might help you in a massive way as a novice.

Call of Duty Mobile: Class system explained

Scout:

As a scout, the player gets a massive power give you an idea about hostile positions in the vicinity. The player gets to use Sensor Darts that can give you an idea about which areas nearby you run a huge risk. Scouts can also track footprints of enemies nearby with the tracker ability.

Clown:

This is nothing like the name suggests. In fact, as a clown, the player gets a very special power summon zombies. Yes, zombies!

With the toy bomb, a clown can summon zombies to protect him/her from the enemies nearby. Zombies will attack the enemy and giving the player time to escape or run for safety. The clown can also limit enemy zombies in their aggression.

Mechanic:

As the name suggests, a mechanic gets to use all the cool gadgets in the team. As a mechanic, the player can summon an EMP drone that will halt all electrical operations on the enemy team.

Apart from the EMP drone, a mechanic can also get to use the Engineer ability that will help him/her get an augmented view of vehicles, traps set up by enemies and other items.

Medic:

As a Medic, the player is essentially the one responsible for looking after the team members. The Medic gets to heal players nearby. Additionally, the rate at which the Medic can heal himself/herself is faster than other players.

Call of Duty Mobile vs PUBG MOBILE: Two splendid battle royale games but is the Chicken Dinner stale now?

Activision’s popular battle title Call of Duty is now on both the mobile platforms – Android and iOS. Published by Tencent, it sits in the same space as PUBG MOBILE with a dedicated battle royale mode. So, is this the new game of the year and does it make the Chicken Dinner stale?

HIGHLIGHTS

  • Call of Duty Mobile offers regular mission based game modes and battle royale mode.
  • Both PUBG MOBILE and Call of Duty Mobile have great console-quality graphics.
  • Both PUBG MOBILE and Call of Duty Mobile have an impressively detailed roster of ammunition

Since PUBG stepped into the mobile gaming arena, mobile games haven’t been the same since then. New titles keep coming out every few weeks with graphics and gameplay that can challenge proper console games any given day. However, the battle royale formula is superhit and every PC gaming franchise wants to be a part of this – there are talks that EA could bring Apex Legends to smartphones soon. Activision, who’s responsible for the worldwide-hit franchise Call of Duty (COD), has worked with Tencent to bring it to the mobile platform and it’s already available in beta now.

Simply titled Call of Duty Mobile, it aims to bring the familiar COD gameplay to the mobile for fans of the franchise. In addition, to tackle the competition, it also brings in the viral battle royale mode that challenges you to win as the last man standing. Sounds familiar? On paper, the concept sounds very similar to PUBG MOBILE’s gameplay. And when I tried it in person, it did feel very much like PUBG in a lot of ways. And that makes it interesting – a proper PUBG MOBILE rival is finally here after a long time.

So after playing it for a couple of hours, here’s how I feel it compares to PUBG MOBILE.

Gameplay: Classic Call of Duty experience with a PUBG twist

PUBG has immortalized the battle royale genre in the world of mobile games. Ever since PUBG MOBILE, the idea of fighting it out with up to 100 real-life players in a desolated map sprinkled with weapons has appealed to a larger crowd and pulled in more people in the world of games. Call of Duty carries that idea forward with its own twist to make it slightly different from what we are used to in PUBG MOBILE.

The pace of the game in PUBG MOBILE seems fast

The pace of the game in PUBG MOBILE seems fast, even in the Classic mode matches. In comparison, Call of Duty multiplayer mode matches have a more relaxed pace. I often found spending more time looking at the environment during the gameplay – something that I have always struggled to do in a PUBG match. Of course, you have to keep in mind that PUBG is themed around hardcore battle royale-style survival while Call of Duty Mobile has a more mission-based approach to its gameplay (excluding the Battle Royale mode). The missions require you to work on the strategies and focus more on ammunition management. This is classic Call of Duty gameplay.

In the Battle Royale mode, there’s not really much difference between Call of Duty and PUBG. Both the games have the same concept – you need to jump in a big map, collect weapons, protect your team members, move around using vehicles, kill enemies using smart strategies and be the last man (or team) standing to win the match. However, in PUBG MOBILE, a player is just part of a team and has no superiority over others, apart from the playing skills. Call of Duty goes for a different approach by offering each player to play a role with a special weapon or be a medic to look after your team.

What I love about Call of Duty is its approach to make new players more comfortable. For example, the game offers you an option to either let you fire the weapon on your own or let the game fire for you once you aim. For new players like me, it was a great way to increase the involvement in a match and have a better chance in playing with the professionals. PUBG MOBILE has always gone for a more rough approach by not offering any training or tips on how to play.

Graphics: Great graphics aren’t just restricted to PC anymore

PUBG MOBILE has led the mobile gaming industry in terms of graphics quality for a while until Gameloft dropped Asphalt 9: Legends. That said, the game still looks good on high graphics and each update has been improving the visual effects – the latest one added rain to two maps.

Call of Duty Mobile in comparison has noticeably better graphics. If you were impressed with the details in PUBG MOBILE, then Call of Duty Mobile will simply blow you away. The detailing on the character’s dresses are impeccable – all the pockets on the dress, the weapons, the stitching and the colour patterns – this is on par with what you get in PC games now.

The detailing also extends beyond the characters. The lighting effects are impeccable and the reflections on puddles surely look close to what you see in the console games. The textures are quite detailed for a mobile game and map design is very clever.

Weapons: Both are equally good

Both PUBG MOBILE and Call of Duty Mobile have an impressively detailed roster of ammunition with extreme attention to details. Players need to learn about weapons and how they work in order to have a better shot at killing enemies. Call of Duty has a slightly serious approach to the weapon design and modification whereas PUBG goes for a slightly more fun approach.

Early impressions: Does the Chicken Dinner still hold its relevance over “the Duty”?

Not very much. Since Call of Duty Mobile dropped in, I have mostly noticed many PUBG players spending more time on the new game instead of logging hours in PUBG MOBILE. However, a major reason for that is that Call of Duty is new and will draw people’s fancy for the first few days. In comparison, PUBG MOBILE hasn’t changed much, even with the new Zombie modes.

However, Call of Duty Mobile has a better chance at scooping out a lot of PUBG followers in its favour. Those who have been yearning for a more serious military-based gameplay will find Call of Duty Mobile appealing. The graphics is also good and the game offers a lot many modes to get hooked to it. The gameplay is slightly relaxed but holds the classic Call of Duty vibe, which in itself will help its cause. And this is a great thing considering the game is still in the beta stage.

If you have registered for the closed beta, go ahead and download it. When this comes out, PUBG MOBILE will have serious competition and it would be interesting to see whether gamers embrace Call of Duty like PUBG or ignore it like Fortnite.

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Scholarships for Students

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Scholarships for Students

State Wise Scholarships

Top Scholarships for Class 1 to Class 10

Popular Scholarships in India

Best Scholarships in India

  • NTSE – National Talent Search Examination
  • KVPY – Kishore Vaigyanik Protsahan Yojana 2019
  • NSP – National Scholarship Portal

State Level National Talent Search Exam (NTSE) 2019 – 2020

Top Scholarships for Class 1 to Class 10

Pre Matric Scholarship for SC, ST & General Students, Uttar Pradesh 2019-20

Eligibility
  • Be a domicile of Uttar Pradesh
  • Be studying in class 9 and 10
  • Belong to ST/SC/General Category
  • Have a family income of not more than INR 1 Lakh per annum
Important Dates
  • Last date to apply under fresh application: 10 September 2019
  • Last date to submit an application for renewal: 10 August 2019
Important Links

Pre Matric Scholarship for OBC Students, Uttar Pradesh 2019-20

Eligibility
  • Be a domicile of Uttar Pradesh
  • Belong to OBC category
  • Have a family income less than INR 1 Lac per annum from all sources
Important Dates
  • Last date to apply under fresh application: 10 September 2019
  • Last date to submit an application for renewal: 10 August 2019
Important Links

Pre Matric Scholarship for Minority Students, Uttar Pradesh 2019-20

Eligibility
  • Be a domicile of Uttar Pradesh
  • Belong to the Minority community
  • Have the family income of less than INR 1 Lakh per annum from all sources
  • Be studying in class 9 and 10
Important Dates
  • Last date to apply under fresh application: 10 September 2019
  • Last date to submit application for renewal: 10 August 2019
Important Links

West Bengal Pre Matric Scholarship

Eligibility
  • Be a domicile of West Bengal
  • Be studying in class 1 to 10 at a school or institution which is affiliated with a Council/Educational Board/University of State or Central Government
  • Have scored at least 50% marks in his/her last qualifying exam
  • Have a family income of less than INR 2 Lakhs per annum
  • Belong to minority section of West Bengal

Note – Students pursuing their studies outside West Bengal are not eligible for this scholarship

Important Dates
  • Application deadline – 15th September 2019
Important Links

National Scholarship Exam (NSE) 2019

Eligibility
  • Students in Class 5 to 12 (SSC/ICSE/CBSE board)
  • Students enrolled in a Diploma course (any stream and any year)
  • Students enrolled in a Degree (any stream and any year)
Important Dates
  • Registrations open: 1 April 2019
  • Last date to apply: 30 September 2019
  • Date of exam: 15th December 2019
Important Links

Kind Scholarship for Meritorious Students

Kind Scholarship for Meritorious Students is an initiative to support academically meritorious students coming from under-privileged section of society to build a foundation for their bright future.  The scholarship is funded by  donations received from Individuals & professionals who want to support meritorious students in need.

Scholarship award varies as per the need of candidates. However, the standard scholarship awards are the following:-

  • For Class 9 & 10 students: INR 6,000 per year
  • For Class 11 & 12 students: INR 12,000 per year
  • For Polytechnic / ITI / Diploma / Graduation & Others: INR 18,000 per year
Eligibility
  • Be studying in any Indian school (Class 9 to 12) or college (Graduation; ITI, Polytechnic, Vocational & Professional Courses)
  • Have an annual household income less than INR 4 Lakhs
  • Have cleared the previous examination with at least 60% marks

Note: Preference will be given to candidates having high merit, single parent, orphan or wards of Indian Armed Forces died on duty.

Important Dates
  • Starting date: July 1, 2019
  • End date: September 30, 2019

Begum Hazrat Mahal National Scholarship Scheme for Minorities Girls 2019-20

Eligibility
  • Only girl students belonging to Muslim, Christian, Sikh, Buddhist, Jain, and Parsi communities are eligible for this scholarship.
  • They must be studying in class 9 to 12.
  • The annual family income of the student should be less than INR 2 Lakhs.
  • The students must have secured a minimum of 50% marks (in aggregate) in the previous class.
Important Dates
  • Last date to submit the application: 30th September 2019
Important Links

24th Anuvrat Essay Writing Competition 2019

Eligibility
  • Junior Group: Class 1 to 8
  • Senior Group: Class 9 to 12

What are the benefits?

  • 3 graded prizes for 1st, 2nd  and 3rd winning essays in each group
  • Some consolation prizes for each participating group
  • Honor for best participants
  • Merit/appreciation certificate for commendable essay writers
Important Dates
  • Deadline for essay submission – 30th September 2019
  • Result declaration – December 2019
Important Links

The Gaud Saraswat Brahman (G.S.B.) Scholarship 2019

The scholarship offers the following-

  • Free scholarship- Awarded to students from Class 5 to Graduate level
  • Foreign loan scholarship- Up to INR 17 lakhs (INR 1.7 million) with a loan scholarship of INR 2 lakhs per student
Eligibility
  • Applicants must belong to the Gaud Saraswat Brahman community.
  • Students of class 5th to undergraduate courses will be eligible for this scholarship scheme.
  • All Students enrolled in courses like diploma /B.A/B.Sc/B.Com/B.Arch/MBBS/B.Pharma/B.E can also apply.
Important Dates
  • Application deadline for students of Class 5 to 10 – 15th July 2019
  • Application deadline for students of PUC I & II/Jr. College – 15th August 2019
  • Application deadline for students of Degree (BA/BSc/B.Com) & Diploma – 15th September 2019
  • Application deadline for students of BE/BArch/BPharm/MBBS etc. – 15th October 2019
Important Links

Pre Matric Scholarships Scheme for Minorities 2019-20

Eligibility
  • Must be studying in class 1 to 10
  • Must have secured at least 50% marks in the previous final examination
  • Must have a family income of not more than INR 1 lakh per annum from all sources
  • Must belong to the minority community (Muslims, Sikhs, Christians, Buddhists, Jains and Zoroastrians/Parsis)
Important Dates
  • Scholarship announcement date: 15 July 2019
  • Scholarship closing date: 15 October 2019
  • Last date for defect verification: 31 October 2019
  • Last date for Institute verification: 31 October 2019
Important Links

Pre-Matric Scholarship for Students with Disabilities 2019-20

Eligibility
  • Be a regular full-time student of class 9 or class 10 in government or recognised school.
  • Have more than 40% disability and a valid certificate for the same.
  • Belong to the family where the annual income is not more than INR 2.50 Lakhs from all the sources.
Important Dates
  • Scholarship announcement date: 15 July 2019
  • Scholarship closing date: 15 October 2019
  • Last date for defect verification: 31 October 2019
  • Last date for Institute verification: 31 October 2019
Important Links

Financial Assistance for Education of the Wards of Beedi/Cine/IOMC/LSDM Workers – Post-Matric 2019-20

The selected scholar will receive the following benefits:

  • Girls studying in PUC I & II will receive INR 2,440
  • Boys studying in PUC I & II will receive INR 2,000
  • Girls and boys enrolled in ITI courses will receive INR 10,000
  • Girls and boys enrolled in Degree courses will receive INR 3,000
  • Girls and boys enrolled in Professional courses such as BE/MBBS/BSc-Agri. will receive INR 15,000
Eligibility
  • One or both the parents of the applicants should be working as a Beedi worker/ Iron Ore Manganese & Chrome Ore Mines (IOMC) worker/ Limestone & Dolomite Mines (LSDM) worker/ Cine worker for at least last six months.
  • The monthly income of the family must not exceed INR 10,000 from all the sources except for Cine workers where the income must not exceed INR 8,000 per month or INR 1,00,000 per annum.
  • The student must have passed the last qualifying examination in the first attempt.
  • The student must have enrolled in a regular course of general or technical education, including medical, engineering and agricultural studies.

Note: This scholarship is also for the children of Contract/ Gharkhataworkers.

Important Dates
  • Scholarship announcement date: 15 July 2019
  • Scholarship closing date: 31 October 2019
  • Last date for defective verification: 15 November 2019
  • Last date for institute verification: 15 November 2019
Important Links
  • please visit NSP website https://scholarships.gov.in/

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K.C. Mahindra Scholarship 2019-20 | Dates, Eligibility, Awards, and Application Process 

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K.C. Mahindra Scholarship 2019: KC Mahindra Scholarship is an initiative of the KC Mahindra Education Trust, also known as KCMET. It offers scholarships and grants to the most deserving and needy students. Some of these instituted in the mid-1950s and others founded recently. It has an effort to bring social and economic development through literacy and higher education in the country. 45% of this scholarship awardees secured admissions in the top-ranked universities worldwide. Universities such as Harvard, Oxford, Stanford, Pennsylvania, Cambridge, and so forth.

KCMET founded by the late K.C. Mahindra in 1953. It has an objective to change the lives of people in India through education by providing financial support and recognition to them. KCMET has implemented various initiatives to make a difference in over 40,000 lives of the disadvantaged students. The article below provides more information about the KC Mahindra Scholarship 2019.

K.C. Mahindra Scholarship 2019

K.C. Mahindra Scholarship grants interest-free loans or scholarships exclusively to needy students. Since its inception in 1956, KCMET mainly working to provide an opportunity for bright students. Students can pursue higher education in the selected universities abroad without financial burden. As a part of Corporate Social Responsibility (CSR), the Mahindra Group has also involved in different fields. These fields are utility vehicles, financial services, and information technology. KCMET has provided more than $65 million for grants, scholarships, and loans. These funds are derived from the KCMET investment portfolio and CSR grants. KCMET consists of the following scholarships to encourage and motivate students.

K.C. Mahindra Scholarship for Post Graduation study Abroad

Since 1956, KCMET has granted interest-free loan scholarships to deserving and needy students. These students can pursue post-graduate in various fields in Abroad. In the academic year 2018-19, KC Mahindra Scholarship disbursed grants around Rs. 2.92 Crores. Students from top institutions who placed in reputed universities were using this opportunity.

Rewards

The study in Abroad has a maximum of 2 years duration. The scholars can extend the studies more than 2 years. But, they have to get specific approval for an extension from the trust. The shortlisted scholars have to repay the scholarship amount to KCMET. It should be repaid within 24 months of completing their course. Otherwise, 48 months after availing the scholarship grant. It is the discretion of the trust to decide the expiry period. 62 scholarships are offered to deserving students. KCMET offers the following scholarships every year.

  • The top 3 KC Mahindra fellows awarded a maximum of Rs. 8 Lakh per scholar
  • The remaining successful scholars awarded a maximum of Rs. 4 Lakh per scholar

Eligibility Criteria

Candidates must fulfill the following eligibility criteria to study in Abroad.

  • Candidates must possess a first-class degree or diploma of equivalent standard. Candidates must pursue their education from a recognized University.
  • Candidates must be Indian nationals.
  • Candidates who have secured admission or applied for admission in reputed foreign universities. Admission for courses starting from August 2019 but not after February 2020.
  • Candidates going abroad for conferences, seminars, and UG studies are not eligible.

Mahindra Talent Search Scholarship

Mahindra Talent Search Scholarship was initiated in 1983. This scholarship aims to enthuse and award excellence in academics. It has been continuing in 37 educational institutions across the country.

Rewards

  • Candidates receive this Scholarship more than once will be awarded the “Honour Scholarship”.
  • Candidates can avail a cash prize of Rs. 5000/- and a citation from KCMET in Honour Scholarship.

Eligibility

  • Candidates who have secured the highest aggregate marks based on the year-end examination.

KC Mahindra United World College Scholarship

This scholarship offers to students for studying at the United World Colleges.

Rewards

This scholarship providing the below benefits at the Mahindra United World College

  • Experience of international education
  • Shared learning
  • Community service

Eligibility

  • The age of the deserving candidates should be between 16 to 18 years.

KC Mahindra All India Talent Scholarship (MAITS)

The Mahindra All India Talent Scholarship was established by KCMET in 1995. This scholarship offered to students belonging to economically disadvantaged families. This scholarship helps students to pursue a job-oriented diploma course in recognized Govt. Polytechnic in India. This scholarship encourages and supports the lower-income family students. Students belong to rural and urban areas can pursue job-oriented diplomas. Application releases in national and regional newspapers in June/July every year. The Shortlisted candidates will be informed regarding their interview date and venue details. So that they can attend the interview at 12 centers across India.

Rewards

  • This scholarship awarded to 9640 students till date across India.
  • KCMET awards Rs. 10,000/- per annum to 550 students every year for a period of 3 years.
  • Candidates will be paid the value of travel to the interview center up to a certain amount.

Eligibility

  • Candidates who are studying in the first-year diploma in Govt. Polytechnics.
  • Candidates who have passed SSC/HSC or similar exams in class 10th/12th.
  • Candidates should have secured admission in Govt. or any other recognized Polytechnic for diploma courses.
  • Candidates should have secured more than 60% marks in the board examinations.
  • Girl and lower-income families candidates are given preference.
  • Candidates from differently-abled and armed forces personnel are also preferred.

KC Mahindra Scholarship 2019 – Overview

ParticularsDetails
Organization NameKC Mahindra Education Trust
Scholarship NameKC Mahindra Scholarship
Start date of KC Mahindra PG Study in Abroad Scholarship ApplicationJanuary 2019
Last date of KC Mahindra PG Study in Abroad Scholarship Application SubmissionApril 2019
Final Interview of KC Mahindra PG Study in Abroad Scholarship Shortlisted CandidatesJuly 2019
Start date of KC MAITS ApplicationJune/July 2019
Last date of KC MAITS Application SubmissionBetween August to October 2019
Websitewww.kcmet.org

KC Mahindra Scholarship 2019 – Selection Process

The trustees of KCMET has appointed a specific selection committee. This committee has the responsibility of selecting the deserving and needy students. The committee analyses and evaluates the application based on some qualities of students. These qualities are merit, ambitions, aptitude, character, and others. Students can work in any organization or institution after completion of the course. The trustees of the KCMET are not responsible to provide any employment to any student. Preference will be given to students who are interested to pursue their studies in specific subjects and areas. These specific subjects and areas related to the country’s development and its importance. Some of the examples are Biogas technology for rural areas, Oceanography, Fisheries and Survey, and so forth.

KC Mahindra Scholarship 2019 – Application Process

KC Mahindra Scholarship application will be available in both online and offline mode. The application process for PG Study Abroad Scholarship has closed in April 2019. The PG Study Abroad Scholarship application starts in December/January every year. The application process for KC MAITS closes between August to October 2019. The KC MAITS application starts in June/July every year. Candidates go through the rules and regulations of this scholarship to avoid errors. Refer to the below points of online as well as the offline application process.

Online Application Process

  • Visit the official website of the KC Mahindra Education Trust.
  • Click on apply to fill the application form available in pdf format.
  • Candidates should keep ready all the relevant documents while filling an application.
  • Fill the accurate and necessary details in capital letters in the form.
  • Recheck the filled application to avoid rejection by KCMET during verification.
  • Attach attested copies of the relevant documents to complete the online application process.
  • Then, submit the filled application along with the attached documents.

Offline Application Process

  • Visit the official website www.kcmet.org.
  • Download the application form available in pdf format in Scholarships and Grants page.
  • Take a hard copy of the application form and fill the essential details correctly.
  • Recheck the filled application to avoid rejection by KCMET during verification.
  • Attach attested copies of the relevant documents to complete the offline application process.
  • Then, submit the filled application along with the documents to the following address:
    • KC Mahindra Education Trust, 3rd Floor,
      Near Regal Cinema Colaba, Cecil Court, M.B. Marg,
      Apollo Bandar Colaba, Mumbai – 400001.

KC Mahindra Scholarship 2019 – Checklist of Documents

Candidates have to attach all the essential documents for verification. Candidates must attach the following documents to apply for the KC Mahindra Scholarship.

  • One recommendation letter
  • One copy of the admission letter
  • Passport size photograph with signature
  • A statement was written by the candidate constituting their ambitions, and other aspirations
  • One copy of GRE/GMAT score of the candidate, if applicable
  • One copy of IELTS/TOEFL score of the candidate, if applicable
  • Attested copies of candidates course and degree certificates and mark sheets
  • Candidates rank certificate, if applicable
  • Attested copies of candidates 10th, 12th, and school leaving certificate
  • A self-attested copy of the candidate’s age proof
  • Copy of Family income certificate of the candidate
  • Copy of Aadhaar card
  • Self-attested copy of the first page of bank passbook or canceled cheque

KC Mahindra Scholarship 2019 – Contact Details

In case of any queries related to KC Mahindra Scholarship or any assistance contact on the below-mentioned details.

For queries on KC Mahindra Scholarship for Postgraduate study Abroad contact below

Phone Number022-22895526
AddressKC Mahindra Education Trust, 3rd Floor,
Near Regal Cinema Colaba, Cecil Court, M.B. Marg, Apollo Bandar Colaba, Mumbai – 400001
Email Idrodrigues.kieran@mahindra.com

For queries on KC Mahindra All India Talent Scholarship (MAITS) contact below

Phone Number022-22897848
AddressKC Mahindra Education Trust, 3rd Floor,
Near Regal Cinema Colaba, Cecil Court, M.B. Marg, Apollo Bandar Colaba, Mumbai – 400001
Email IdRAMCHANDRAN.p2@mahindra.com

FAQ’s on KC Mahindra Scholarship 2019

Question 1.
What is KCMET?

Answer:
KC Mahindra Scholarship is an initiative of the KC Mahindra Education Trust, also known as KCMET. It offers scholarships and grants to the most deserving and needy students.

Question 2.
What are the scholarships offered by the KC Mahindra Education Trust?

Answer:
KCMET offers the following scholarships to encourage the lower-income family students.

  • KC Mahindra Scholarship for Post Graduation study Abroad
  • Mahindra Talent Search Scholarship
  • KC Mahindra United World College Scholarship
  • KC Mahindra All India Talent Scholarship (MAITS)

Question 3.
What are the application starting and closing dates for the KC Mahindra PG Study in Abroad Scholarship?

Answer:
The application process for this scholarship starts in January 2019. Whereas the closing date of application submission is April 2019.

Question 4.
What are the application starting and closing dates for the KC MAITS?

Answer:
The application process starts on June/July 2019 for the KC MAITS. Whereas the closing date of application submission is between August to October 2019.

Question 5.
What is the duration of the KC Mahindra PG Study Abroad Scholarship?

Answer:
The duration of this scholarship is 2 years. If the scholars want to extend it then they have to get specific approval from KCMET.

Hope this article will help you to know more about the KC Mahindra Scholarship 2019. If you have queries related to KC Mahindra Scholarship, then leave it in the comment box to get in touch with us.

The post K.C. Mahindra Scholarship 2019-20 | Dates, Eligibility, Awards, and Application Process  appeared first on Learn CBSE.

ePASS Karnataka 2019 | KAR ePass Dedicated Scholarship Portal for Backward Classes Welfare

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ePASS Karnataka 2019: Karnataka education board has launched ePASS Karnataka which is also known as the KARePASS is a dedicated electronic and payment system for scholarships. This scheme is presented by the department of backward class welfare by the government of Karnataka. The official government portal looks after the online disbursement of the scholarships to the students that fall under the Karnataka domicile.

The main aim behind the e PASS Karnataka portal is to make sure that the students of Karnataka are educationally uplifted. Also, it links welfare departments, welfare, banks, colleges, and secondary school leaving certificate database together. Thus, it ensures that the disbursal of scholarships is hassle-free. scholarship Karnataka will be given to the students who are educationally Uplifted.

ePASS Karnataka Overview

Name of the AuthorityKarnataka Education Government
Name of ScholarshipVidyasiri Scholarship
SchemeKarnataka Vidayasiri Scholarship 2018
Kar Vidyasiri Scholarship EligibilityIntermediate 12th, UG, and PG Courses
Kare Pass Scholarship1500/- (Varied Yearly Wise)
Kare Pass Application SubmissionVia Online Only
official Websitewww.karepass.cgg.gov.in

ePASS Karnataka – Key Features

In order to make the process of inviting applications simple for the scholarships, the ePASS Karnataka portal was created. This portal focuses majorly on the post-matric scholarships and below are some of the features that can be useful for the users:

  • Checking Application Status: This feature allows the candidate to track the real-time status for their application by providing details like the academic year, the application number, SSLC pass type, SSLC registration number, year of passing SSLC, and the date of birth
  • Knowing your application number: The candidates that do not remember their application number can search for this using the facility provided on the portal. There are certain details that need to be provided on the portal kike SSLC pass type, year of passing, and date of birth.
  • Hostel application status: You can also know your hostel Karepass application status online via this portal by simply providing your date of birth and application number.
  • Pratibha acknowledgment: You download the Pratibha puraskar scholarship acknowledgment through this portal by either providing your application reference number or other details.

ePass Karnataka Status – Check Application Status

S.No.ParticularsImportant URL
1.Know the application numberClick here
2.Check application statusClick here
3.Check hostel application statusClick here
4.Get Prathibha acknowledgmentClick here

ePASS Karnataka – Schemes Listed

The ePASS Karnataka portal enlisted s variety of schemes offered by the department of backward class welfare for students that belongs to backward class and are studying at different levels of education. The main schemes that are available on the portal are as follows

  • Food and accommodation scholarship scheme (PMS)
  • Post-matric scholarship scheme (PMS)
  • Fee concession scheme (FC)

Besides the above-mentioned schemes, the portal also provides and processes the applications for Vidyasiri and pre-matric scholarship scheme.

ePASS Karnataka Scholarship Details

There are different eligibility conditions that one needs to fulfill for schemes available on the ePASS portal. Also, the financial assistance rendered to the students under the given schemes is different.

You can find all these details in the table given below. Also, if you are a permanent resident of Karnataka and belong to the backward class, you are automatically eligible to apply for the scholarship schemes which are available on the ePASS portal.

Detailed Overview of ePASS Scholarship schemes

Scholarship NameEligibilityAward Details
Post-Matric Scholarship (PMS)For students who are studying at the post-matriculation level of education, their annual family income should be less than Rs. 1.5 Lakhs (for Category 1) while it should Rs. 2 Lakhs (for 2A, 3A, and 3B categories).Scholarship granted up to Rs. 3,500 per annum
Food & Accommodation Scholarship (FAAS)For students that are studying at the post-matric level in Government or Government-aided/ housing colleges, their annual family income should be less than Rs. 2.50 Lakhs (for category 1) and Rs. 5 Lakhs (for 2A, 3A, and 3B categories).Upto Rs. 1,500 per month for 10 months
Fee Concession (FC) SchemeStudents that are pursuing post-graduate courses can apply if their annual family income should be below Rs. 1 Lakh (for category 1) and Rs. 2.50 Lakhs (for 2A, 3A, and 3B categories).Sports Fee
Training Fee
Laboratory Fee
Readers Charge up to Rs. 1,750 per annum

KAR ePass Application Process

The process to apply for each scholarship mentioned on the ePASS Karnataka is easy and simple. The students that qualify the eligibility criteria for any of the given scholarship can apply online through the steps given below. ePASS application number will be given to students. Depending on the timeline for each scholarship, the official application page remains open for a specific period only.

How To Apply for KAR ePASS Portal?

  • Go to the official website of ePASS Karnataka i.e. karepass.cgg.gov.in/
  • On the main website, look for the scholarship notification.
  • There read the application guidelines given carefully.
  • For application, you need to start by registering yourself on the portal.
  • Fill up all the details required in the application form and upload the relevant documents.
  • Finally, click on the ‘submit’ button and submit your application form.

Required Documents for ePASS Karnataka Scholarship

Candidates that are applying for the Karnataka ePASS scholarship should have some required documents. Students can check the details of these required documents that are given below:

  • Aadhar card of father and mother/guardian
  • Aadhar card of the candidate
  • Income certificate
  • Caste certificate
  • Bank passbook that contains the bank number and IFSC code
  • Residential certificate
  • SSLC certificate and bonafide certificate of the prospective college for the candidate

Key Statistics for PMS Scheme at KAR ePass

Academic SessionsApplications Received – VerifiedApplications Sanctioned
ePass Karnataka 2018-19917,762 – 666,771500,505
2017-18884,511 – 667,018541,273
2016-17767,526 – 618,882514,702
2015-16712,049 – 525,985344,689
2014-15578,439 – 436,462338,470

Key Data for FC Scheme at KAR ePASS

Academic SessionsApplications Received – VerifiedApplications Sanctioned
ePass Karnataka 2018-19917,762 – 877,938845,178
2017-18884,511 – 859,625823,716
2016-17767,526 – 747,644710,464
2015-16712,049 – 673,950650,320
2014-15453,142 – 416135402,692

Key Data for FAAS at KAR ePASS

Academic SessionsApplications Received – VerifiedApplications Sanctioned
ePass Karnataka 2018-19917,762 – 537,886115,622
2017-18884,511 – 544,22888,328
2016-17767,526 – 481,95979,894
2015-16712,049 – 434,16191,704
2014-15578,439 – 375,46066,648

ePASS Karnataka – Contact Details

In case, you come across any queries related to the ePASS Karnataka scholarship or its application, feel free to contact the provider at the below-mentioned address

Karnataka Backward Classes Welfare Department
No. 16/D, 3rd Floor, Devraj Urs Bhavan,
Millers Tank Bed Road, Vasanth Nagar,
Bangalore – 560052.
Phone: 8050770005
Email: bcdbng@kar.nic.in

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PUBG Mobile Lite new update brings Golden Woods map, War mode and more

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PUBG Mobile Lite has received a new 0.14.1 update to introduce a new map, arcade mode, and several new weapons. Check out the full changelog below.

PUBG Mobile introduced “Lite” version of the game in India in July, targeting the wider audience who still do not have high-end smartphones to support seamless gameplay. With toned-down graphics and certain limitations, PUBG Mobile Lite became an instant hit with 10M+ downloads. There’s no reason to skip PUBG Mobile Lite if you have a low-end device, especially after the new update.

PUBG Mobile Lite new update arrives
PUBG Mobile Lite new update arrives – Download PUBG Mobile APK Download

PUBG Mobile Lite 0.14.1 update brings several changes to the game, promoting intense gameplay. The biggest highlight of the new update is the introduction of a new map, Golden Woods, which engages PUBG Mobile Lite players into a tight battleground for intense combat. If you’ve picked up your pace in PUBG Mobile Lite and wish to test your quick-acting skills, the new Golden Woods map is the right place to start.

According to PUBG Mobile developers, the Golden Woods map is smaller and has small towns to loot. There’s also a lot of shrubbery for intense combat scenes. If we have to draw similarities, Golden Woods could be the Sanhok of PUBG Mobile Lite with its own unique taste.

PUBG Mobile Lite’s new map isn’t everything in the 0.14.1 update. There’s also a new Arcade Mode, dubbed War Mode, which as the name suggests is for action-filled combat. Players in the War mode will have RPG-7s.

As in the case of most updates, PUBG Mobile Lite 0.14.1 update brings new weapons, including PP-19 sub-machine gun, QBZ, QBU DMR rifle and the classic UAZ four-wheeled vehicle. In addition, the latest update brings a new ranked season with new rewards starting October 1 and new challenges are available in the Missions menu for players to win valuable prizes with their in-game skills.

PUBG Mobile Lite is several regions of South Asia, Africa and East Europe, with the target audience being owners of low-end phones. The game is optimised to run on smartphones with less than 2GB RAM. In fact, the game itself weighs in about 40MB. But the reduced size comes with certain limitations, such as the graphics are not even close to the original PUBG Mobile game, there are 60 players instead of 100 and the armoury is different too. But it caters to a completely new userbase, who often feel left out from the growing PUBG Mobile hype.

PUBG MOBILE LITE is here! Built with Unreal Engine 4, this version of PUBG MOBILE is smaller in size and compatible with more devices with less RAM, yet without compromising the amazing experience that attracted millions of fans around the world! PUBG MOBILE LITE features fast-paced matches and a smaller map made for 60 players, providing a more exhilarating combat experience in the traditional PUBG MOBILE setting. When duty calls, fire away freely on the battlefield for survival!

1. PUBG MOBILE LITE
60 players parachute onto a graphically rich 2km x 2km island for a winner-takes-all showdown. Players have to scavenge for their own weapons, vehicles, and supplies while battling it out in an ever-shrinking play zone to be the last player standing. Get ready to land, and do whatever it takes to survive.

2. High-quality Graphics and HD Audio
The powerful Unreal Engine 4 creates a jaw-dropping visual experience with stunning detail, realistic gameplay effects and a massive HD map, perfect for the tactical action genre. Feel free to fire away on the battlefield as you play with high-quality audio and rich 3D sound effects.

3. Team Up with Friends
Invite and team up with your friends to coordinate your battle plan through voice chat and set up the perfect ambush for your enemies. Answer the call when your friends need help, or do your part when Clan duty calls!

4. Fair Gaming Environment
Powerful anti-cheating mechanisms ensure a fun and fair environment for all PUBG MOBILE LITE players.

The post PUBG Mobile Lite new update brings Golden Woods map, War mode and more appeared first on Learn CBSE.

सीबीएसई कक्षा 10 बोर्ड परीक्षा 2020: नवीनतम नमूना पत्रों को डाउनलोड करें, सभी विषयों की अंकन योजना

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सीबीएसई कक्षा 10 बोर्ड परीक्षा 2020: नवीनतम नमूना पत्रों को डाउनलोड करें, सभी विषयों की अंकन योजना

कक्षा 10 बोर्ड परीक्षा 2020 के लिए सीबीएसई नमूना प्रश्न पत्र यहां उपलब्ध हैं। सीबीएसई अंकन योजना के साथ नमूना प्रश्न पत्र डाउनलोड करें।

केंद्रीय माध्यमिक शिक्षा बोर्ड, सीबीएसई ने कक्षा 10 और कक्षा 12 के लिए नमूना प्रश्न पत्र जारी किए हैं। सीबीएसई बोर्ड परीक्षा 2020 के लिए सभी विषयों के नमूना प्रश्न पत्र छात्रों को बोर्ड परीक्षा में प्राप्त होने वाले प्रश्न पत्रों की संरचना का अनुमान लगाने में मदद करने के लिए जारी किए जाते हैं। पहले CBSE अक्टूबर के महीने में सैंपल पेपर्स जारी करता था लेकिन इस साल एडवांस में एक महीने पहले सैंपल पेपर्स जारी करने से छात्रों को बड़ा फायदा होता है क्योंकि एग्जाम से पहले सैंपल पेपर्स का विश्लेषण और अभ्यास करने के लिए उनके पास पर्याप्त समय होगा।

हम यहां बोर्ड परीक्षा 2020 के लिए मार्किंग स्कीम्स के साथ सीबीएसई क्लास 10 सैंपल पेपर्स उपलब्ध करा रहे हैं।

CBSE Sample Papers for Class 10 Maths

नीचे दिए गए लिंक से सभी प्रमुख विषयों के लिए कक्षा 10 के नमूना पत्र और अंकन योजनाएं डाउनलोड करें:

SubjectSample Question PaperMarking Scheme
Mathematics (Standard)View/DownloadView/Download
Mathematics (Basic)View/DownloadView/Download
ScienceView/DownloadView/Download
Social ScienceView/DownloadView/Download
English (Language and Literature)View/DownloadView/Download
Hindi (Course A)View/DownloadView/Download
Hindi (Course B)View/DownloadView/Download
Computer ApplicationView/DownloadView/Download
Home ScienceView/DownloadView/Download

सीबीएसई नमूना पत्रों का महत्व

सीबीएसई नमूना पत्रों की मदद से छात्र बोर्ड परीक्षा में पूछे जाने वाले प्रारूप और प्रश्नों के प्रकार को समझ सकते हैं और वे बोर्ड प्रश्न पत्रों के डिजाइन को भी जान सकते हैं, जिसके अनुसार वे अपनी बोर्ड परीक्षा की तैयारियों के लिए एक प्रभावी योजना तैयार कर सकते हैं। नमूना प्रश्न पत्रों के साथ, सीबीएसई ने उन सभी विषयों के लिए अंकन योजनाएं भी जारी की हैं, जो पेपर में विभिन्न प्रश्नों के अंकों के विराम को बताते हैं और छात्रों के सुविधाजनक के लिए सुझाए गए उत्तर भी देते हैं।

प्रश्न पत्रों के पैटर्न में बदलाव जानने के लिए सीबीएसई नमूना पत्रों की जाँच करें

सीबीएसई नमूना पत्रों के माध्यम से जा रहे हैं, छात्रों को बोर्ड परीक्षा के लिए पेपर पैटर्न में किए गए बदलावों का पता चल जाएगा। इस साल, CBSE प्रश्न पत्रों में प्रत्येक अंक के साथ वस्तुनिष्ठ प्रकार के प्रश्नों की संख्या अधिक होगी। इन वस्तुनिष्ठ प्रकार के प्रश्नों में बहुविकल्पीय प्रकार के प्रश्न शामिल होंगे, कॉलम से मेल खाएँगे, रिक्त स्थान भरें, एक शब्द उत्तर प्रकार के प्रश्न, अभिकथन-कारण प्रकार के प्रश्न या कुछ चित्र आधारित प्रश्न। यह निश्चित रूप से लंबे व्यक्तिपरक प्रकार के प्रश्न लिखने के दबाव को कम करेगा जो अधिक समय का उपभोग करते थे। बोर्ड प्रश्न पत्रों के पैटर्न को जानने के लिए, यहां दिए गए CBSE क्लास 10 सैंपल पेपर्स का अच्छी तरह से विश्लेषण करें।

The post सीबीएसई कक्षा 10 बोर्ड परीक्षा 2020: नवीनतम नमूना पत्रों को डाउनलोड करें, सभी विषयों की अंकन योजना appeared first on Learn CBSE.

NCERT Solutions for Class 11 Maths Chapter 3 Miscellaneous Exercise

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Get Free NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Miscellaneous Exercise PDF in Hindi and English Medium. Trigonometric Functions Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. Trigonometric Functions Miscellaneous Exercise Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 3 Class 11 Trigonometric Functions Miscellaneous Exercise provided in NCERT Textbook.

Free download NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Miscellaneous Exercise PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 11 Maths Chapter 3 Miscellaneous Exercise

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Miscellaneous Ex
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Miscellaneous Ex

Miscellaneous Exercise chapter 3 class 11 Question 1:
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Miscellaneous Exercise chapter 3 class 11  Question 2:
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NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-24
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-25

त्रिकोणमितीय फलन विविध प्रश्नावली का हल हिंदी मे

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 1

प्रश्न 2.
सिद्ध कीजिए : (sin 3x + sin x) sin x + (cos 3x – cos x) cos x = 0.
हल :
बायाँ पक्ष = (sin 3x + sin x) sin x + (cos 3x – cos x) cos x
= sin 3x sin x + sin2x + cos 3x cos x – cos²x
= (cos 3x cos x + sin 3x sin x) – (cos² x – sin² x)
= cos 2x – cos 2x [cos (A – B) = cos A cos B + sin A sin B]
= 0
= दायाँ पक्ष।

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 4

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 5
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 5.1

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 6

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 7

निम्नलिखित प्रत्येक प्रश्न में sin \frac { x }{ 2 } , cos \frac { x }{ 2 } और tan \frac { x }{ 2 } ज्ञात कीजिए।

प्रश्न 8.
tan x = \frac { -4 }{ 3 } , x द्वितीय चतुर्थाश में हैं।
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 8
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 8.1
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 8.2

प्रश्न 9.
cosx = \frac { -1 }{ 2 } , x तृतीय चतुर्थाश में है।
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 9
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 9.1
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 9.2

प्रश्न 10.
sin x = \frac { 1 }{ 4 } , x द्वितीय चतुर्थाश में है।
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 10
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 10.1
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 10.2

The post NCERT Solutions for Class 11 Maths Chapter 3 Miscellaneous Exercise appeared first on Learn CBSE.

NCERT Solutions for Class 11 Maths Chapter 3 Ex 3.3

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Get Free NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 PDF in Hindi and English Medium. Trigonometric Functions Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. Trigonometric Functions Exercise 3.3 Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 3 Class 11 Trigonometric Functions Ex 3.3 provided in NCERT Textbook.

Free download NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 11 Maths Chapter 3 Ex 3.3

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3

Ex 3.3 Class 11 Question 1:

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-44
Ans:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-45
Ex 3.3 Class 11 Question 2:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-46
Ans:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-47
Ex 3.3 Class 11 Question 3:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-48
Ans:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-49
Ex 3.3 Class 11 Question 4:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-50
Ans:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-51
Ex 3.3 Class 11 Question 5:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-52
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NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-53
Ex 3.3 Class 11 Question 6:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-54
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NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-55
Ex 3.3 Class 11 Question 7:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-56
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NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-57
Ex 3.3 Class 11 Question 8:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-58
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NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-59
Ex 3.3 Class 11 Question 9:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-62
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NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-63
Ex 3.3 Class 11 Question 10:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-64
Ans:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-65
Ex 3.3 Class 11 Question 11:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-66
Ans:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-67
Ex 3.3 Class 11 Question 12:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-68
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NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-69
Ex 3.3 Class 11 Question 13:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-70
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NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-71
Ex 3.3 Class 11 Question 14:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-72
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NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-73
Ex 3.3 Class 11 Question 15:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-74
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NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-75
Ex 3.3 Class 11 Question 16:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-76
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NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-77
Ex 3.3 Class 11 Question 17:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-84
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NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-85
Ex 3.3 Class 11 Question 18:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-78
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NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-79
Ex 3.3 Class 11 Question 19:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-80
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NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-81
Ex 3.3 Class 11 Question 20:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-82
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NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-83
Ex 3.3 Class 11 Question 21:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-86
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NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-87
Ex 3.3 Class 11 Question 22:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-88
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NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-89
Ex 3.3 Class 11 Question 23:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-90
Ans:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-91
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-92
11 Maths Chapter 3 Exercise 3.3 Question 24:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-93
Ans:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-94
11 Maths Chapter 3 Exercise 3.3 Question 25:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-95
Ans:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-96

त्रिकोणमितीय फलन प्रश्नावली 3.3 का हल हिंदी में

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 1

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 2
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 2.1

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 3

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 4
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 4.1

प्रश्न 5.
मान ज्ञात कीजिए:
(i) sin (75°)
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 5
(ii) tan 15°
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 5.1

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 6

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 7

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 8

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 9

प्रश्न 10.
सिद्धि कीजिए : sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n + 2)x = cos x.
हल :
बायां पक्ष = sin (n + 1)x sin (n + 2) x + cos (n + 1)x cos (n + 2)x
मान लीजिए (n + 2)x = A, (n + 1) x = B
= sin B sin A + cos B cos A
= cos A cos B + sin A sin B
= cos (A – B)
= cos ((n + 2) x – (n + 1) x] [A और B के मान रख कर ]
= cos (nx + 2x – nx – x)
= cos x = दाया पक्ष

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 11

प्रश्न 12.
सिद्धि कीजिए : sin² 6x – sin² 4x = sin 2x sin 10x
हल :
बायां पक्ष = sin² 6x – sin² 4x
= sin (6x + 4x) sin (6x – 4x)
( सूत्र sin² A – sin² B = sin (A + B) sin (A – B) का प्रयोग करे]
sin 10x sin 2x
sin 2x sin 10x = दाया पक्ष

प्रश्न 13.
सिद्धि कीजिए : cos² 2x – cos² 6x = sin 4x sin 8x
हल :
बायां पक्ष = cos² 2x – cos² 6x
= 1 – sin² 2x – (1 – sin² 6x)
= sin² 6x – sin² 2x
sin² A – sin² B = sin (A + B) sin (A – B)
= sin² 6x – sin² 2x
= sin (6x + 2x) sin (6x – 2x)
= sin 8x sin 4x
= sin 4x sin 8x = दाया पक्ष

प्रश्न 14.
सिद्धि कीजिए : sin 2x + 2 sin 4x + sin 6x = 4 cos² x sin 4x
हल :
बायां पक्ष = sin 2x + 2 sin 4x + sin 6x
= (sin 2x + sin 6x) + 2 sin 4x
= 2 sin 4x cos 2x + 2 sin 4x
= 2 sin 4x (cos 2x + 1)
= 2 sin 4x (2 cos² x – 1 + 1)
= 4 sin 4x cos² x
= 4 cos² x sin 4x = दाया पक्ष

प्रश्न 15.
सिद्धि कीजिए : cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x)
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 15

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 16
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 16.1

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 17

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 18

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 19

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 20

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 21
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 21.1

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 22

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 23

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 24

UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.3 25

The post NCERT Solutions for Class 11 Maths Chapter 3 Ex 3.3 appeared first on Learn CBSE.

NCERT Solutions for Class 11 Maths Chapter 3 Ex 3.2

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Get Free NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 PDF in Hindi and English Medium. Trigonometric Functions Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. Trigonometric Functions Exercise 3.2 Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 3 Class 11 Trigonometric Functions Ex 3.2 provided in NCERT Textbook.

Free download NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCE1RT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 11 Maths Chapter 3 Ex 3.2

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2

Ex 3.2 Class 11 Question 1:

Calculate the values of five trigonometric func. if cosy = - \frac { 1 }{ 2 } and y lies in 3rd quadrant.
(i) sec y
(ii) sin y
(iii) cosec y
(iv) tan y
(v) cot y

Ans:
11 Maths Chapter 3 Exercise 3.3 solutions updated for up board
11 Maths Chapter 3 ex 3.3 ke hal hindi me
Ex 3.2 Class 11  Question 2:

Calculate the other five trigonometric function if we are given the values for sin y = \\ \frac { 3 }{ 5 } , where y lies in second quadrant.

Ans:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-23
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-24
Ex 3.2 Class 11  Question 3:

Find the values of other five trigonometric functions if coty=\\ \frac { 3 }{ 4 } , where y lies in the third quadrant.

Ans:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-26
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-27
Ex 3.2 Class 11 Question 4:

Find the values of other five trigonometric if secy=\\ \frac { 13 }{ 5 } , where y lies in the fourth quadrant.

Ans:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-29
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-30
Ex 3.2 Class 11 Question 5:

Find the values of other five trigonometric function if tan y = - \frac { 5 }{ 12 } and y lies in second quadrant.

Ans:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-32
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-33
Ex 3.2 Class 11 Question 6:

Calculate the value of trigonometric function sin 765°.

Ans:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-35
Ex 3.2 Class 11 Question 7:

Calculate the value of trigonometric function cosec [-1410°]

Ans:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-37
Ex 3.2 Class 11 Question 8:

Calculate the value of the trigonometric function tan \frac { 19\pi }{ 3 } .

Ans:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-43
Ex 3.2 Class 11 Question 9:

Calculate the value of the trigonometric function sin -\frac { 11\pi }{ 3 } .

Ans:
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-39
Ex 3.2 Class 11 Question 10:

Calculate the value of the trigonometric function cot -\frac { 15\pi }{ 4 }

Ans:

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions-41

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions in Hindi Medium

निम्नलिखित प्रश्नों में से पाँच अन्य त्रिकोणमितीय फलनों का मान ज्ञात कीजिए।

प्रश्न 1.
cos x = \frac { -1 }{ 2 } , x तीसरे चतुर्थाश में स्थित है।
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.2 1
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.2 1.1

प्रश्न 2.
sin x = \frac { 3 }{ 5 } , x दूसरे चतुर्थाश में स्थित है।
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.2 2
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.2 2.1

प्रश्न 3.
cot x = \frac { 3 }{ 4 } , x तृतीय चतुर्थाश में स्थित है।
हलः
cot x = \frac { 3 }{ 4 }
OA = 3 इकाई
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.2 3

प्रश्न 4.
sec x = \frac { 13 }{ 5 } , x चतुर्थ चतुर्थाश में स्थित है।
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.2 4
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.2 4.1

प्रश्न 5.
tan x = \frac { -5 }{ 12 } , x दुसरे चतुर्थाश में स्थित है।
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.2 5
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.2 5.1

प्रश्न संख्या 6 से 10 तक के मान ज्ञात कीजिए:
प्रश्न 6.
sin 765°
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.2 6

प्रश्न 7.
cosec (-1410)°
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.2 7

प्रश्न 8.
tan \frac { 19\pi }{ 3 }
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.2 8

प्रश्न 9.
sin (\frac { -11\pi }{ 3 }).
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.2 9
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.2 9.1

प्रश्न 10.
cot (\frac { -15\pi }{ 4 }).
UP Board Solutions for Class 11 Maths Chapter 3 Trigonometric Functions 3.2 10

 

 

The post NCERT Solutions for Class 11 Maths Chapter 3 Ex 3.2 appeared first on Learn CBSE.

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Miscellaneous Exercise

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Get Free NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Miscellaneous Exercise PDF in Hindi and English Medium. Complex Numbers and Quadratic Equations Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. Complex Numbers and Quadratic Equations Miscellaneous Exercise Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 5 Class 11 Complex Numbers and Quadratic Equations Miscellaneous Exercise provided in NCERT Textbook.

Free download NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Miscellaneous Exercise PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 11 Maths Chapter 5 Miscellaneous Exercise

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Miscellaneous Exercise
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Miscellaneous Exercise

NCERT Solutions for Class 11 Maths Chapter 5 Miscellaneous Solutions

Miscellaneous Exercise Chapter 5 Class 11 Question 1:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-65
Ans:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-66
Miscellaneous Exercise Chapter 5 Class 11 Question 2:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-67
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NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-68
Miscellaneous Exercise Chapter 5 Class 11 Question 3:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-69
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NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-70
Miscellaneous Exercise Chapter 5 Class 11 Question 4:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-71
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NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-72
Miscellaneous Exercise Chapter 5 Class 11 Question 5:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-73
Ans:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-74
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-75
Miscellaneous Exercise Chapter 5 Class 11 Question 6:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-76
Ans:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-77
Miscellaneous Exercise Chapter 5 Class 11 Question 7:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-78
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NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-79
Miscellaneous Exercise Chapter 5 Class 11 Question 8:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-80
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NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-81
Miscellaneous Exercise Chapter 5 Class 11 Question 9:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-82
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NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-83
Miscellaneous Exercise Chapter 5 Class 11 Question 10:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-84
Ans:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-85
Miscellaneous Exercise Chapter 5 Class 11 Question 11:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-86
Ans:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-87
Chapter 5 Maths Class 11 Miscellaneous Solutions Question 12:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-88
Ans:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-89
Miscellaneous Exercise Chapter 5 Class 11 Question 13:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-90
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NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-91
Class 11 Maths Chapter 5 Miscellaneous Exercise Question 14:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-92
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NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-93
Class 11 Maths Chapter 5 Miscellaneous Exercise Question 15:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-94
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NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-95
Class 11 Maths Chapter 5 Miscellaneous Exercise Question 16:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-96
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NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-97
Class 11 Maths Chapter 5 Miscellaneous Exercise Question 17:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-98
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NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-99
Class 11 Maths Chapter 5 Miscellaneous Exercise Question 18:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-100
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NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-101
Class 11 Maths Chapter 5 Miscellaneous Exercise Question 19:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-102
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NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-103
Class 11 Maths Chapter 5 Miscellaneous Exercise Question 20:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-104
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NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-105

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations (सम्मिश्र संख्याएँ और द्विघातीय समीकरण) Hindi medium Miscellaneous Exercise

NCERT Solutions for class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations
NCERT Solutions for Class 11 Maths Chapter 5 सम्मिश्र संख्याएँ और द्विघातीय समीकरण
NCERT Solutions for Class 11 Maths Chapter 5 Miscellaneous Exercise in english medium pdf
NCERT Solutions for Class 11 Maths Chapter 5 Miscellaneous Exercise for cbse and up board high school
NCERT Solutions for Class 11 Maths Chapter 5 Miscellaneous Exercise in Hindi medium for CBSE, Gujrat and up board students
NCERT Solutions for Class 11 Maths Chapter 5 Miscellaneous Exercise in hindi updated for 2018-19.
NCERT Solutions for Class 11 Maths Chapter 5 Miscellaneous Exercise सम्मिश्र संख्याएँ और द्विघातीय समीकरण
NCERT Solutions for Class 11 Maths Chapter 5 Miscellaneous Exercise in PDF
NCERT Solutions for Class 11 Maths Chapter 5 Miscellaneous Exercise in Hindi
NCERT Solutions for Class 11 Maths Chapter 5 Miscellaneous Exercise
Class 11 Maths Chapter 5 Miscellaneous Exercise in Hindi
Chapter 5 Miscellaneous Exercise in Hindi medium
Chapter 5 Miscellaneous Exercise
NCERT Solutions for Class 11 Maths Chapter 5
11 Maths Chapter 5 Miscellaneous Exercise in Hindi

NCERT Solutions for Class 11 Maths All Chapters

The post NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Miscellaneous Exercise appeared first on Learn CBSE.

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3

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Get Free NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 PDF in Hindi and English Medium. Complex Numbers and Quadratic Equations Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. Complex Numbers and Quadratic Equations Ex 5.3 Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 5 Class 11 Complex Numbers and Quadratic Equations Ex 5.3 provided in NCERT Textbook.

Free download NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3

NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5.3

Ex 5.3 Class 11 Question 1:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-45
Ans:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-46
Ex 5.3 Class 11 Question 2:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-47
Ans:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-48
ch 5 Maths Class 11 Ex 5.3 Question 3:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-49
Ans:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-50
ch 5 Maths Class 11 Ex 5.3 Question 4:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-51
Ans:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-52
ch 5 Maths Class 11 Ex 5.3 Question 5:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-53
Ans:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-54
ch 5 Maths Class 11 Ex 5.3 Question 6:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-55
Ans:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-56
ch 5 Maths Class 11 Ex 5.3 Question 7:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-57
Ans:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-58
ch 5 Maths Class 11 Ex 5.3 Question 8:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-59
Ans:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-60
ch 5 Maths Class 11 Ex 5.3  Question 9:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-61
Ans:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-62
ch 5 Maths Class 11 Ex 5.3 Question 10:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-63
Ans:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-64

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations (सम्मिश्र संख्याएँ और द्विघातीय समीकरण) Hindi medium Ex 5.3

NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5.3 सम्मिश्र संख्याएँ और द्विघातीय समीकरण
Class 11 Maths Chapter 5 Exercise 5.3 for cbse and up board high school
NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5.3 in PDF
Class 11 Maths Chapter 5 Exercise 5.3 in Hindi medium for CBSE,
NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5.3 in Hindi
NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5.3 for cbse and up board high school
NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5.3 in Hindi medium for CBSE, Gujrat and up board students

NCERT Solutions for Class 11 Maths All Chapters

The post NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 appeared first on Learn CBSE.

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.2

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Get Free NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.2 PDF in Hindi and English Medium. Complex Numbers and Quadratic Equations Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. Complex Numbers and Quadratic Equations Ex 5.2 Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 5 Class 11 Complex Numbers and Quadratic Equations Ex 5.2 provided in NCERT Textbook.

Free download NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.2 PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 11 Maths Chapter 5 Ex 5.2

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.2
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.2

NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5.2

Exercise 5.2 Class 11 Question 1:
NCERT Solutions for Class 11 Maths Chapter 5 Mis. 5
Ans:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-30
Exercise 5.2 Class 11 Question 2:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-31
Ans:
NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations-32
Exercise 5.2 Class 11 Question 3:
NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5.1 in Hindi guide free
Ans:
11 Maths Chapter 5 Exercise 5.2 solutions in Hindi
Exercise 5.2 Class 11 Question 4:
11 Maths Chapter 5 Exercise 5.2 solutions in Hindi for up board
Ans:
11 Maths Chapter 5 Exercise 5.2 solutions in Hindi for intermediate first year
Exercise 5.2 Class 11 Question 5:
11 Maths Chapter 5 Exercise 5.2 solutions in Hindi intermediate pdf
Ans:
Class 11 Maths Chapter 5 Exercise 5.3 sols in Hindi
Ex 5.2 Class 11 Question 6:
Class 11 Maths Chapter 5 Exercise 5.3 sols in Hindi pdf for inter
Ans:
Class 11 Maths Chapter 5 Exercise 5.3 sols in Hindi all question answers
Ex 5.2 Class 11 Question 7:
NCERT Solutions for Class 11 Maths Chapter 5 Miscellaneous Exercise 5 in Hindi
Ans:
NCERT Solutions for Class 11 Maths Chapter 5 Miscellaneous Exercise 5
Ex 5.2 Class 11 Question 8:
NCERT Solutions for Class 11 Maths Miscellaneous 5
Ans:
misc. question ch. 5 class 11

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations (सम्मिश्र संख्याएँ और द्विघातीय समीकरण) Hindi medium Ex 5.2

NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5.2 सम्मिश्र संख्याएँ और द्विघातीय समीकरण in PDF
NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5.2 in PDF
NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5.2 in Hindi
NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5.2 for cbse and up board high school
NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5.2 in Hindi medium for CBSE, Gujrat and up board students
NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5.2 in hindi updated for 2018-19.
NCERT Solutions for Class 11 Maths Chapter 5 सम्मिश्र संख्याएँ और द्विघातीय समीकरण

NCERT Solutions for Class 11 Maths All Chapters

The post NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.2 appeared first on Learn CBSE.

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3

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Get Free NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 PDF in Hindi and English Medium. Linear Inequalities Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. Linear Inequalities Ex 6.3 Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 6 Class 11 Linear Inequalities Ex 6.3 provided in NCERT Textbook.

Free download NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 11 Maths Chapter 6 Ex 6.3

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3

Question 1:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-73
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-74
Question 2:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-75
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-76
Question 3:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-77
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-78
Question 4:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-79
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-80
Question 5:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-81
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-82
Question 6:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-83
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-84
Question 7:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-85
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-86
Question 8:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-87
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-88
Question 9:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-89
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-90
Question 10:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-91
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-92
Question 11:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-93
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-94
Question 12:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-95
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-96
Question 13:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-97
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-98
Question 14:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-99
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-100
Question 15:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-101
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-102

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities (रैखिक असमिकाएँ) Hindi medium Ex 6.3

Class 11 Maths Chapter 6 Exercise 6.3 Linear Inequalities solutions in Hindi
Class 11 Maths Chapter 6 Exercise 6.3 Linear Inequalities solutions in Hindi for up board
Class 11 Maths Exercise 6.3 Linear Inequalities in Hindi Medium
11 Maths Exercise 6.3 Lines and angles in Hindi Medium in PDF
NCERT Solutions for class 11 Maths Chapter 6 Exercise 6.3 in English
NCERT Solutions for class 11 Maths Chapter 6 Exercise 6.3 for cbse and gujrat board
11 Maths Exercise 6.3 Lines and angles solutions in Hindi
NCERT Solutions for class 11 Maths Chapter 6 Exercise 6.3 in English
NCERT Solutions for class 11 Maths Chapter 6 Exercise 6.3 for cbse and gujrat board
11 Maths Exercise 6.3 Linear Inequalities solutions in Hindi
11 Maths Exercise 6.3 Linear Inequalities solutions in Hindi PDF
Class 11 Maths Chapter 6 Exercise 6.3 Linear Inequalities solutions in Hindi for up board
Class 11 Maths Exercise 6.3 Lines and angles in Hindi Medium
11 Maths Exercise 6.3 Lines and angles in Hindi Medium in PDF
Class 11 Maths Exercise 6.3
Exercise 6.3 Linear Inequalities solutions
11 Maths Exercise 6.3

The post NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.3 appeared first on Learn CBSE.

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Exercise

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Get Free NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Exercise PDF in Hindi and English Medium. Linear Inequalities Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. Linear Inequalities Miscellaneous Exercise Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 6 Class 11 Linear Inequalities Miscellaneous Exercise provided in NCERT Textbook.

Free download NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Exercise PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 11 Maths Chapter 6 Miscellaneous Exercise

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Ex

Question 1:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-103
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-104

Question 2:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-105

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-106

Question 3:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-107

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-108

Question 4:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-109

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-110

Question 5:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-111

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-112

Question 6:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-113

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-114

Question 7:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-115

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-116

Question 8:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-117

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-118

Question 9:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-119

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-120

Question 10:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-121

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-122

Question 11:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-123

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-124

Question 12:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-125

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-126

Question 13:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-127

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-128

Question 14:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-129

Ans:

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-130

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities (रैखिक असमिकाएँ) Miscellaneous Exercise Hindi medium

Class 11 Maths Chapter 6 Miscellaneous Exercise Linear Inequalities solutions in Hindi
Class 11 Maths Chapter 6 Miscellaneous Exercise Linear Inequalities solutions in Hindi for up board
Class 11 Maths Miscellaneous Exercise Linear Inequalities in Hindi Medium
11 Maths Miscellaneous Exercise Lines and angles in Hindi Medium in PDF
NCERT Solutions for class 11 Maths Chapter 6 Miscellaneous Exercise for cbse and gujrat board
11 Maths Miscellaneous Exercise Linear Inequalities solutions in Hindi
Class 11 Maths Chapter 6 Miscellaneous Exercise Linear Inequalities solutions in Hindi for up board

Class 11 Maths Miscellaneous Exercise Lines and angles in Hindi Medium
11 Maths Miscellaneous Exercise Lines and angles in Hindi Medium in PDF

The post NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Miscellaneous Exercise appeared first on Learn CBSE.

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2

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Get Free NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 PDF in Hindi and English Medium. Linear Inequalities Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. Linear Inequalities Ex 6.2 Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 6 Class 11 Linear Inequalities Ex 6.2 provided in NCERT Textbook.

Free download NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 11 Maths Chapter 6 Ex 6.2

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2

Question 1:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-53
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-54
Question 2:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-55
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-56
Question 3:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-57
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-58
Question 4:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-59
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-60
Question 5:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-61
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-62
Question 6:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-63
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-64
Question 7:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-65
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-66
Question 8:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-67
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-68
Question 9:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-69
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-70
Question 10:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-71
Ans:
NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities-72

NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities (रैखिक असमिकाएँ) Hindi medium Ex 6.2

NCERT Solutions for class 11 Maths Chapter 6 Exercise 6.2 for cbse and gujrat board
11 Maths Exercise 6.2 Lines and angles solutions in Hindi
Class 11 Maths Chapter 6 Exercise 6.2 Linear Inequalities solutions in Hindi
Class 11 Maths Chapter 6 Exercise 6.2 Linear Inequalities solutions in Hindi for up board
Class 11 Maths Exercise 6.2 Linear Inequalities in Hindi Medium
11 Maths Exercise 6.2 Lines and angles in Hindi Medium in PDF
NCERT Solutions for class 11 Maths Chapter 6 Exercise 6.2 in English

The post NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities Ex 6.2 appeared first on Learn CBSE.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2

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Get Free NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 PDF in Hindi and English Medium. Binomial Theorem Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. Binomial Theorem Ex 8.2 Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 8 Class 11 Binomial Theorem Ex 8.2 provided in NCERT Textbook.

Free download NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 11 Maths Chapter 8 Exercise.8.2

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2

Question-1

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-1

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-2

Question-2

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-3

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-4

Question-3

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-5

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-6

Question-4

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-7

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-8

Question-5

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-9

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-10

Question-6

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-11

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-12

Question-7

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-13

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-14

Question-8

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-15

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-16

Question-9

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-17

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-18

Question-10

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-19

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-20
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-21

Question-11

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-22

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-23
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-24

Question-12

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-25

Ans.

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem-26

NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem (द्विपद प्रमेय) Hindi medium Ex 8.2

11 Maths solutions exercise 8.2 Binomial Theorem
11 Maths chapter 8 Exercise 8.2 solutions in Hindi medium
11 Maths Exercise 8.2 solutions updated for UP Board 2018-2019.
11 Maths Exercise 8.2 solutions in hindi PDF
11 Maths Exercise 8.2 solutions for CBSE and UP Board students 2018-2019.
NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem
NCERT Solutions for Class 11 Maths Chapter 8 Exercise 8.2

NCERT Solutions for Class 11 Maths All Chapters

The post NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2 appeared first on Learn CBSE.

NCERT Solutions for Class 11 Maths Chapter 10 Ex 10.2

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Get Free NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2. Class 11 Maths NCERT Solutions are extremely helpful while doing homework. Exercise 10.2 Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 10 Maths Straight Lines Class 11 Exercise 10.2 Provided in NCERT Textbook.

You can also save the NCERT Solutions Class 11 Maths images and take the print out to keep it handy for your exam preparation.

Topics and Sub Topics in Class 11 Maths Chapter 10 Straight Lines:

Section NameTopic Name
10Straight Lines
10.1Introduction
10.2Slope of Line
10.3Various Forms of the Equation of Line
10.4General Equation of Line
10.5Distance of a Point From a Line

NCERT Solutions for Class 11 Maths Chapter 10 Ex 10.2

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 are part of NCERT Solutions for Class 11 Maths. Here we have given Class 11 Maths NCERT Solutions Straight Lines Exercise 10.2.

Ex 10.2 Class 11 Maths Question-1
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines-1
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines-2

Ex 10.2 Class 11 Maths Question-2
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines-3
Ans.
Class 11 Maths NCERT Solutions Chapter 10 Straight Lines-4

Ex 10.2 Class 11 Maths Question-3
Class 11 Maths NCERT Solutions Chapter 10 Straight Lines-5
Ans.
Class 11 Maths NCERT Solutions Chapter 10 Straight Lines-6

Ex 10.2 Class 11 Maths Question-4
Class 11 Maths NCERT Solutions Chapter 10 Straight Lines-7
Ans.
Class 11 Maths NCERT Solutions Chapter 10 Straight Lines Exercise 10.2 8

Ex 10.2 Class 11 Maths Question-5
Maths NCERT Solutions Class 11 Chapter 10 Straight Lines Exercise 10.2 9
Ans.
Maths NCERT Solutions Class 11 Chapter 10 Straight Lines Exercise 10.2 10

Ex 10.2 Class 11 Maths Question-6
NCERT Class 11 Maths Solutions Chapter 10 Straight Lines Exercise 10.2 11
Ans.
NCERT Class 11 Maths Solutions Chapter 10 Straight Lines Exercise 10.2 12

Ex 10.2 Class 11 Maths Question-7
NCERT Solutions Class 11 Maths Chapter 10 Straight Lines Exercise 10.2 13
Ans.
NCERT Solutions Class 11 Maths Chapter 10 Straight Lines Exercise 10.2 14

Ex 10.2 Class 11 Maths Question-8
NCERT Solutions Class 11 Maths Chapter 10 Straight Lines Exercise 10.2 15
Ans.
NCERT Solutions Class 11 Maths Chapter 10 Straight Lines Exercise 10.2 16

Ex 10.2 Class 11 Maths Question-9
Maths Class 11 NCERT Solutions Chapter 10 Straight Lines Exercise 10.2 17
Ans.
Maths Class 11 NCERT Solutions Chapter 10 Straight Lines Exercise 10.2 18
Maths Class 11 NCERT Solutions Chapter 10 Straight Lines Exercise 10.2 19

Ex 10.2 Class 11 Maths Question-10
NCERT Solution for Class 11 Maths Chapter 10 Straight Lines Exercise 10.2 20
Ans.
NCERT Solution for Class 11 Maths Chapter 10 Straight Lines Exercise 10.2 21

Ex 10.2 Class 11 Maths Question-11
NCERT Solution Class 11 Maths Chapter 10 Straight Lines Exercise 10.2 22
Ans.
NCERT Solution Class 11 Maths Chapter 10 Straight Lines Exercise 10.2 23

Ex 10.2 Class 11 Maths Question-12
Class 11 Maths NCERT Solution Chapter 10 Straight Lines Exercise 10.2 24
Ans.
Class 11 Maths NCERT Solution Chapter 10 Straight Lines Exercise 10.2 25

Ex 10.2 Class 11 Maths Question-13
Class 11 Maths NCERT Solution Chapter 10 Straight Lines Exercise 10.2 26
Ans.
Maths Class 11 NCERT Solution Chapter 10 Straight Lines 10.2-27
Maths Class 11 NCERT Solution Chapter 10 Straight Lines 10.2-28

Ex 10.2 Class 11 Maths Question-14
Maths Class 11 NCERT Solution Chapter 10 Straight Lines 10.2-29
Ans.
NCERT Maths Class 11 Solution Chapter 10 Straight Lines 10.2-30

Ex 10.2 Class 11 Maths Question-15
NCERT Maths Class 11 Solution Chapter 10 Straight Lines 10.2-31
Ans.
NCERT Maths Class 11 Solution Chapter 10 Straight Lines 10.2-32

Ex 10.2 Class 11 Maths Question-16
CBSE Class 11 Maths NCERT Solutions Chapter 10 Straight Lines 10.2-33
Ans.
CBSE Class 11 Maths NCERT Solutions Chapter 10 Straight Lines 10.2-34

Ex 10.2 Class 11 Maths Question-17
CBSE Class 11 Maths NCERT Solutions Chapter 10 Straight Lines 10.2-35
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines 10.2-36

Ex 10.2 Class 11 Maths Question-18
LearnCBSE Class 11 NCERT Solutions Maths Chapter 10 Straight Lines 10.2-37
Ans.
LearnCBSE Class 11 NCERT Solutions Maths Chapter 10 Straight Lines 10.2-38
LearnCBSE Class 11 NCERT Solutions Maths Chapter 10 Straight Lines Ex 10.2 39

Ex 10.2 Class 11 Maths Question-19
Solution of Class 11 NCERT Maths Chapter 10 Straight Lines Ex 10.2 40
Ans.
Class 11 Maths NCERT Solution Chapter 10 Straight Lines Ex 10.2 41
Class 11 Maths NCERT Solution Chapter 10 Straight Lines Ex 10.2 42

Ex 10.2 Class 11 Maths Question-20
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2 43
Ans.
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.2-44

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines (सरल रेखाएँ) Hindi Medium Ex 10.2

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines (सरल रेखाएँ)
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Exercise 10.2NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Exercise 10.2
11 Maths Exercise 10.2
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Exercise 10.2 Hindi Medium
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Exercise 10.2 in Hindi Medium
11 Maths Exercise 10.2 in Hindi
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Exercise 10.2 in pdf form free download
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Exercise 10.2 in english medium
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Class 11 Maths Chapter 10 Straight Lines Exercise
Chapter 10 Straight Lines Exercise 10.2
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11 Maths Exercise 10.2 free
11 Maths Exercise 10.2 in hindi medium
11 Maths Exercise 10.2 for gujrat board
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Maths NCERT Solutions Class 11 Maths Chapter 10 Exercise.10.2

 Q-1. Write all the possible equations for the two axis, which is x- axis and y- axis.

Q-3. Write the equation for the line which passes through the point (0, 0) with having slope S.

Q-4. Write the equation for the line which passes through ( 3, 3√3 ) which is inclined on x- axis at an angle 75.

Q-5. Write the equation for the line which intersects x – axis at a distance 4 units away from the left side of the origin having slope -3.

Q-6. Write the equation for the line which intersects the y – axis at a distance 3 units above the origin which makes an angle 60 along the positive direction of the corresponding axis, i.e., x- axis.

Q-7. Write the equation of the line passing through the two points (-2, 2) and (3, -5).

Q-8. Write the equation for the line which is at a perpendicular distance of 7 units from the point (0, 0) and the perpendicular makes an angle of 45 along the positive x- axis.

Q-9. Consider a triangle ABC whose vertices are A (3, 2), B (-3, 4) and C (5, 6). Write the equation for the median through one of the vertex of the triangle say, C.

Q-10. Get the equation for the line which is passing through (-4, 5) and which is perpendicular to the line passing through two points (3, 6) and (-4, 7).

Q-11. Consider a line which is perpendicular to the line segment joining the two points (2, 0) and (3, 4) dividing it in 1 : p ratio. Find the equation for such a line.

Q-12. What will be the equation for the line which cuts off intercepts equally on the co-ordinate axes and which passes through the point (3, 4).

Q-13. A line is passing through (3, 3) and making intercepts on the coordinate axes. The sum of the two intercepts is 12. Find the equation of the line.

Q-15. What will be the equation of the line perpendicular to the line from the origin meets at       (-3, 10)?

Q-16. Consider a copper rod having length L (in centimeters) which is a linear function of the Celsius temperature which is C. Express L in terms of C, for an experiment. Assume that, L = 127.952 when C = 24, and L = 128.987 when C = 114.

Q-17. A milk store owner observed that, he can sell at least 1000 liters of milk every week at a price of Rs. 15/liter and also, 1240 liters of milk every week at a price of Rs. 17/liter. Consider a linear relation between the demand and estimated selling price, find how many liters would he will sell every week at a cost of Rs.18/liters?

Q-19. The point R (m, n) divides the line segment PQ in the ratio of 2: 3 between both the axes. What will be the equation of the line?

Q-20. Show that the three points (4, 1), (-3, -3) and (11, 5) are collinear by using the concept of the equation of a line.

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