CBSE Previous Year Question Papers Class 10 Maths SA2 Outside Delhi – 2012

CBSE Previous Year Question Papers Class 10 Maths SA2 Outside Delhi – 2012

Time allowed: 3 hours                                                                                           Maximum marks: 90

GENERAL INSTRUCTIONS:

1. All questions are compulsory.
2. The Question Taper consists of 31 questions divided into four Sections A, B. C. and D.
3. Section A contains 4 questions of 1 mark each. Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains 11 questions of 4 marks each.
4.  Use of calculators is not permitted.

SET I

SECTION A
Questions number 1 to 4 carry 1 mark each.
Question.1 In Figure 1, AP, AQ and BC are tangents to the circle. If AB = 5 cm, AC = 6 cm and BC = 4 cm, then calculate the length of AP (in cm).

Solution.

Question.2 The circumference of a circle is 22 cm. Calculate the area of its quadrant (in cm²).
Solution.

Question.3 A solid right circular cone is cut into two parts at the middle of its height by a plane parallel to its base. Find the ratio of the volume of the smaller cone to the whole cone.
Solution.

Question.4. Find the distance of the point (-3, 4) from the .Y-axis.
Solution.

SECTION B
Questions number 5 to 10 carry 2 marks each.
Question.5 The 7^th term of an A.P. is 20 and its 13^th term is 32. Find the A.P.
Solution.

Question.6 PQRS is a diameter of a circle of radius 6 cm. The equal lengths PQ, QR and RS are drawn on PQ and QS as diameters, as shown in Fig. 2. Find the perimeter of the shaded region.

Solution.

Question.7 Find the value of for which the roots of the equation px(x-2)+6 = 0 are equal
Solution.

Question.8 How many two-digits number are divisible by 3?
Solution.

Question.9 In figure 3, a right triangle ABC, circumscribes a circle of radius r if AB and BC are of lenths 8cm and 6cm respectively, find the value of r

Solution.

Question.10 Prove that the tangents drawn at the ends of a diameter of a circle of parallel
Solution.

SECTION C
Question.11 In figure 4, ABCD is a square of side 4 cm. A quadrant of a circle of radius 1 cm is drawn at each vertex of the square and a circle of diameter 2 cm is also drawn. Find the area of shaded region. (Use π = 3.14)

Or
From a rectangular sheet of paper ABCD with AB = 40 cm and AD = 28 cm, a semi-circular
portion with BC as diameteris cut off. Find the area of remining paper (use π = 22/7)
Solution.

Question.12 A solid sphere of radius 10.5 cm is melted and recast into smeller solid cones, each of radius 3.5 cm and hight 3 cm. Find the number of cones so formed. (Use π = 22/7)
Solution.

Question.13 Find the value of k, if the point P(2, 4) is equidistant from the points A(5, k) and B(k, 7).
Solution.

Question.14 A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability of getting
(i) a red king. (ii) a queen or a jack.
Solution.

Question.15 Solve the following quadratic equation for x: x² – 4ax – b² + 4a² = 0
Or
If the sum of two natural numbers is 8 and their product is 15, find the numbers.
Solution.

Question.16Find the sum of all multiples of 7 lying between 500 and 900.
Solution.

Question.17 Draw a triangle ABC with BC = 7 cm, ∠B = 45° and ∠C = 60°. Then construct another
triangle, whose sides are 3/5 times the corresponding sides of ΔABC.
Solution.

Question.18 In Figure 5, a circle is inscribed in a triangle PQR with PQ = 10 cm, QR = 8 cm and PR = 12 cm. Find the lengths of QM, RN and PL.

Solution.

Question.19 In Figure 6, O is the centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of the shaded region. (Use π = 3.14)

Or
In Figure 7, find the area of the shaded region, if ABCD is a square of side 14 cm and APD and BPC are semicircles.

Solution.

Question.20 An icecream seller sells his icecreams in two ways:
(A) In a cone of r = 5 cm, h- 8 cm
(B) In a cup in shape of cylinder with r = 5 cm, h = 8 cm He charges the same price for both but prefers to sell his icecream in a cone.
(a) Find the volume of the cone and the cup.
(b) Which out of the two has more capacity?
(c) By choosing a cone, which value is not being followed by the icecream seller?

Solution.

SECTION D
Questions number 21 to 31 carry 4 marks each.
Question.21 The angles of depression of the top and bottom of a tower as seen from the top of a 60 √3 m high cliff are 45° and 60° respectively. Find the height of the tower.
Solution.

Question.22 Find the coordinates of a point P, which lies on the line segment joining the points A(-2, -2)
and B(2, -4) such that AP = 3/7 AB.
Or
Find the area of the quadrilateral ABCD whose vertices are A(-3, -1), B(-2, -4), C(4, -1) and D(3, 4).
Solution.

Question. 23 If the points A(x, y), B(3, 6) and C(-3, 4) are collinear, show that x – 3y + 15 = 0.
Solution.

Question.24 All kings, queens and aces are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn from it. Find the probability that the drawn card is (i) a black face card. (ii) a red card.
Solution.

Question.25 The numerator of a fraction is 3 less than its denominator. If 1 is added to the denominator, the fraction is decreased by . Find the fraction.
Or
In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100 km/h and time increased by 30 minutes. Find the original duration of the flight.
Solution.

Question.26 Find the common difference of an A.P. whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.
Solution.

Question.27 Prove that the length of tangents drawn from an external point to a circle are equal.
Solution.

Question.28 A hemispherical tank, full of water, is emptied by a pipe at the rate of y litres per sec.
How much time will it take to empty half the tank if the diameter of the base of the tank is 3 m?
Or
A drinking glass is in the shape of the frustum of a cone of height 14 cm. The diameters of
its two circular ends are 4 cm and 2 cm. Find the capacity of the glass. [Use π = 22/7 ]
Solution.

Question.29 A military tent of height 8.25 m is in the form of a right circular cylinder of base diameter 30 m and height 5.5 m surmounted by a right circular cone of same base radius. Find the length of the canvas used in making the tent, if the breadth of the canvas is 1.5 m.
Solution.

Question.30 The angles of elevation and depression of the top and bottom of a light-house from the top of a 60 m high building are 30° and 60° respectively. Find
(i) the difference between the heights of the light-house and the building.
(ii)the distance between the light-house and tire building.
Solution.

Question.31 If the centroid of ΔABC, in which A (a, b), B(F, c), C(c, a) is at the origin, then calculate the value of (a³ + b³ + c³).
Solution.

SET II

Note: Except for the following questions, all the remaining questions have been asked in Set-I.
Question.13 Find the value of k for which the roots of the equation kx (3x – 4) + 4 = 0, are equal.
Solution.

Question.14 How many three-digit numbers are divisible by 11?
Solution.

Question.21 A box contains 70 cards numbered from 1 to 70. If one card is drawn at random from the box, find the probability that it bears
(i) a perfect square number. (ii) a number divisible by 2 and 3.
Solution.

Question.22 Find the value of k, for which the points A(6, -1), B(k, -6) and C(0, -7) are collinear.
Solution.

Question.23 Draw a right triangle in which the sides (other than hypotenuse) are of lengths 8 cm and 6
cm. Then construct another triangle whose sides are 3/4 times the corresponding sides of the given triangle.
Solution.

Question.24 Find the sum of all multiples of 8 lying between 201 and 950.
Solution.

Question.29 If the sum of the first 7 terms of an A.P. is 119 and that of the first 17 terms is 714, find the sum of its first n terms.
Solution.

Question.30 Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
Solution.

SET III

Note: Except for the following questions, all the remaining questions have been asked in Set-I and Set-11.
Question.13 Find the value of m for which the roots of the equation
mx (6x + 10) + 25 = 0, are equal.
Solution.

Question.14 Flow many three-digit numbers are divisible by 12?
Solution.

Question.21 Find the sum of all multiples of 9 lying between 400 and 800.
Solution.

Question.22 Find the value of p, if the points A(l, 2), B(3, p) and C(5, -4) are collinear.
Solution.

Question.23 Red kings and black aces are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn from it. Find the probability that the drawn card is
(i) a black face card. (ii) a red card.
Solution.

Question.24 Draw a triangle with sides 5 cm, 6 cm and 7 cm. Then construct another triangle whose
sides are 2/3 times the corresponding sides of the first triangle.
Solution.

Question.30 A sum of Rs 1,600 is to be used to give ten cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.
Solution.

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