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

**Time allowed: 3 hours Maximum marks: 90**

**GENERAL INSTRUCTIONS:**

**All questions are compulsory.****The Question Taper consists of 31 questions divided into four Sections A, B. C. and D.****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.****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 cm ^{2}).**

**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: x ^{2} – 4ax – b^{2} + 4a^{2} = 0**

**Or**

**If the sum of two natural numbers is 8 and their product is 15, find the numbers.**

**Solution.**

**Question.16**

**Find 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 (a ^{3} + b^{3} + c^{3}).**

**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.**