**CBSE Previous Year Question Papers Class 10 Maths SA2 Outside Delhi – 2013**

**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.l In Fig. 1, a circle is inscribed in a quadrilateral ABCD touching its sides AB, BC, CD and AD at P, Q, R and S respectively. If the radius of the circle is I Q cm, BC = 38 cm, PB = 27 cm and AD ⊥ CD, then calculate the length of CD.**

**Solution.**

**Question.2 A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then calculate the height of the wall.**

** Solution.**

**Question.3 A box contains cards numbered 6 to 50. A card is drawn at random from the box. Calculate the probability, that the drawn card has a number which is a perfect square.**

** Solution.**

**Question.4 If n is taken as 22/7 calculate the distance (in metres) covered by a wheel of diameter 35 cm, in one revolution.**

** Solution.**

**SECTION B**

**Questions number 5 to 10 carry 2 marks each.**

** Question.5 Solve the following for x:**

**Solution.**

**Question.6 Find the number of all three-digit natural numbers which are divisible by 9.**

** Solution.**

**Question.7 In Fig. 2, two circles touch each other at the point C. Prove that the common tangent to the circles at C, bisects the common tangent at P and Q.**

**Solution.**

**Question.8 In Fig. 3, a quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.**

**Solution.**

**Question.9 Two coins are tossed simultaneously. Find the probability of getting at least one head.**

** Solution.**

**Question.10 The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.**

** Solution.**

**SECTION C**

**Questions number 11 to 20 carry 3 marks each.**

** Question.11 For what values of k, are the roots of the quadratic equation:**

** (k + 4) x ^{2}+ (k + l) x + 1 = 0 equal?**

**Solution.**

**Question.12 The 19th term of an AP is equal to three times its 6th term. If its 9th term is 19, find the A.P.**

** Solution.**

**Question.13 Draw a pair of tangents to a circle of radius 4 cm, which are inclined to each other at an angle of 60°.**

** Solution.**

**Question.14 As observed from the top of a 60m high light-house from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the light-house, find the distance between the two ships. [Use √3 = 1.732]**

** Solution.**

**Question.15 Prove that the points A(2, 3), B(-2, 2), C(-l, -2) and D(3, -1) are the vertices of a square ABCD**

** Solution.**

**Question.16 Find the ratio in which point P(-l, y) lying on the line segment joining points A(-3,10) and B(6, -8) divides it. Also find the value of y.**

** Solution.**

**Question.17 In Fig. 4, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 21 cm, find the area of the shaded region. [Use π = 22/7 ]**

**Solution.**

**Question.18 A toy is in the form of a cone mounted on a hemisphere of same radius 7 cm. If the total**

** height of the toy is 31 cm, find its total surface area. [Use π = 22/7 ]**

** Solution.**

**Question.19 A solid cone of base radius 10 cm is cut into two parts through the mid-point of its height, by; a plane parallel to its base. Find the ratio in the volumes of the two parts of the cone.**

** Solution.**

**Question.20 A solid metallic sphere of diameter 8 cm is melted and drawn into a cylindrical wire of uniform width. If the length of the wire is 12 m, find its width.**

** Solution.**

**SECTION D**

**Questions number 21 to 31 carry 4 marks each.**

** Question.21 Solve for x:**

**Solution.**

**Question.22 A box contains cards numbered 3, 5, 7, 9,…,35, 37. A card is drawn at random from the**

** box. Find the probability that the number on the drawn card is a prime number.**

** Solution.**

**Question.23 The sum of first n terms of an A.P. is 5n ^{2} + 3n. If its m^{th} term is 168, find the value of m. Also find the 20^{th} term of this A.P.**

**Solution.**

**Question.24 Prove that the lengths of tangents drawn from an external point to a circle are equal.**

** Solution.**

**Question.25 In Fig. 5, the sides AB, BC and CA of triangle ABC touch a circle with centre O’and radius r at P, Q and R respectively.**

** Prove that:**

** (i) AB + CQ = AC + BQ**

** (ii) Area (ΔABC) = 1/2 (Perimeter of ΔABC ) x r**

**Solution.**

**Question.26 The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 60 m high, find the height of the building.**

** Solution.**

**Question.27 If the points A(l, -2), B(2,3), C(-3,2) and D(-4, -3) are the vertices of parallelogram ABCD, then taking AB as the base, find the height of this parallelogram.**

** Solution.**

**Question.28 Water running in a cylindrical pipe of inner diameter 7 cm, is collected in a container at the rate of 192.5 litres per minute. Find the rate of flow of water in the pipe in km/h. [Use π = 22/7 ]**

** Solution.**

**Question.29 While boarding an aeroplane, a passenger got hurt. The pilot, showing promptness and concern, made arrangements to hospitalise the injured and so the plane started late by 30 minutes. To reach the destination, 1500 km away, in time, the pilot increased the speed by 100 km/hour. Find the original speed/hour of the plane.**

** Do you appreciate the values shown by the pilot, namely, promptness in providing help to the injured and his efforts to reach in time?**

** Solution.**

**Question.30 A container, open at the top and made up of metal sheet is in the form of a frustum of a cone of height 16 cm with diameters of its lower and upper ends as 16 cm and 40 cm respectively. Find the cost of metal sheet used to make the container, if it costs Rs 10 per 100 cm2. [Take π = 3.14]**

** Solution.**

**Question.31 Find the probability that a leap year selected at random, will contain 53 Mondays.**

** Solution.**

**SET II**

**Note: Except for the following questions, all the remaining questions have been asked in Set-I.**

** Question.1 Calculate the common difference of the A.P.**

** **

** Solution.**

**Question.10 Three coins are tossed simultaneously. Find the probability of getting exactly two heads.**

** Solution.**

**Question.17 For what value of k, are the roots of the quadratic equation (k – 12)x ^{2} + 2(k – 12)x + 2 = 0 equal?**

**Solution.**

**Question.18 The 8th term of an A.P. is equal to three times its third term. If its 6th term is 22, find the A.P.**

** Solution.**

**Question.19 Draw a pair of tangents to a circle of radius 4.5 cm, which are inclined to each other at an angle of 45°.**

** Solution.**

**Question.20 Prove that the points A(2, -1), B(3, 4), C(-2, 3) and D(-3, -2) are the vertices of a rhombus ABCD. Is ABCD a square?**

** Solution.**

**Question.28 Solve for x:**

**Solution.**

**Question.29 For the triangle ABC formed by the points A(4, -6), B(3, -2) and C(5, 2), verify that median divides the triangle into two triangles of equal area.**

** Solution.**

**Question.30 The sum of first m terms of an AP is 4m ^{2} – m. If its n^{th} term is 107, find the value of n. Also find the 21^{th} term of this A.P.**

**Solution.**

**SET III**

**Note: Except for the following questions, all the remaining questions have been asked in Set-I and Set-II.**

** Question.1 Calculate the common difference of the A.P**

** **

** Solution.**

**Question.10 Two dice are thrown simultaneously. Find the probability of getting a doublet.**

** Solution.**

**Question.17 For what value of k, are the roots of the quadratic equation x ^{2} + k^{2} = 2 (k + l)y equal?**

**Solution.**

**Question.18 The 9 ^{th} term of an A.P. is equal to 6 times its second term. If its 5^{th} term is 22, find the A.P.**

**Solution.**

**Question.19 Draw two tangents to a circle of radius 3.5 cm, from a point P at a distance of 6.2 cm from its centre.**

** Solution.**

**Question.20 Find that value of k for which point (0, 2), is equidistant from two points (3, k) and (k, 5).**

** Solution.**

**Question.28. Solve for x:**

** **

** Solution.**

**Question.29 The sum of first q terms of an A.P. is 63q – 3q ^{2}. If its p^{th} term is -60, find the value of p. Also find the 11th term of this A.P.**

**Solution.**

**Question.30 Find the area of a parallelogram ABCD if three of its vertices are A(2, 4), B(2 + √3,5) and C(2, 6).**

** Solution.**