**CBSE Previous Year Question Papers Class 10 Maths SA2 Delhi 2015**

**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. If x = -1/2, is a solution of the quadratic equation 3x ^{2}+ 2kx -3 = 0, find the value of k.**

**Answer.**

**Question.2. The tops of two towers of height x and y, standing on level ground, subtend angles of 30° and 60° respectively at the centre of the line joining their feet, then find x : y.**

** Answer.**

**Question. 3. A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is a consonant.**

** Answer.**

**Question. 4. In Fig. 1, PA and PB are tangents to the circle with centre O such that ∠APB = 50°. Write the measure of ∠OAB.**

**Answer.**

**SECTION B**

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

** Question.5. In Fig, 2, AB is the diameter of a circle with centre O and AT tangent. If ∠AOQ = 58°, find ∠ATQ.**

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** Answer.**

**Question.6. Solve the following quadratic equation for x:**

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** Answer.**

**Question.7. From a point T outside a circle of centre O, tangents TP and TQ are drawn to the circle. Prove that OT is the right bisector of line segment PQ.**

** Answer.**

**Question.8. Find the middle term of the A.P. 6,13, 20, …, 216.**

** Answer.**

**Question.9. If A(5, 2), B(2, -2) and C(-2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t.**

** Answer.**

**Question.10. Find the ratio in which the point P(3/4, 5/12) divides the line segment joining the points A(1/2, 3/2) and B(2,-5).**

** Answer.**

**SECTION C**

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

** Question.11. Find the area of the triangle ABC with A(1, -4) and mid-points of sides through A being (2, -1) and (0, -1).**

** Answer.**

**Question.12. Find that non-zero value of k, for which the quadratic equation kx ^{2} + 1 – 2(k – l)x +x^{2} = 0 has equal roots. Hence find the roots of the equation.**

**Answer.**

**Question.13. The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 45°. If the tower is 30 m high, find the height of the building.**

** Answer.**

**Question.14. Two different dice are rolled together. Find the probability of getting:**

** (i) the sum of numbers on two dice to be 5.**

** (ii) even numbers on both dice.**

** Answer.**

**Question.15. If S _{n}, denotes the sum of first n terms of an A.P., prove that S_{12} =3(S_{8} – S_{4}).**

**Answer.**

**Question.16. In Fig. 3, APB and AQO are semicircles, and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region. [Use π = 22/7]**

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** Answer.**

**Question. 17. In Fig. 4, from the top of a solid cone of height 12 cm and base radius 6 cm, a cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid. (Use π = 22/7 and √5 = 2.236)**

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** Answer.**

**Question. 18. A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 166 (5/6) cm ^{3}. Find the height of the toy. Also, find the cost of painting the hemispherical part of the toy at the rate of Rs 10 per cm^{2}. [Use π = 22/7 ]**

**Answer.**

**Question. 19. In Fig. 5, from a cuboidal solid metallic block, of dimensions 15 cm x 10 cm x 5 cm, a cylindrical hole of diameter 7 cm is drilled out. Find the surface area of the remaining block. [Use π = 22/7]**

** Answer.**

**Question. 20. In Fig. 6, find the area of the shaded region. [Use π= 3.14]**

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** Answer.**

**SECTION D**

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

** Question. 21. The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and original fraction is 29/20 . Find the original fraction.**

** Answer.**

**Question. 22. Ramkali required Rs 2500 after 12 weeks to send her daughter to school. She saved Rs 100 in the first week and increased her weekly saving by Rs 20 every week. Find whether she will be able to send her daughter to school after 12 weeks. What value is generated in the above situation?**

** Answer.**

**Value:** Small savings can fulfill your big desires.

**Question. 23. Solve for x:**

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** Answer.**

**Question. 24. Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.**

** Answer.** See 27 (Theorem), 2012 (I Delhi).

**Question. 25. In Fig. 7, tangents PQ and PR are drawn from an external point P to a circle with centre O, such that ∠RPQ = 30°. A chord RS is drawn parallel to the tangent PQ. Find ∠RQS.**

** **

** Answer.**

**Question.26. Construct a triangle ABC with BC = 7 cm, ∠B = 60° and AB = 6 cm. Construct another triangle whose sides are 3/4 times the corresponding sides of ∆ABC.**

** Answer.** See Q. 23, 2012 (II Delhi).

**Question. 27. From a point P on the ground the angle of elevation of the top of a tower is 30° and that of the top of a flag staff fixed on the top of the tower, is 60°. If the length of the flag staff is 5m, find the height of the tower.**

** Answer.**

**Question. 28. A box contains 20 cards numbered from 1 to 20. A card is drawn at random from the box. Find the probability that the number on the drawn card is (i) divisible by 2 or 3, (ii) a prime number.**

** Answer.**

**Question.29. If A(-4, 8), B(-3, -4), C(0, -5) and D(5, 6) are the vertices of a quadrilateral ABCD, find its area.**

** Answer.**

**Question.30. A well of diameter 4 m is dug 14 m deep. The earth taken out is spread evenly all around the well to form a 40 cm high embankment. Find the width of the embankment.**

** Answer.**

**Question.31. Water is flowing at the rate of 2.52 km/hr. through a cylindrical pipe into a cylindrical tank, the radius of whose base is 40 cm. If the increase in the level of water in the tank, in half an hour is 3.15 m, find the internal diameter of the pipe.**

** Answer.**

**SET II**

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

** Question. 10. Find the middle term of the A.P. 213, 205, 197, … 37.**

** Answer.**

**Question. 18. If the sum of the first n terms of an A.P. is 1/2 (3n ^{2} + 7n), then find its n th term. Hence write its 20th term.**

**Answer.**

**Question. 19. Three distinct coins are tossed together. Find the probability of getting (i) at least 2 heads (ii) at most 2 heads.**

** Answer.**

**Question. 20. Find that value of p for which the quadratic equation (p + 1)x ^{2} – 6(p +1)x + 3 (p + 9) = 0, p ≠ -1 had equal roots. Hence find the roots of the equation.**

**Answer.**

**Question. 28. To fill a swimming pool two pipes are to be used. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter for 9 hours, only half the pool can be filled. Find, how long it would take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool.**

** Answer.**

**Question. 29. Prove that the lengths of tangents drawn from an external point to a circle are equal.**

** Answer.** See Q. 27, 2012 (I Outside Delhi).

**Question. 30. Construct an isosceles triangle whose base is 6 cm and altitude 4 cm. Then construct another triangle whose sides are 3/4 times the corresponding sides of the isosceles triangle.**

** Answer.**

**Question. 31. If P(-5, -3), Q(-4, -6), R(2, -3) and S(1, 2) are the vertices of a quadrilateral PQRS, find its area.**

** Answer.**

**SET III**

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

** Question. 10. Solve the following quadratic equation for x:**

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** Answer.**

**Question.18. All red face cards are removed from a pack of playing cards. The remaining cards were well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is ****(i) a red card (ii) a face card (iii) a card of clubs.**

** Answer.**

**Question.19. Find the area of the triangle PQR with Q(3, 2) and the mid-points of the sides through Q being (2, -1) and (1, 2).**

** Answer.**

**Question.20. If Sn denotes the sum of first n terms of an A.P., prove that S _{30}_{ }= 3[S**

_{20}– S_{10}].**Answer.**

**Question.28. A 21 m deep well with diameter 6 m is dug and the earth from digging is evenly spread to form a platform 27 m x 11 m. Find the height of the platform. [Use π = 22/7]**

** Answer.**

**Question. 29. A bag contains 25 cards numbered from 1 to 25. A card is drawn at random from the bag. Find the probability that the number on the drawn card is: (i) divisible by 3 or 5 (ii) a perfect square number.**

** Answer.**

**Question. 30. Draw a line segment AB of length 7 cm. Taking A as centre, draw a circle of radius 3 cm and taking B as centre, draw another circle of radius 2 cm. Construct tangents to each circle from the centre of the other circle.**

** Answer.** Same as Q. 19, 2014 (II O.D.).

**Question. 31. Solve for x:**

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** Answer.**