**CBSE Previous Year Question Papers Class 10 Maths SA2 Delhi 2016**

**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. From an external point P, tangents PA and PB are drawn to a circle with centre O. If ∠PAB = 50° then find ∠AOB.**

** Answer.**

**Question 2. In Fig. 1, AB is a 6 m high pole and CD is a ladder inclined at an angle of 60° to the horizontal and reaches up to a point D of pole. If AD = 2.54 m. Find the length of the ladder. (Use √3 = 1.73)**

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** Answer.**

**Question 3. Find the 9th term from the end (towards the first term) of the A.P. 5, 9,13, …, 185.**

** Answer.**

**Question 4. Cards marked with number 3,4,5,…., 50 are placed in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the selected card bears a perfect square number.**

** Answer.**

**SECTION B**

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

** Question 5. If x = 2/3 and x = -3 are roots of the quadratic equation a****x ^{2 }**

**+ 7x + b = a and b.**

**Answer.**

**Question 6. Find the ratio in which y-axis divides the line segment joining the points A(5, -6), and B(-1, -4). Also find the coordinates of the point of division.**

** Answer.**

**Question 7. In Fig. 2, a circle is inscribed in a ΔABC, such.that it touches the sides AB, BC and CA at points D, E and F respectively. If the lengths of sides AB, BC and CA are 12 cm, 8 cm and 10 cm respectively, find the lengths of AD, BE and CF.**

** **

** Answer.**

**Question 8. The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q (2, -5) and R(-3, 6), find the coordinates of P.**

** Answer**.

**Question 9. How many terms of the A.P. 18,16,14,…. be taken so that their sum is zero?**

** Answer.**

**Question 10. In Fig. 3, AP and BP are tangents to a circle with centre O, such that AP = 5 cm and ∠APB = 60°. Find the length of chord AB.**

**Answer.**

**SECTION C**

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

** Question 11. In Fig. 4, ABCD is a square of side 14 cm. Semi-circles are drawn with each side of square as diameter. Find the area of the shaded region. [Use π = 22/7 ]**

**Answer.**

**Question 12. In Fig. 5, is a decorative block, made up of two solids—a cube and a hemisphere. The base of the block is a cube of side 6 cm and the hemisphere fixed on .the top has a diameter of 3.5 cm. Find the total surface area of the block. [Use π = 22/7 ]**

** **

** Answer.**

**Question 13. In Fig. 6, ABC is a triangle Coordinates of whose vertex A are (0, -1). D and E respectively are the mid-points of the sides AB and AC and their coordinates are (1, 0) and (0, 1) respectively. If F is the mid-point of BC, find the areas of ΔABC and ΔDEF.**

** **

** Answer.**

**Question 14. In Fig. 7, are shown two arcs PAQ and PBQ. Arc PAQ is a part of circle with centre O and radius OP while arc PBQ is a semicircle drawn on PQ as diameter with centre M. If OP = PQ = 10 cm, show that area of shaded region is 25(√3-π /6)cm ^{2}.**

**Answer.**

**Question 15. If the sum of first 7 terms of an A.P is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.**

** Answer.**

**Question 16. Solve for x:**

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** Answer.**

**Question 17. A well of diameter 4 m is dug 21 m deep. The earth taken out of it has been spread evenly all abound it in the shape of a circular ring of width 3 m to form an embankment. Find the height of the embankment.**

** Answer.**

**Question 18. The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder.[Use π = 22/7 ]**

** Answer.**

**Question 19. The angles of depression of the top and bottom of a 50 m high building from the top of a tower are 45° and 60° respectively. Find the height of the tower and the horizontal distance between the tower and the building. [Use√3 = 1.73]**

** Answer.**

**Question 20. In a single throw of a pair of different dice, what is the probability of getting (i) a prime number on each dice? (ii) a total of 9 or 11?**

** Answer.**

**SECTION D**

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

** Question 21. A passenger, while boarding the plane, slipped from the stairs and got hurt. The pilot took the passenger in the emergency clinic at the airport for treatment. Due to this, the plane got delayed by half an hour. To reach the destination 1500 km away in time, so that the passengers could catch the connecting flight, the speed of the plane was increased by 250 km/hour than the usual speed. Find the usual speed of the plane. What value is depicted in this question?**

** Answer.**

**Value:** By giving utmost importance to the health and well-being of the passenger the pilot displays the value of compassion. By making up for the time lost due to this delay he displays concern for the passengers’ time and money and shows dedication towards his airline and job.

**Question 22. Prove that the lengths of tangents drawn from an external point to a circle are equal. ‘**

** Answer.** See Q. 27 (Theorem), 2011 (I Delhi).

**Question 23. Draw two concentric circles of radii 3 cm and 5 cm. Construct a tangent to smaller circle from a point on the larger circle. Also measure its length.**

** Answer.**

**Question 24. In Fig. 8, O is the centre of a circle of radius 5 cm. T is a point such that OT 13 cm and OT intersects circle at E. If AB is a tangent to the circle at E, find the length of AB, where TP and TQ are two tangents to the circle.**

**Answer.**

**Question 25. Find x in terms of a, b and c:**

** **

** Answer.**

**Question 26. A bird is sitting on the top of a 80 m high tree. From a point on the ground, the angle of elevation of the bird is 45°. The bird flies away horizontally in such a way that it remained at a constant height from the ground. After 2 seconds, the angle of elevation of the bird from the same point is 30°. Find the speed of flying of the bird. (Take √3 = 1.732)**

** Answer.**

**Question 27. A thief runs with a uniform speed of 100 m/minute. After one minute a policeman runs after the thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by 10 m/ minute every succeeding minute. After how many minutes the policeman will catch the thief.**

** Answer.**

**Question 28. Prove that the area of a triangle with vertices (f, t. – 2), (f + 2/ f + 2) and (f + 3, f) is independent of f.**

** Answer.**

**Question 29. A game of chance consists of spinning an arrow on a circular board, divided into 8 equal parts, which comes to rest pointing at one of the numbers 1, 2, 3, …., 8 (Fig. 9), which are equally likely outcomes. What is the probability that the arrow will point at (i) an odd number (ii) a number greater than 3 (iii) a number less than 9.**

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** Answer.**

**Question 30. An elastic belt is placed around the rim of a pulley of radius 5 cm. (Fig. 10) From one point C on the belt, the elastic belt is pulled directly away from the centre O of the pulley until it is at P, 10 cm from the point O. Find the length of the belt that is still in contact with the pulley. Also find the shaded area. Use (π = 3.14 and √3 = 1.73)**

** **

** Answer.**

**Question 31. A bucket open at the top is in the form of a frustum of a cone with a capacity of 12308.8 cm ^{3}. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket and the area of metal sheet used in making the bucket. (Use π= 3.14)**

**Answer.**

**SET II**

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

** Question 10. How many terms of the A.P. 27, 24, 21, … should be taken so that their sum is zero?**

** Answer.**

**Question 18. Solve for x:**

** **

** Answer.**

**Question 19. Two different dice are thrown together. Find the probability of:**

** (i) getting a number greater than 3 on each die**

** (ii) getting a total of 6 or 7 of the numbers on two dice**

** Answer.**

**Question 20. A right circular cone of radius 3 cm, has a curved surface area of 47.1 cm2. Find the volume of the cone. (Use π = 3.14)**

** Answer.**

**Question 28. The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are 60° and 30° respectively. Find the height of the tower.**

** Answer.**

**Question 29. Construct a triangle ABC in which BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct another triangle whose sides are 3/4 times the corresponding sides of ∆ABC.**

** Answer.**

**Question 30. The perimeter of a right triangle is 60 cm. Its hypotenuse is 25 cm. Find the area of the triangle.**

** Answer.**

**Question 31. A thief, after committing a theft, runs at a uniform speed of 50 m/minute. After 2 minutes, a policeman runs to catch him. He goes 60 m in first minute and increases his speed by 5 m/ minute every succeeding minute. After how many minutes, the policeman will catch the thief?**

** Answer**.

**SET III**

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

** Question 10. How many terms of the A.P. 65, 60, 55, … be taken so that their sum is zero?**

** Answer.**

**Question 18. A box consists of 100 shirts of which 88 are good, 8 have minor defects and 4 have major defects. Ramesh, a shopkeeper will buy only those shirts which are good but ‘Kewal’ another shopkeeper will not buy shirts with major defects. A shirt is taken out of the box at random. What is the probability that**

** (i) Ramesh will buy the selected shirt?**

** (ii) ‘Kewal’ will buy the selected shirt?**

** Answer.**

**Question 19. Solve the following quadratic equation for x:**

** **

** Answer.**

**Question 20. A toy is in the form of a cone of base radius 3.5 cm mounted on a hemisphere of base diameter 7 cm. If the total height of the toy is 15.5 cm, find the total surface area of the toy. [Use π = 22/7]**

** Answer.**

**Question 28. The sum of three numbers in A.P. is 12 and sum of their cubes is 288. Find the numbers.**

** Answer.**

**Question 29. Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.**

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

**Question 30. The time taken by a person to cover 150 km was 2 1/2 hours more than the time taken in the return journey. If he returned at a speed of 10 km/hour more than the speed while going, find the speed per hour in-each direction.**

** Answer.**

**Question 31. Draw a triangle ABC with BC = 7 cm, ∠B -=45° and ∠A = 105°. Then construct a triangle whose sides are 4/5 times the corresponding sides of ΔABC.**

** Answer.**