uc ce ss The U ate ltim Q.P. Set - III N 403 S Seat No. MATHEMATICS (X - CBSE) 2014 I 29 Time : 3 Hours. Max. Marks : 90 General Instructions: i) All questions are compulsory. ii) The question paper consists of 34 questions divided into four sections A,B,C and D. Section A comprises of 8 questions of 1 mark each, section B comprises of 6 questions of 2 marks each, section C comprises of 10 questions of 3 marks each and section D comprises 10 questions of 4 marks each. iii) Question numbers 1 to 8 in section-A are multiple choice questions where you are to select one correct option out of the given four. iv) There is no overall choice. v) Use of calculator is not permitted. Section-A Question numbers 1 to 8 carry one mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice. 1. If 2 is a root of the equation x2 + bx + 12 = 0 and the equation x2 + bx + q = 0 has equal roots, then q = A) 8 B) -8 C) 16 D) -16 2. If 18, a, b, -3 are in A.P, then a + b = A) 19 B) 7 C) 11 D) 15 3. PQ and PR are the tangents Q from P to a circle with centre O O, if  OPQ = 350 then A) a = 300, b = 600 B) a = 350, b = 550 C) a = 400, b = 500 D) a = 450, b = 450 b R 35 0 a P :: 2 :: 4. The ratio of the length of a rod and its shadow is 1 : 3 . The angle of elevation of the sun is : A) 300 B) 45 0 C) 600 D) 900 5. The difference between the circumference and radius of a circle is 37 cm. The area of the circle is A) 111cm2 B) 148 cm2 C) 154 cm2 D) 259 cm2 6. The curved surface area of a right circular cone of height 15cm and base diameter 16cm is : A) 60  cm2 B) 68  cm2 C) 120  cm 2 D) 136  cm2 7. The distance of the point P(2, -3) from the x-axis is : A) 2 B) 3 C) -3 D) -2 8. The area of a circle that can be inscribed in a square of side 10cm is : A) 100  cm2 B) 50  cm2 C) 20  cm2 D) 25  cm2 Section - B Question numbers 9 to 14 carry two marks each. 9. The product of two consecutive positive integers is 240. Find the numbers. 10. Show that the sequence an = 5n - 7 is an A.P. find its common difference. 11. A quadrilateral ABCD is drawn to circumcribed a circle. Prove that AB + CD = AD + BC D R Q S A C P B 12. Draw a circle of radius 3cm. Take two points P and Q on one of its extended diameter each at a distance of 6cm from the centre. Draw tangents to the circles from these two points P and Q. :: 3 :: 13. The diameter of the driving wheel of a bus is 140cm. How many revolution per minute must the wheel make in order to keep a speed of 66 km per hour ? 14. Three coins are tossed together. Find the probability of getting i) at least two heads ii) at most two heads. Section - C Question numbers 15 to 24 carry three marks each. 15. Solve by using quadratic formula 9x2 - 9(a + b) x + (2a2 + 5ab + 2b2) = 0 ? 16. The sum of 5th and 9th terms of an AP is 72 and the sum of 7th and 12th terms is 97 find the AP. A (4, -2) 17. In the adjoining Fig, in  ABC, D and E are E the midpoints of the sides BC and AC respectively Find the length DE. (2, -2) B D C (-6, -1) 18. Prove that the length of two tangents drawn from an external point to a circle are equal. 19. An electrician has to repair an electric fault on a pole of height 4m. He needs to reach a point 1.3m below the top of the pole to undertake the repair work. What should be the length of the ladder that he should use which when inclined at an angle of 600 to the horizontal would enable him to reach the required position ? 20. Card marked with the number thoroughly one card is drawn number on the card is i) a perfect square iii) less than 40 2 to 101 are placed in a box and mixed from this box. Find the probability that the ii) a prime number iv) a multiple of 5 :: 4 :: 21. Construct a triangle with sides 4cm, 5cm and 7cm. Then construct rd 2 a triangle similar to it whose sides are of the corresponding sides 3 of the given triangle. 22. How many terms are there in an A.P. whose first and fifth terms are -14 and 2 respectively and the sum of terms is 40 ? 23. An elastic rubber is placed round the rim of a bangle of radius 3cm. One point of this rubber is pulled away O from the centre of the bangle until it is at P, where OP = 6cm, O is the centre of the bangle. Find the length of the rubber in contact with the bangle. Also find the shaded area. A P B 24. A solid sphere of radius 3cm is melted and then cast into small spherical balls of each of diameter 0.6cm. Find the number of balls thus obtained. Section - D Question numbers 25 to 34 carry Four marks each. 25. From the top of a building 60m high the angles of depressions of the top and the bottom of a tower are observed to be 300 and 600. Find the height of the tower. 26. A bucket is in the form of a frustum of a cone with a capacity of 12308.8cm3. The radius of the top and bottom circular ends of the bucket are 20cm and 12cm respectively. Find the height of the bucket and also find the area of the metal sheet used in making it. (  = 3.14) 27. The sum of the areas of two squares is 640m2. If the difference in their perimeter be 64m, find the sides of the two squares. 28. A manufacturer of radio-sets produced 600 units in the third year and 700 units in 7th year. If units produced are in A.P. , then find. :: 5 :: i) production in the 1st year ii) total production in first seven years iii) Production in tenth year. 29. The points (3, -4) and (-6, 5) are the end points of a diagonal of a parallelogram if the third vertex is (-2, 1) find the fourth vertex. Also find its area. 30. A circle touches the sides of a quadrilateral ABCD at P,Q,R,S respectively. Show that the angles subtended at the centre by a pair of opposite sides are supplementary. Q B 31. ABC is a quadrant of a circle of radius 14cm and a semicircle P is drawn with BC as diameter. Find the area of the shaded portion. A C C 32. A circle is inscribed in a  ABC having sides 8cm, 10cm and 12cm F E as shown in the figure. Find AD, BE and CF. A D B 33. Two dice are thrown simultaneously find the probability of getting i) a doublet of even number ii) a multiple of 2 on one dice and a multiple of 3 on the other iii) an even number as the sum iv) a total of atleast 10. 34. A solid consisting of a right circular cone standing on a hemisphere is placed upright in a right circular cylinder full of water and touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60cm and its height is 180cm, the radius of the hemisphere is 60cm and height of the cone is 120cm. oooXoXoXooo