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CBSE Class 10 Pre Board 2020 : Mathematics Standard - Prelim 2 (Kendriya Vidyalaya (KV) Agra)

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KENDRIYA VIDYALAYA SANGATHAN, AGRA REGION PRE-BOARD EXAM.2019-20 CLASS X SUBJECT- MATHEMATICS (STANDARD) SET D Time alloted: 3 Hours Max. Marks: 80 General Instructions: 1. All the questions are compulsory. 2. The question paper consists of 40 questions divided into 4 sections A, B, C and D. 3. Section A comprises of 20 questions of 1 mark each. Section B comprises of 6 questions of 2 marks each. Section C comprises of 8 questions of 3 marks each. Section D comprises of 6 questions of 4 marks each. 4. There is no overall choice. However, an internal choice has been provided in two questions of 1 mark each, two questions of 2 marks each, three questions of 3 marks each and three Questions of 4 marks each. You have to attempt only one of the alternatives in all such questions. 5. Use of calculators is not permitted. Section-A 1. If the probability of an event is p, the probability of its complementary event will be: 1 (a) 1 p (b) p (c) p 1 (d) 2. If P ( 2 , 4 ) is the mid-point of the line-segment joining the points A ( -6, 5 ) and B ( -2, 3), then the value of a is: (a) 4 (b) 3 (c) -4 (d) -8 3. Distance between the points (2, -2) and ( -1, x) is 5, one of the values of x is: (a) 6 (b) 2 (c) -1 (d) 1 4. If the quadratic equation 2x2 kx + k = 0 has equal roots, then the value(s) of k is / are: (a) 0 only (b) 4 only (c) 8 only (d) 0,8 5. LCM of 5, 8, 12, 20 will not be a multiple of: (a) 5 (b)3 (c) 9 (d) 2 6. The pair of equations 2x 3y = 1 and 3x 2y = 4 has : (a) Unique solution (b) Two solutions (c)No solution (d) Many solutions 7. The angle of elevation of a ladder leaning against a wall is 600 and the foot of the ladder is 9.5 m away from the wall. The length of the ladder is: (a) 19 m (b) 19 3 m (c) 9.5 2 m (d) 9.5 3 m 8. What is the common difference of an AP in which a18 a14 = 32? (a) 2 (b) 4 (c) 8 (d) 16 Page 1 of 4 9. (a) PQR CAB (b) PQR CBA 10. If in two triangles ABC and PQR, = = then: (c) PQR ABC (d) PQR BCA The number of zeroes of the polynomial f(x) = (x 2)2 4 is : (a) 1 (b) 2 (c) 0 (d) 3 OR The sum of the zeroes of the polynomial 2x2 -8x +6 is: (a) 3 (b) 4 (c) -3 (d) -4 11. Write the empirical relationship between the three measures of central tendency 12. The base radii of two right circular cones of the same height are in the ratio3 : 5. What is the ratio of their volumes ? 13. 14. PQR is right angled isosceles triangle, right angled at R. Find the value of sin P. If 15 cot A = 8, then find the value of cosec A. 15. If the first three terms of an AP are b, c and 2b, then find the ratio of b and c. 16. A line intersecting a circle in two points is called ______________ OR Number of tangents that can be drawn from the external points to a circle is___ 17. The distance of the point P (-3, -4 ) from the X-axis (in units) is ____________ 18. The sides of two similar triangles are in the ratio 2:3, then the areas of these triangles are in the ratio _____________ 19. The decimal representation of 136/1400 will be_______________ (Terminating / Non terminating) 20. If the HCF of 65 and 117 is expressible in the form 65 m 117 , then the value of m is _______________ SECTION B 21. Which term of the AP 53, 48, 43, ....................... is the first negative term? 22. Find the angle of elevation if the height of the pole is equal to shadow of the pole. Page 2 of 4 23. ABC is an equilateral triangle of side 2a. Find each of its altitudes. OR Let ABC ~ DEF and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC. 24. Prove that the tangents drawn at the ends of a diameter of a circle are parallel. 25. 2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid. 26. One ticket is drawn at random from a bag containing tickets numbered 1 to 40. Find the probability that the selected ticket has a number which is a multiple of 5. OR What is the probability that there are 53 Wednesdays in a leap year? SECTION C 27. Find all zeroes of the polynomial 2 4 9 3 + 5 2 + 3 1, if two of its zeroes are (2 + 3) and (2 3). 28. Prove that 2 + 2 3 is an irrational number. OR 29. Use Euclid s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m. A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream. OR Solve the following pairs of equations: 6x + 3y = 6xy 2x + 4y = 5xy 30. Find the 20th term from the last term of the AP 3,8,13,-----------------------,253. 31. Find the ratio in which the y-axis divides the line segment joining the points (5, 6) and ( 1, 4). Also find the point of intersection. 32. Prove that: +1 = 1 + tan + cot OR sin +1 1 Prove that sin + 1 = sec . 1 Page 3 of 4 33. ABCP is a quadrant of a circle of radius 14 cm. With AC as diameter, a semi-circle is 22 drawn. Find the area of the shaded region. (take = 7 ) 34. The mean of the following data is 50. Find the missing frequencies 1 and 2 . Classes 0-20 20-40 40-60 60-80 80-100 TOTAL Frequencies 17 1 32 2 19 120 SECTION D 35. A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train. OR 3 Two water taps together can fill a tank in 9 hours. The tap of larger diameter takes 10 8 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank. 36. 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 complementary. Find the height of the tower. 37. In an equilateral triangle ABC, D is a point on side BC such that BD = 3 BC. 1 Prove that 9 AD2 = 7 AB2. 38. Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it 2 whose sides are of the corresponding sides of the first triangle. 3 OR Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60 . Page 4 of 4 39. The radii of the ends of a frustum of a cone 45 cm high are 28 cm and 7 cm. Find its volume, the curved surface area. OR A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs 500 per m2. 40. The following distribution gives the daily income of 50 workers of a factory. Daily income(in Rs) Frequency 100 - 120 12 120- 140 14 140 - 160 8 160 - 180 6 180- 200 10 Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive. END OF PAPER Page 5 of 4

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