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CBSE Class 10 Pre Board 2020 : Mathematics Basic - Prelim 2 (Delhi Public School (DPS), Jammu)

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DELHI PUBLIC SCHOOL, JAMMU PRE BOARD-II Assignment (Basic) Class:X Sub:-Mathematics Section A ( Objective Type) MCQ (Q 1 to 10) Section A (Objective Type) 1. Given the HCF (253,550) = 11 and LCM(253,550) = 253x R . The value of R is (a) 400 (b) 40 (c) 440 (d) 50 2. Which of the following is irrational? (a) 16 + 9 (b) 25 + 4 (1) (c) 4 + 9 (d) 3 + 5 3. If the zeroes of the quadratic polynomial x2 +a x + b are 2 and -3, then (a) a = 0, b = -6 (b) a = 2, b = -6 (c) a = 5, b = -1 (d) a=1, b= -1.5 4. If and are the zeroes of p(x) = x2- 5x + 6, then the value of + - is (a) -23 (b) -1 (c) 13 (d) 23 1 5. If sin = 3, then the value of 2 cot2 + 2 is equal to: (a) 6 (b) 9 (c) 4 (d) 18 6. (1) (1) (1) (1) In a right triangle ABC , right angled at B, BC=15cm, AB=8cm. A circle is inscribed in triangle ABC .The radius of the circle is (1) (a) 1cm (b) 2cm (c) 3cm (d) 4cm. 7. If D,E,F are mid points of sides BC, CA, AB respectively of triangle ABC, then the ratios of the area of triangle DEF and ABC is (1) (a) 1:4 (b) 1:2 (c) 2:3 (d) 4:5 8. If ABC and DEF are similar such that 2AB = DE and BC= 10cm, then EF= (1) (a) 16cm (b) 12cm (c) 20cm (d) 4cm 9. If (x,2), (-3,-4) and (7,-5) are collinear, then x= (a) 60 (b) 63 (c) -63 (d) -60 10. The ratio in which (4,5) divides the join of (2,3) and (7,8) is (a) 4:3 (b) 5:2 (c) 3:2 (1) (1) (d) 2:3 Fill in the blanks (11-15) 11. Probability of definite event is _______________________________________ 12. Probability of an even prime number in a die is ___________________________ 13. Total number of outcomes when three dice are thrown simultaneously __________ 14. If a and b are the roots of x2+ 2ax + 3b=0 , a+b = __________________________ 15. For AP 10,15,20,25,--- . 200th term is _____________________________________ Very short type (16-20) pg. 1 (1) (1) (1) (1) (1) 16. In deck of playing cards, find probability of red face card. 17. Find discriminant for 3x2 + 8x 5=0. 18. Find k if x=1 is zero of 3x2 +2 kx -2 = 0. 19. Find first term and common difference for 6,2,-2,-6,--------20. Which term of AP 3,8,13,18,----,is 98. Section B (1) (1) (1) (1) 21. Find HCF of k,2k,3k, and 5k, where k is positive integer. 22 Find altitude of Equilateral triangle when each of its side is a cm. 23. Find point on x-axis which is equidistant from (2,-5) and (-2, 9) 90 1 24. Evaluate: 45 + 30 25. Find the ratio in which P(4,m) divides the line segment joining the points A(2,3) and B(6,-3). Hence, find the value of m. 26. Find area of square that can be inscribed in a circle of radius 8 cm, 27. Find area of major sector of circle of radius 7cm with its angle as half of a right angle. 28. Find x, if mode of the data is 20; data is 15, 20, 25, 18, 13, 15, 25, 15, 18, 17, 20, 25, 20, x, 18. Section C (3 10 = 30) 29. Find HCF by Euclid s division algorithm of the numbers 92690, 7378, 7161. 30. If one zero of polynomial 3x2 8x + 2k + 1 is seven times other, find the value of k. 31. Solve the pair linear equations by substitution method: 3x + 2y -7 =0 ; 4x + y -6 = 0 32. If A(-2,1), B(a,0),C(4,b) and D(1,2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides. 33. For what value of k, kx (x-2 3 ) + 10 = 0 are equal. 34. How many three- digit numbers are divisible by 7? 35. If the area of two similar triangles is equal, prove that they are congruent 36. If C(-1,2) divides the line segment joining A(2,5) and B(x,y) in the ratio 3:4. Find x and y. 37. The angle of elevation of the top of tower from two points on the ground at a distance of 4 m and 9 m from the base of tower and in the same straight line with it are complementary. Prove that the height of the tower is 6m. 38. In PQR, right angled at Q, QR = 9 cm and PR PQ = 1 cm. Determine the value of Sin R+ Cos R. 1 39. Prove that (Cot Cosec )2 = 1+ 40. If tan 2A =cot(A-18 ), where 2A is an acute angle, find the value of A 41. A heap of rice is in the form of a cone of base diameter 24m and height 3.5m. Find the volume of the rice. How much canvas as cloth is required to just cover the heap? 42. A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of solid so formed, at the rate of Rs 5 per 100 sq. cm. (use = 3.14) Section D 43. .In adjoining figure ABC is a quadrant of the circle of radius 14cm and a semi-circle is drawn with AC as a diameter. Find the area of region between quadrant and triangle. pg. 2 44. A sum of Rs 700 is to be used to give seven cash prizes to the students for overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of all prizes. 45. State and prove Thales theorem 46. Prove that, in a right angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides 47. Construct an Isosceles triangle whose base is 6cm and the altitude 4 cm. Then construct 3 another triangle whose sides are 4 times the corresponding sides given isosceles triangle. 48. a, b and c are the sides of a right triangle, where c is hypotenuse. A circle of radius r, touches + the sides of triangle. Prove that r = 2 . 49. A motor boat whose speed is 18km/hr in still water takes 1 hr more to go 24km upstream than tA 21 m deep well with diameter 6 m is dug and earth dug out is evenly spread to form a platform of 27 m 11m. Find the height of platform. 50. For the data of 400 students, calculate mean and median. Ages (in years) No. of students 5-7 7-9 9-11 11-13 13-15 15-17 17-19 70 120 32 100 45 28 5 51. The following distribution gives the daily income of 50 workers of a factory: Daily income (in Rs.) 100-120 120-140 140-160 160-180 180-200 Convert the distribution above to ogive. Number of workers 12 14 8 6 10 a less than type cumulative frequency distribution and draw its 52. Two dies are thrown simultaneously. find the probability of: (i) a doublet (ii) 5 appear on at least one of the die (iii) sum of number on both dies equal to 9. pg. 3

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