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Roll No. ______________, D A V CENTENARY PUBLIC SCHOOL, PASCHIM ENCLAVE, NEW DELHI-110087, PRE-BOARD for FIRST TERM (2021-2022), CLASS X, SUBJECT: MATHEMATICS, (SET A), Time: 90 minutes, , Max. Marks: 40, , General Instructions:, 1. The question paper contains three sections A, B and C., 2. Section A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted., 3. Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted., 4. Section C consists of 10 questions based on two Case Studies. Attempt any 8 questions., 5. There is no negative marking., SECTION A, 1. If 𝐿𝐶𝑀(𝑥, 18) = 36 and 𝐻𝐶𝐹(𝑥, 18) = 2, then ‘𝑥’ is, (a) 2, , (b) 3, , (c) 4, 𝐴𝐵, , (d) 5, , 𝐵𝐶, , 𝐶𝐴, , 2. If in two triangles ABC and PQR, 𝑄𝑅 = 𝑃𝑅 = 𝑃𝑄 , then, (a) ΔPQR ~ ΔCAB, , (b) ΔPQR ~ ΔABC, , (c) ΔCBA ~ ΔPQR, , (d) ΔBCA ~ ΔPQR, , 3. The ratio between the LCM and HCF of 5, 15, 20 is:, (a) 9 : 1, 4. In, , ABC,, , (a) 20, , (b) 4 : 3, , (c) 11 : 1, , (d) 12 : 1, , C = 3 B = 2( A+ B), the measure of, (b) 40, , (c) 60, , B is, (d) 80, , 5. A card is drawn from a well-shuffled deck of 52 playing cards. The probability that the card, will not be an ace is, (a), , 1, 13, , (b), , 1, 4, , (c), , 12, , 6. The decimal expansion of the rational number, place(s)., (a) one, , (b) two, , (d), , 13, 14587, 1250, , (c) three, , 3, 4, , will terminate after _______ decimal, , (d) four, , 7. If P(1, 2); Q(4, 6); R(5, 7) and S(a, b) are the vertices of a parallelogram PQRS, then, (a) a = 2, b = 4, , (b) a = 3, b = 4, , (c) a = 2, b = 3, , (d) a = 3, b = 5

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8. In the given figure, if DE ⊥ AB, CA ⊥ AB and AB = 14 cm, then the value of tan B is:, , 4, , (a) 3, , (b), , 14, , 5, , (c) 3, , 3, , 9. If sin x + cosec x = 2, where 0, (a) 219, , (d), , 13, 3, , 90 , then the value of sin19 x + cosec20 x is, , x, , (b) 220, , (d) 239, , (c) 2, , 10. Five years ago, A was thrice as old as B and ten years later A shall be twice as old as B,, then the present age of A is, (a) 20 years, , (b) 30 years, , (c) 45 years, , (d) 50 years, , 11. If two positive integers a and b are written as a = x3y2 and b = xy3, where x and y are prime, numbers, then HCF(a, b) is, (b) xy2, , (a) xy, , (c) x3y3, , (d) x2y2, , 12. The sum and the product of the zeroes of a quadratic polynomial are 3 and –10 respectively., The quadratic polynomial is, (a) 𝑥2 − 3𝑥 + 10, , (b) 𝑥2 + 3𝑥 + 10, , (c) 𝑥 2 + 3𝑥 − 10, , (d) 𝑥2 − 3𝑥 − 10., , 13. In given figure, AD = 3 cm, AE = 5 cm, BD = 4 cm, CE = 4 cm, CF = 2 cm, BF = 2.5 cm,, then, , (a) DE || BC, , (b) DF || AC, , (c) EF || AB, , (d) none of these, , 14. The value of sin2 30° – cos2 30° is, (a) −, , 1, 2, , (b), , √3, 2, , (c), , 3, 2, , (d) 1

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15. In the given figure, ∆ABC ~ ∆PQR. The value of ‘x’ is, , (a) 4.5 cm, , (b) 3 cm, , (c) 2.75 cm, , (d) 2 cm, , 16. ∆ABC ~ ∆PQR. Area of ∆ABC = 81 cm2 and area of ∆PQR = 121 cm2., If altitude AD = 9 cm, then PM =, , (a) 9 cm, , (b) 10 cm, , (c) 11 cm, , (d) 12 cm, , 17. A vertical stick 20 𝑚 long casts a shadow 10m long on the ground. At the same time, a, tower casts a shadow of 50 𝑚 long on the ground. The height of the tower is, (a) 100 𝑚, , (b) 120 𝑚, , (c) 25𝑚, , (d) 200 m, , 18. In the fig., PQ = 24 cm, QR = 26 cm, PAR = 90°, PA = 6 cm and AR = 8 cm. The measure, of 𝑄𝑃𝑅 is, , (a)75°, , (b) 101°, , (c)90°, , (d) 95°, , 19. If 2 𝑥+𝑦 = 2 𝑥−𝑦 = √8, then the value of ‘y’ is, (a) 0, , 1, , (b) 2, , 3, , (c) 1, , (d) 2, , 20. Which of the following cannot be the probability of an event?, (a) 1.5, , (b), , 3, 5, , (c) 25%, , (d) 0.3

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SECTION B, 21. In the figure given below, ABCD is a rectangle. The values of ‘x’ and ‘y’ are, , (a) x = 8; y = 3, , (b) x = 3; y = 8, , (c) x = 11; y = 5, , (d) x = 5; y = 11, , 22. In the given figure, three sectors of a circle of radius 7 cm, making angles of 60°, 80° and, 40° at the centre are shaded. The area of the shaded region (in cm2) is, , (a) 77, , (b) 154, , (c) 44, , 𝑎, , 23. If tan θ = 𝑏, then the value of, (a), , 𝑎2 −𝑏2, 𝑎2 +𝑏2, , (b), , 𝑎𝑠𝑖𝑛𝜃+𝑏𝑐𝑜𝑠𝜃, 𝑎𝑠𝑖𝑛𝜃−𝑏𝑐𝑜𝑠𝜃, , 𝑎2 +𝑏2, , (c), , 𝑎2 −𝑏2, , (d) 22, is, , 𝑎, , (d), , 𝑎2 +𝑏2, , 𝑏, 𝑎2 +𝑏2, , 24. Two alarm clocks ring their alarms at regular intervals of 50 seconds and 48 seconds. If, they first beep together at 12 noon, at what time will they beep again for the first time?, (a) 12.20 pm, , (b) 12.12 pm, , (c) 12.11 pm, , (d) 12.10 pm, , 25. If 2x – 3y = 7 and (a + b)x – (a + b - 3)y = 4a + b have infinite number of solutions, then, (a) a =5; b = 1, , (b) a = -5; b = 1, , (c) a = 5; b = -1, , (d) a = -5; b = -1, , 26. tan A =, (a), , cos 𝐴, √1−𝑐𝑜𝑠 2𝐴, , (b), , sec 𝐴, √1−𝑠𝑒𝑐 2 𝐴, , (c), , sin 𝐴, √1−𝑠𝑖𝑛2 𝐴, , (d), , 1, √1−𝑠𝑖𝑛2 𝐴, , 27. Find the ratio in which line formed by joining (–1, 1) and (5, 7) is divided by the line, x + y = 4., (a) 2:3, , (b) 1:3, , (c) 2:5, , (d) 1:2

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28. If one zero of 3𝑥2 + 8𝑥 + 𝑘 be the reciprocal of the other, then the value of ‘𝑘’ is, (a) 3, , (b) −3, , (c), , 1, , (d), , 3, , −1, 3, , 29. If sin θ – cos θ = 0, then the value of sin4 𝜃 + cos4 𝜃 is, (a) 1, , (b), , 3, , (c), , 4, , 1, , (d), , 2, , 1, 4, , 30. If 𝐴 = 30°, then sin 2𝐴 equals:, (a), , 1, 2, , (b), , √3, 2, , (c), , 1, , (d) 1, , √2, , 1, 𝛼, , 1, 𝛽, , 31. If 𝛼, 𝛽 are the zeroes of the polynomial 𝑥2 + 6𝑥 + 2, then, the value of ( + ) is, (a) 3, , (b) -3, , (c) 12, , (d) -12, , 32. There are 576 boys and 448 girls in a school that are to be divided into equal sections of, either boys or girls alone. The total number of sections thus formed are:, (a) 22, , (b) 16, , (c) 36, , (d) 21, , 33. The diameter of a wheel is 1.26 m. The distance travelled in 500 revolutions is, (a) 2.670 km, , (b) 2.880 km, , (c) 1.980 km, , (d) 1.596 km, , 34. If 2 and 3 are zeroes of polynomial 3x2 – 2kx + 2m, the values of ‘k’ and ‘m’ are, (a) 9, 8, , 12, , (b) 13 , 7, , (c), , 15, 2, , ,9, , (d), , −3, 2, , 3, , ,2, , 35. If 𝜃 is an acute angle and 4 sin 𝜃 = 3, then the value of 4 sin2𝜃 − 3 cos2 𝜃 + 2 is, 45, , (a) 16, , 35, , 32, , (b) 18, , (c) 16, , (d), , 47, 16, , 36. A coin is tossed twice. The probability of getting both heads is, (a), , 1, 2, , (b), , 1, 3, , (c), , 1, 4, , (d) 1, , 37. Which of the following is not the graph of a quadratic polynomial?

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38. The probability of a non-leap year having 53 Mondays is, (a), , 1, 365, , (b), , 1, 7, , (c), , 2, 7, , (d) 1, , 39. If 3x + 2y = 13 and 3x – 2y = 5, then the value of (x + y) is:, (a) 2, , (b) 3, , (c) 5, , (d) 6, , 40. If one of the zeroes of the quadratic polynomial (k–1)x2 + kx + 1 is –3, then the value of ‘k’, is, (a), , 4, 3, , (b), , −4, 3, , (c), , 2, 3, , (d), , −2, 3, , SECTION C, (Q41 to Q45 are based on Case Study 1), A brooch is a small piece of jewellery which has a pin at the back so it can be fastened on a, dress, blouse or coat. Designs of some brooch are shown below., , Observe them carefully., , Design A: Brooch A is made with silver wire in the form of a circle with diameter 28mm. The, wire used for making 4 diameters which divide the circle into 8 equal parts., Design B: Brooch B is made two colours:- Gold and silver. Outer part is made with Gold. The, circumference of silver part is 44mm and the gold part is 3mm wide everywhere.

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Refer to Design A, 41. The total length of silver wire required is, (a) 180 𝑚𝑚, , (b) 200 𝑚𝑚, , (c) 250 𝑚𝑚, , (d) 280 𝑚𝑚, , 42. The area of each sector of the brooch is, (a) 44 𝑚𝑚2, , (b) 52 𝑚𝑚2, , (c) 77 𝑚𝑚2, , (d) 68 𝑚𝑚2, , (c) 51 𝜋, , (d) 64 𝜋, , Refer to Design B, 43. The area (in mm2) of silver part is, (a) 18𝜋, , (b) 49 𝜋, , 44. The area (in mm2) of golden part is, (a) 18𝜋, , (b) 49 𝜋, , (c) 51 𝜋, , (d) 64 𝜋, , 45. A boy is playing with brooch B. He makes revolution with it along its edge. How many, complete revolutions must it take to cover 80𝜋 𝑚𝑚?, (a) 2, , (b) 3, , (c) 4, , (d) 5, , (Q46 to Q50 are based on Case Study 2), Ajay, Bhishm and Colin are best friends since childhood. They always want to sit in a row in, the classroom. But teacher doesn’t allow them and rotate the seats row-wise every day. Bhishm, is very good in maths and he does distance calculation every day. He considers the centre of, class as origin and marks their position on a paper in a co-ordinate system. One day Bhishm, make the following diagram of their seating position.

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46. What is the coordinate of point A?, (a) (2, 2 ), , (b) (2, −2 ), , (c) (−2, 2 ), , (d) (−2, −2 ), , 47. What is the distance of the point A from the origin?, (a) 8 units, , (b) 2√2 units, , (c) 4 units, , (d) 4√2 units, , 48. What is the distance between A and B?, (a) 3√19 units, , (b) 3√5 units, , (c) √17 units, , (d) 2√5 units, , 49. A point D lies on the line segment between points A and B such that 𝑨𝑫: 𝑫𝑩 = 𝟒: 𝟑. What, are the coordinates of point D?, 10 2, , (a) ( , ), 7, , 7, , 2, , (b) ( , 1), 7, , (c) (, , −10 −2, 7, , ,, , 7, , ), , −2, , (d) (, , 7, , , −1), , 50. What is the distance between B and C?, (a) 3√19 units, , (b) 3√5 units, , (c) 2√17 units, , (d) 2√5 units

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ANSWER KEY (SET A), , SECTION A, SECTION B, 1., (c), 21. (b), 2., (a), 22. (a), 3., (d), 23. (b), 4., (b), 24. (a), 5., (c), 25. (d), 6., (d), 26. (c), 7., (c), 27. (d), 8., (a), 28. (a), 9., (c), 29. (c), 10., (d), 30. (b), 11., (b), 31. (b), 12., (d), 32. (b), 13., (c), 33. (c), 14., (a), 34. (c), 15., (b), 35. (d), 16., (c), 36. (c), 17., (a), 37. (d), 18., (c), 38. (b), 19., (a), 39. (c), 20., (a), 40. (a), SECTION C, CASE STUDY 1, CASE STUDY 2, 41., (b), 46. (c), 42., (c), 47. (b), 43., (b), 48. (c), 44., (c), 49. (c), 45., (c), 50. (d)