Class 10 TERM-I SET-3 Series NBSE/X/2021 Code No. 041/10/3 Roll No. Candidates must write the Code No. on the title page of the OMR sheet. l Please check that this question paper contains 8 pages. l Code number given on the right hand side of the question paper should be written on the title page of the OMR sheet. l Please check that this question paper contains 50 questions. l 15 minutes time has been allotted to read this question paper. MATHEMATICS–STANDARD Time Allowed : 90 Minutes Maximum 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. 6. Use of calculator is not permitted. NBSE 2021 1 [P.T.O.
SECTION-A Section-A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted. 1. From point X, Alok walks 112 m east to reach at point Y. From point Y, Alok walks 15 m towards north to reach point Z. What is the straight line distance between positions when he started and his position now? 1 (a) 113 m (b) 117 m (c) 123 m (d) 127 m 2. Which of the following can be the probability of an event? 1 (a) 2 (b) –1 (c) 0.3 (d) 1.12 3. In the adjoining figure, D, E and F are the midpoints of the side BC, AC and AB respectively of triangle ABC then ar(∆DEF) : ar(∆ABC) is 1 A FE BD C (a) 1 (b) 1 (c) 1 2 4 9 (d) None of these 4. If the distance between the points (2, –2) and (–1, x) is 5, one of the values of x is 1 (a) –2 (b) 2 (c) –1 (d) 1 5. The product of a non-zero rational and irrational number is 1 (a) Always irrational (b) Always rational (c) Rational or irrational (d) 1 6. If a = 23 × 3, b = 2 × 3 × 5, c = 3n × 5 and LCM (a, b, c) = 23 × 32 × 5, then n is equal to 1 (a) 1 (b) 2 (c) 3 (d) 4 7. The ratio of the areas of two similar right triangles is 9:16. The length of one of the sides of the smaller triangle is 15 cm. How much longer is the length of the corresponding side of the larger triangle from smaller triangle? 1 (a) 2 cm (b) 3 cm (c) 4 cm (d) 5 cm 8. If HCF (26, 169) = 13 then LCM (26, 169) is 1 (a) 26 (b) 52 (c) 338 (d) 13 9. T he value of k for which the system of equations x + y – 4 = 0 and 2x + ky = 3, has no solution, is 1 (a) –2 (b) ≠ 2 (c) 3 (d) 2 3 − sin2 60° 1 10. What is the value of tan 30° tan 60° ? (a) 2 1 (b) 3 1 (c) 23 (d) 33 4 4 4 4 NBSE 2021 2
11. The decimal representation of 11 will 1 23 × 5 (a) Terminate after 1 decimal place (b) Terminate after 2 decimal places (c) Terminate after 3 decimal places (d) Not terminate 12. If am ≠ bl, then the system of equations, ax + by = c, lx + my = n 1 (a) Has a unique solution (b) Has no solution (c) Has infinitely many solutions (d) May or may not have a solution 13. If sin q + cos q = 2 cos q, (q ≠ 90°) then the value of tan q is 1 (a) 2 −1 (b) 2 + 1 (c) 2 (d) − 2 14. Two numbers are in the ratio 1 : 3. If 5 is added to both the numbers, the ratio becomes 1 : 2. The numbers are 1 (a) 4 and 12 (b) 5 and 15 (c) 6 and 18 (d) 7 and 21 15. Kirti has a box containing four cards labelled A, B, C and D. She randomly picks a card from the box, records the label on the card and put it back in the box. She repeats this experiment 80 times and records her observation in the table shown below: Card A Card B Card C Card D 11 16 25 28 Which of the following shows the empirical probability and theoretical probability of picking Card C the next time? 1 (a) Empirical probability = 5 ; Theoretical probability = 1 11 2 (b) Empirical probability = 5 ; Theoretical probability = 1 11 4 (c) Empirical probability = 5 ; Theoretical probability = 1 16 2 (d) Empirical probability = 5 ; Theoretical probability = 1 16 4 16. If cos A + cos2 A = 1, then sin2 A + sin4 A is equal to 1 (a) –1 (b) 0 (c) 1 (d) None of these 4 − sin2 45° 17. The value of cot k tan 60° is 3.5 What is the value of k? 1 (a) 30° (b) 45° (c) 60° (d) 90° 18. Three bells tolls at the interval of 9, 12, 15 minutes respectively. If they start tolling together after what time will they next toll together? 1 (a) 180 mins (b) 80 mins (c) 100 mins (d) 160 mins NBSE 2021 3 [P.T.O.
19. The area of the square is same as the area of a circle. Then their perimeters are in the ratio 1 1 (a) 1 : 1 (b) π : 2 (c) 2 : π (d) None of these 20. In the given figure, DE is parallel to BC. If AD = 3 and AE = 2.7 cm, then EC is equal to DB 2 (a) 2.0 cm (b) 1.8 cm (c) 4.0 cm (d) 2.7 cm SECTION-B Section-B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted. 1 21. Consider the graph: Y 10 8 6 x– x+y=5 y = 4 2 2 X' 02 X –10 –8 –6 –4 –2 4 6 8 10 –2 –4 –6 –8 –10 Y' Which of these is true about the given graph? (a) These lines have infinitely many solutions as they lie in the same quadrant. (b) These lines have a unique solution as they are intersecting at a point. (c) These lines have a unique solution as the coefficient of x in both the equations is equal. (d) These lines have infinitely many solutions as they lie in different quadrants. 22. If a + b = 90° and a = 2b, then cos2 a + sin2 b is equal to 1 (a) 1 1 23. Point P (b) 2 (c) 0 (d) 2 a , 4 is the midpoint of the line segment joining the points A (–5, 2) and B (4, 6). 8 The value of ‘a’ is 1 (a) –4 (b) 4 (c) –8 (d) –2 NBSE 2021 4
24. The ratio of the areas of two similar triangles, ABC and PQR shown below is 25:144. What is the ratio of their medians AM and PN? 1 (a) 5 : 12 (b) 5 : 16 (c) 12 : 5 (d) 25 : 144 25. The distance of the point P(–3, –4) from the x-axis (in units) is 1 (a) 3 (b) –3 (c) 4 (d) 5 26. If a letter of the English alphabet is chosen at random, then the probability that the letter is a consonant is 1 (a) 21 (b) 10 (c) 21 (d) 5 23 13 26 26 27. If a number x is chosen from numbers 1, 2, 3 and a number y is selected from the numbers 1, 4, 9, then P (xy < 9) is 1 (a) 3 (b) 4 (c) 1 (d) 5 9 9 9 9 28. Raghav earned ` 3,550 by selling some bags each for ` 500 and some baskets each for ` 150. Aarav earned ` 3,400 by selling the same number of bags each for ` 400 and the same number of baskets each for ` 200 as Raghav sold. Which of these equations relate the number of bags x and the number of baskets y? 1 (a) 500x + 150y = 3400 and 400x + 200y = 3550 (b) 400x + 150y = 3550 and 500x + 200y = 3400 (c) 500x + 150y = 3550 and 400x + 200y = 3400 (d) 500x + 200y = 3550 and 400x + 150y = 3400 29. The largest number which divides 615 and 963 leaving remainder 6 in each case is 1 (a) 82 (b) 95 (c) 87 (d) 93 30. Given that sin α = 1 and cos β= 1 , then the value of (a + b) is 1 2 2 1 (a) 0° (b) 30° (c) 60° (d) 90° 31. Consider the diagram below: Which of the following statements is true? (a) Side PR is adjacent to angle y in triangle PMR and side QR is adjacent to angle y in triangle PMR NBSE 2021 5 [P.T.O.
(b) Side MR is adjacent to angle y in triangle PMR and side PR is adjacent to angle y in triangle PQR (c) Side PR is adjacent to angle y in triangle PMR and side MR is adjacent to angle y in triangle PQR (d) Side PR is adjacent to angle y in triangle PMR and triangle PQM 32. If the zeroes of the quadratic polynomial x2 + (a + 1) x + b are 2 and –3 then 1 (a) a = –7, b = –1 (b) a = 5, b = –1 (c) a = 2, b = –6 (d) a = 0, b = –6 33. To form a circle of radius r, four minor sectors of equal measure are joined. Which of these options completes the sentence below? 1 The sum of the area of four minor sectors is equal to the…… (a) area of the semicircle of diameter 2r (b) area of the circle of diameter 2r (c) circumference of the circle of radius r (d) circumference of the circle of diameter r 34. The sum of the digits of a two-digit number is 9. If 27 is added to it, the digit of number gets reversed. The number is 1 (a) 25 (b) 72 (c) 63 (d) 36 35. The decimal representation of 6 is 1 1250 (a) 0.0048 (b) 0.048 (c) 0.48 (d) 0.000048 36. In the given figure DE is parallel to BC. If AD = x, BD = x – 2, AE = x + 2 and EC = x – 1 the value of x is 1 (a) 4 (b) 8 (c) 16 (d) 32 37. If the point P(6, 2) divides the line segment joining A(6, 5) and B(4, y) in the ratio 3 : 1, then the value of y is 1 (a) 4 (b) 3 (c) 2 (d) 1 38. Two poles are to be installed on an elevated road as shown in the figure. The figure also shows the starting and ending points of the road. 1 (8, 8) QR (14, 11) NBSE 2021 6
Which of the following are the coordinates of the poles? (a) Q(10, 9) and R(12, 8) (b) Q(10, 9) and R(12, 10) (c) Q(10, 8) and R(12, 11) (d) Q(–10, 9) and R(0, 11) 39. The number of polynomials having zeroes as –2 and 5 is 1 (a) 1 (b) 2 (c) 3 (d) More than 3 40. ABC is an equilateral triangle. The area of the shaded region if the radius of each of the circle is 1 cm, is 1 AB C (a) 2 − π (b) 3 − π (c) 3 − π (d) 3 − π 3 2 4 SECTION-C Section-C consists of 10 questions of 1 mark each. Any 8 questions are to be attempted. Q41 – Q45 are based on Case Study-1 Case Study-1 An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modern yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one can observe the poses that can be related to representation of a quadratic polynomial. Adho Y Mukha 6 Svanasana 4 2 X X' –3 –2 –1–2 0 1 2 3 4 Trikonasana –4 –6 –8 Adho Mukha Svanasana Y' 41. The shapes of the poses shown are (d) Parabola 1 (d) a > 0 1 (a) Spiral (b) Ellipse (c) Linear (d) 3 1 42. The graph of parabola opens downwards, if (a) a ≥ 0 (b) a = 0 (c) a < 0 43. In the graph, how many zeroes are there for the polynomial? (a) 0 (b) 1 (c) 2 NBSE 2021 7 [P.T.O.
44. The zeroes in the above shown graph are 1 1 (a) 2, 4 (b) –2, 4 (c) –8, 4 (d) 2, –8 45. The zeroes of the quadratic polynomial 4 3x2 + 5x − 2 3 are (a) 2, 3 (b) − 2, 3 (c) 2 ,− 3 (d) − 2 ,− 3 3 4 3 4 3 4 3 4 Q46 – Q50 are based on Case Study-2 Case Study-2 In order to conduct Sports Day activities in your school, lines have been drawn with chalk powder at a distance of 1 m each, in a rectangular shaped ground ABCD, 100 flower pots have been placed at a distance of 1 m from each other along AD as shown in given figure below. Niharika runs 1 th the distance AD on the 2nd line and posts a green flag. Preet runs 1 th the distance AD 45 on the eighth line and posts a red flag. DC 10 9 8 7 6 5 Niharika Preet 4 3 R G Red 2 Green flag flag 1 A 1 2 3 4 5 6 7 8 9 10 B 46. The position of the green flag is 1 1 (a) (2, 25) (b) (2, 0.25) (c) (25, 2) (d) (0, –25) 1 47. The position of the red flag is (a) (8, 0) (b) (20, 8) (c) (8, 20) (d) (8, 0.2) 48. The distance between both the flags is (a) 41 m (b) 11 m (c) 61 m (d) 51 m 49. If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag? 1 (a) (5, 22.5) (b) (10, 22) (c) (2, 8.5) (d) (2.5, 20) 50. If Joy has to post a flag at one-fourth distance from green flag in the line segment joining the green and red flags, then where should he post his flag? 1 (a) (3.5, 24) (b) (0.5, 12.5) (c) (2.25, 8.5) (d) (25, 20) NBSE 2021 8
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