NBSE Question Papers Mathematics Standard Term-1 (Set-2) for Class 10

Class 10  TERM-I SET-2 Series NBSE/X/2021 Code No. 041/10/2 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. The 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 2. Observe the right angled triangle ABC as shown below: 1 B AP C Mr. Shah follows the given steps to prove AB2 + BC2 = AC2 (i) DAPB ~ DABC (ii) AP = AB (iii) AB2 = AP . AC AB AC Which of these could be his next step? (a) To prove DABC ~ DPAB (b) To prove DAPB ~ DCPB (c) To prove DBPC ~ DABC (d) To prove DAPB ~ DBPC 3. The pair of equations y = 0 and y = –7 has 1 (a) One solution (b) Two solutions (c) Infinitely many solutions (d) No solution 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. If HCF (26, 169) = 13 then LCM (26, 169) is 1 (a) 26 (b) 52 (c) 338 (d) 13 6. 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 7. Which of the following can be the probability of an event? 1 (a) 2 (b) –1 (c) 0.3 (d) 1.12 8. In the following figure, D, E and F are the midpoints of the side BC, AC and AB respectively of triangle ABC then ar(DDEF) : ar(DABC) is 1 A FE B DC 1 1 (c) 1 (d) None of these (a) 2 (b) 4 9 NBSE 2021 2

9. What is the value of 3 − sin2 60° ? 1 tan 30° tan 60° (a) 2 1 (b) 2 3 (c) 2 3 (d) 33 4 4 4 4 10. 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 11. The two legs AB and BC of right triangle ABC are in a ratio 1 : 3. What will be the value of sin C? 1 (a) 10 (b) 1 3 (d) 1 10 (c) 10 2 12. The area of the square is same as the area of a circle. Then their perimeters are in the ratio 1 (a) 1 : 1 (b) π : 2 (c) 2 : π (d) None of these 13. 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 14. 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 15. Three bulbs, red, green and yellow flash at intervals of 80 seconds, 90 seconds and 110 seconds. All three flash together at 8 : 00 am. At what time will the three bulbs flash altogether again?1 (a) 8 : 12 am (b) 9 : 12 am (c) 10 : 12 am (d) 11 : 12 am A 16. In the given figure, DE is parallel to BC. If AD = 3 and AE = 2.7 cm, then EC is equal to DE DB 2 1 BC NBSE 2021 3 [P.T.O.

(a) 2.0 cm (b) 1.8 cm (c) 4.0 cm (d) 2.7 cm 17. If sin q + cos q = 2 cos θ, (θ ≠ 90°) then the value of tan q is 1 (a) 2 − 1 (b) 2 + 1 (c) 2 (d) − 2 1 1 18. The product of a non-zero rational and irrational number is 1 (a) Always irrational (b) Always rational (c) Rational or irrational (d) One 19. If a = 23 × 3, b = 2 × 3 × 5, c = 3n × 5 and LCM (a, b, c) = 23 × 32 × 5, then n is equal to (a) 1 (b) 2 (c) 3 (d) 4 20. If cos A + cos2 A = 1, then sin2 A + sin4 A is equal to (a) –1 (b) 0 (c) 1 (d) None of these SECTION-B Section-B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted. 21. Which of these is a linear equation in two variables? 1 (a) 3x – 2y + 2 = 0 (b) x – y2 – 2y + 8 = 0 (c) x + 2y + 10 = y2 + y (d) 5x – 2y2 = 0 22. The largest number which divides 615 and 963 leaving remainder 6 in each case is 1 (a) 82 (b) 95 (c) 87 (d) 93 23. A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets are sold, how many tickets has she bought? 1 (a) 40 (b) 240 (c) 480 (d) 750 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 AP B M CQ N R (a) 5 : 12 (b) 5 : 16 (c) 12 : 5 (d) 25 : 144 (d) 5 25. The distance of the point P(–3, –4) from the x-axis (in units) is  1 1 (a) 3 (b) –3 (c) 4 26. Consider the graph: Yx– y= 102 8 X 6 x+y=5 4 2 X' –10 –8 –6 –4 –2 0 2 4 6 8 10 –2 –4 –6 –8 –10 Y' NBSE 2021 4

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. 27. If a + b = 90° and a = 2b, then cos2 a + sin2 b is equal to 1 (a) 1 1 (d) 2 28. If a number fro(mb)n u2m bers 1, 2, 3 and a(cn)u m0 ber from the x is chosen y is selected numbers 1, 4, 9, then P (xy < 9) is 1 (a) 3 (b) 4 (c) 1 (d) 5 9 9 9 9 29. If sin 77° = x, then the value of tan 77° is 1 (a) 1 1 (b) x x + x2 (c) 1 − x2 (d) None of these 1 + x2 30. Point P  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 31. 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) Q R (14, 11) 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) 32. The number of polynomials having zeroes as –2 and 5 is 1 (a) 1 (b) 2 (c) 3 (d) More than 3 33. To form a circle of radius r, four minor sectors of equal measure are joined. Which of these options completes the sentence below? The sum of the area of four minor sectors is equal to the…… 1 (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 NBSE 2021 5 [P.T.O.

35. Consider the diagram below:  P 1 x M y Q R 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 (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 36. The decimal representation of 6 is 1 1250 (a) 0.0048 (b) 0.048 (c) 0.48 (d) 0.000048 37. 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 C E A DB (a) 4 (b) 8 (c) 16 (d) 32 38. 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 39. If (a, b) is the midpoint of the line segment joining the points A (10, –6) and B (k, 4) and a – 2b = 18, the value of k is 1 (a) 30 (b) 22 (c) 4 (d) 40 40. ABC is an equilateral triangle. The area of the shaded region if the radius of each of the circle is 1cm, is 1 AB C (a) 2 – π (b) 3 − π (c) 3 − π (d) 3 − π 3 2 4 NBSE 2021 6

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 Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feets. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made up of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial. 3 1 24 41. The shape of the path traced shown is 1 1 (a) Spiral (b) Ellipse (c) Linear (d) Parabola (c) a > 0 (d) a ≥ 0 42. The graph of parabola opens downwards, if (a) a = 0 (b) a < 0 43. O bserve the following graph and answer. 6 4 2 –4 –3 –2 –1 0 1 23 4 –2 –4 –6 In the graph, how many zeroes are there for the polynomial? 1 1 (a) 0 (b) 1 (c) 2 (d) 3 1 44. The zeroes in the above shown graph are (a) 2, 3, –1 (b) –2, 3, 1 (c) –3, –1, 2 (d) –2, –3, –1 45. What will be the expression of the polynomial of the shown graph? (a) x3 + 2x2 – 5x – 6 (b) x3 + 2x2 – 5x + 6 (c) x3 + 2x2 + 5x – 6 (d) x3 + 2x2 + 5x + 6 NBSE 2021 7 [P.T.O.

Q46 – Q50 are based on Case Study-2 Case Study-2 The children of a school prepared a dance item for the Republic Day parade for which they were asked to form a rectangle by standing at a fixed distance, taken as one unit. Some children, then formed a pattern inside a rectangle. S R B C A D W X ZY E H GF PQ 46. If P is considered as the origin, the coordinates of B are 1 1 (a) (8, 5) (b) (3, 8) (c) (8, 0) (d) (0, 3) 47. The distance between the children standing at H and G is (a) 8 units (b) 2 units (c) 5 units (d) 8 units 48. The coordinate of point that divides the line segment joining the points A and D in the ratio 2:3 internally are 1 (a)  6, 19 (b) (6, 6) (c) (6, 2) (d)  19 , 6  5   5 49. If a point (x, y) is equidistant from C (6, 8) and F (6, 1) then 1 (a) 2x – 7y + 36 = 0 (b) 14y = 63 (c) x – y = 5 (d) x + y = 5 50. The coordinates of the point P if H is taken as the origin are 1 (a) (2, 3) (b) (–1, –3) (c) (–2, 3) (d) (2, –3) NBSE 2021 8