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

Class 10  TERM-I SET-1 Series NBSE/X/2021 Code No. 041/10/1 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 1. If HCF (26,169) = 13 then LCM (26,169) is  (a) 26 (b) 52 (c) 338 (d) 13 2. 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 3. O bserve the right angled triangle ABC, right angled at B as shown below: 1 A x M 5 x+5 C B What is the length of MC? (a) 2.5 cm (b) 4.5 cm (c) 6 cm (d) 7.5 cm 4. 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 5. Which of the following can be the probability of an event? 1 (a) 2 (b) –1 (c) 0.3 (d) 1.12 6. In the following 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 7. What is the value of 3 − sin2 60° ? 1 tan 30° tan 60° (a) 2 1 (b) 3 1 (c) 2 3 (d) 3 3 4 4 4 4 NBSE 2021 2

8. The decimal representation of 11 will 1 23 × 5 1 (a) Terminate after 1 decimal place (b) Terminate after 2 decimal places 1 1 (c) Terminate after 3 decimal places (d) Not terminate 1 1 9. The pair of equations x = a and y = b graphically represents the lines which are (a) Parallel (b) Intersecting at (b, a) (c) Coincident (d) Intersecting at (a, b) 10. If the distance between the points (2, –2) and (–1, x) is 5, one of the values of x is (a) –2 (b) 2 (c) –1 (d) 1 11. The product of a non-zero rational and irrational number is (a) Always irrational (b) Always rational (c) Rational or irrational (d) 1 12. 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 13. If cos A + cos2 A = 1, then sin2 A + sin4 A is equal to (a) –1 (b) 0 (c) 1 (d) None of these 14. Which of these is equivalent to 2 tan x (sec2 x − 1) ? 1 cos3 x 1 (a) 2 tan3 x cosec x (b) 2 cot3 x cosec3 x (c) 2 tan3 x sec3 x (d) 2 cot3 x sec3 x 15. The area of the square is same as the area of a circle. Then their perimeters are in the ratio (a) 1 : 1 (b) π : 2 (c) 2 : π (d) None of these 16. In the given figure, DE is parallel to BC. If AD = 3 and AE = 2.7 cm, then EC is equal to 1 DB 2 A DE BC (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 18. 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 19. 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: NBSE 2021 3 [P.T.O.

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 20. Arnav has 40 cm long red and 84 cm long blue ribbon. He cuts each ribbon into pieces such that all pieces are of equal length. What is the length of each piece? 1 (a) 4 cm as it is the HCF of 40 and 84 (b) 4 cm as it is the LCM of 40 and 84 (c) 12 cm as it is the LCM of 40 and 84 (d) 12 cm as it is the HCF of 40 and 84 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= 2 4 2 X' 02 4 X –10 –8 –6 –4 –2 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 (b) 1 (c) 0 (d) 2 2 NBSE 2021 4

23. If x2n – 1 + ym–4 = 0 is a linear equation, which of these is also a linear equation? 1 (a) xn + ym = 0 1m (c) x n + 1 + ym+ 4 = 0 (d) n + m =0  2 (b) xn + y 5 = 0 x5 y5 24. The largest number which divides 615 and 963 leaving remainder 6 in each case is 1 (a) 82 (b) 95 (c) 87 (d) 93 25. If a card is drawn from a deck of cards, what is the probability of a card drawn to be a red or a black card and what can we say about the event? 1 (a) 0 and it is a sure event (b) 1 and it is a sure event (c) 0 and it is an impossible event (d) 1 and it is an impossible event 26. 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 27. If 2x = sec q and 2 = tan q, then the value of  x 2 − 1 is 1 x  x2  (a) 4 (b) 1 (c) 2 (d) 1 4 2 28. 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 29. 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 30. The distance of the point P(–3, –4) from the x-axis (in units) is  1 1 (a) 3 (b) –3 (c) 4 31. Consider the diagram given below:  P 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 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. The decimal representation of 6 is 1 1250 (a) 0.0048 (b) 0.048 (c) 0.48 (d) 0.000048 33. 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 34. The coordinates of the point which is reflection of point (–3, 5) in x-axis are 1 (a) (3, 5) (b) (3, –5) (c) (–3, –5) (d) (–3, 5) 35. 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 36. 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) 37. The number of polynomials having zeroes as –2 and 5 is 1 (a) 1 (b) 2 (c) 3 (d) More than 3 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. 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 40. 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 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 6 Mukha 4 Svanasana 2 X' –3 –2 –1–2 0 1 2 3 4 X –4 Trikonasana –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 (d) 2, –8 1 42. T he 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 44. The zeroes in the above shown graph are (a) 2, 4 (b) –2, 4 (c) –8, 4 NBSE 2021 7 [P.T.O.

45. The zeroes of the quadratic polynomial 4 3x2 + 5x − 2 3 are 1 (a) 2, 3 2, 3 (c) 2, 3 (d) − 2, 3 2 4 (b) − 2 4 3 4 3 4 Q46 – Q50 are based on Case Study-2 Case Study-2 The children of a school prepared a dance item for 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 coordinates 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