NBSE Question Papers Mathematics Basic Term-1 (Set-3) for Class 10

Class 10  TERM-I SET-3 Series NBSE/X/2021 Code No. 241/10/3 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–BASIC 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 P(A) denotes the probability of an event A, then  (a) P(A) < 0 (b) P(A) > 0 (c) 0 ≤ P(A) ≤ 1 (d) –1 ≤ P(A) ≤ 1 2. If the perimeter of a circle is equal to that of a square, then the ratio of their areas is 1 (a) 22 : 7 (b) 14 : 11 (c) 7 : 22 (d) 11 : 14 3. I f sin q – cos q = 0, then the value of (sin4 q + cos4 q) is 1 (a) 1 (b) 3 (c) 1 (d) 1 4 2 4 4. If the cost of 8 chairs and 5 tables is ` 10500; while the cost of 5 chairs and 3 tables is ` 6450, then the cost of each chair will be (in `) 1 (a) 750 (b) 600 (c) 900 (d) None of these 5. The pair of equations x + 2y + 5 = 0 and –3x + 6y + 1 = 0 has 1 (a) A unique solution (b) Exactly two solutions (c) Infinitely many solutions (d) No solution 6. The probability of getting a bad egg in a lot of 400 eggs is 0.035. The number of bad eggs in the lot is 1 (a) 7 (b) 14 (c) 21 (d) 28 7. The value of 1 − sin θ is 1 1 + sin θ (a) sec q – tan q (b) sec q + tan q (c) cosec q – cot q (d) cosec q + cot q 8. What is the decimal representation of 14 ? 1 5 (a) 2.88 (b) 2.7 (c) 2.81 (d) 2.8 9. I n the given figure, RS is parallel to PQ. If RS = 3 cm, PQ = 6 cm and ar(∆TRS) = 15 cm2, then ar(∆TPQ) = ? 1 T RS PQ (a) 70 cm2 (b) 58 cm2 (c) 60 cm2 (d) 64 cm2 10. The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the quadrant: 1 (a) I quadrant (b) II quadrant (c) III quadrant (d) IV quadrant NBSE 2021 2

11. I f two positive integers p and q can be expressed as p = ab2 and q = a3b; a, b being prime numbers, then LCM(p, q) is 1 (a) ab (b) a2b2 (c) a3b2 (d) a3b3 12. What will be the value of 1− tan 2 45° ? 1 1+ tan 2 45° (a) tan 90° (b) 1 (c) sin 45° (d) 0 13. If the product of two numbers is 1575 and HCF of these numbers is 5, the LCM of two numbers is given by 1 (a) 415 (b) 305 (c) 315 (d) 45 14. In the given figure, ABCD is a rectangle. The values of x and y, respectively are 1 x+y BC x – y 14 cm A D 30 cm (a) x = 12, y = 16 (b) x = 16, y = 10 (c) x = 22, y = 8 (d) x = 15, y = 18 15. Which set of lengths forms a right triangle? 1 (a) 5 cm, 12 cm, 16 cm (b) 7 cm, 24 cm, 25 cm (c) 3 cm, 3 cm, 4 cm (d) 6 cm, 7 cm, 9 cm 16. The prime factor of 250 is given by 1 (a) 22 × 52 (b) 22 × 53 (c) 2 × 52 (d) 2 × 53 17. Sum of the zeroes of the polynomial x2 + 7x + 10 are 1 (a) 7 (b) –7 (c) 10 (d) 8 18. Which of the following cannot be the probability of an event? 1 (a) 2 (b) –1.5 (c) 15% (d) 0.7 3 19. The mid point of the line segment joining the points (–5, 7) and (–1, 3) is 1 (a) (–3, 7) (b) (–3, 5) (c) (–1, 5) (d) (5, –3) 20. The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is 1 (a) 13 (b) 65 (c) 25 (d) 15 SECTION-B Section-B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted. 1 21. The probability that a non-leap year selected at random will contain 53 Sundays is  (a) 1 (b) 2 (c) 3 (d) 5 7 7 7 7 NBSE 2021 3 [P.T.O.

22. In ∆PQR, PQ = 6 3 cm, PR = 12 cm and QR = 6 cm, then angle Q is 1 (a) 45° (b) 60° (c) 90° (d) 120° 23. If the sum of the areas of two circles with radii R1 and R2 is equal to the area of a circle of radius R, then:  1 (a) R1 + R2 = R (b) R12 + R22 = R2 (c) R1 + R2 < R (d) R12 + R22 < R2 24. The pair of equations x = a and y = b graphically represent lines which are 1 (a) Parallel (b) Intersecting at (b, a) (c) Coincident (d) Intersecting at (a, b) 25. A racetrack is in the form of a ring whose inner circumference is 352 m and outer circumference is 396 m. The width of the track is 1 (a) 4 m (b) 6 m (c) 8 m (d) 7 m 26. If 4 tan x = 3 then cos x + sin x is equal to 1 cos x − sin x (a) 7 (b) 1 (c) –7 (d) – 1 7 7 27. The value of 2 tan 30° is equal to 1 1 − tan2 30° (a) cos 60° (b) sin 60° (c) tan 60° (d) sin 30° 28. The area of the circle that can be inscribed in a square of side 6 cm is 1 (a) 36π cm2 (b) 18π cm2 (c) 12π cm2 (d) 9π cm2 29. The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages, in years, of the son and the father are respectively  1 (a) 4 and 24 (b) 5 and 30 (c) 6 and 36 (d) 3 and 24 30. The value of (sin 30° + cos 30°) – (sin 60° + cos 60°) is 1 (a) –1 (b) 0 (c) 1 (d) 2 31. There is a circular path around a sports field. Priya takes 18 minutes to drive one round of the field. Harish takes 12 minutes. Suppose they both start at the same point and at the same time and go in the same direction. After how many minutes will they meet? 1 (a) 36 mins (b) 18 mins (c) 6 mins (d) They will not meet NBSE 2021 4

32. The LCM of two numbers is 1200. Which of the following cannot be their HCF?  1 (a) 600 (b) 500 (c) 400 (d) 200 33. If in two triangles ABC and PQR, AB = BC = CA then 1 QR PR PQ (a) ∆PQR ~ ∆CAB (b) ∆PQR ~ ∆ABC (c) ∆CBA ~ ∆PQR (d) ∆BCA ~ ∆PQR 34. If the three sides of a triangle are a, 3a, 2a then the measure of the angle opposite to the longest side is 1 (a) 60° (b) 90° (c) 45° (d) 30° 35. Someone is asked to take a number from 1 to 100. The probability that it is a prime number is1 (a) 1 (b) 6 1 (d) 13 5 25 (c) 4 50 36. Area of a sector of angle p (in degrees) of a circle with the radius R is: 1 (a) p × 2πR (b) p × 2πR 2 1 180° 180° 1 (c) p × 2πR (d) p × 2πR 2 190° 720° 37. The pair of equations y = 0 and y = –7 has (a) One solution (b) Two solutions (c) Infinitely many solutions (d) No solution 38. In the given figure, if AD is perpendicular to BC, then AB2 + CD2 equals C D BA (a) AD2 + BC2 (b) AD2 + CD2 (c) BD2 + AC2 (d) None of these 39. What will be the height of an equilateral triangle having each side 6 cm? 1 (a) 2 3 cm (b) 4 3 cm (c) 3 cm (d) 3 3 cm 40. In the equations shown below, a and b are unknown constants.      3ax + 4y = –2      2x + by = 14 If (–3, 4) is the solution of given equations, what are the values of a and b? 1 (a) a = 5, b = 2 (b) a = 5, b = –2 (c) a = 2, b = 5 (d) a = –1, b = 5 NBSE 2021 5 [P.T.O.

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 Due to heavy storm an electric wire got bent as shown in the figure. It followed a mathematical shape. Answer the following questions: 41. The shape in which the wire is bent is 1 1 (a) Spiral (b) Ellipse (c) Linear (d) Parabola 1 (d) 0 1 42. How many zeroes are there for the polynomial (shape of the wire) ? (d) –4, 2 1 (d) x2 + 2x + 3 (a) 2 (b) 3 (c) 1 (d) 0 43. The zeroes of the polynomial are (a) –1, 5 (b) –1, 3 (c) 3, 5 44. What will be the expression of the polynomial? (a) x2 + 2x – 3 (b) x2 – 2x + 3 (c) x2 – 2x – 3 45. What will be the value of the polynomial if x = –1? (a) 6 (b) –18 (c) 18 Q46 – Q50 are based on Case Study-2 Case Study-2 Using of mobile screens for long hours makes a child lazy, affect eyesight and give headache. Those who are addicted to playing PUBG can get easily stressed out or face anxiety issues in public due to lack of social interaction. To raise social awareness about ill effects of playing NBSE 2021 6

PUBG, a school decided to start ‘BAN PUBG’ campaign. Students are asked to prepare campaign board in the shape of a rectangle (as shown in the figure). Y C D (8, 6) (2, 6) BAN PUBG A B X X¢ (2, 2) (8, 2) Y¢ 46. The area of the board is  1 1 (a) 15 sq. units (b) 20 sq. units (c) 24 sq. units (d) 40 sq. units 1 47. If the cost of 1 cm2 of board is ` 10, the cost of board is  1 1 (a) ` 240 (b) ` 244 (c) ` 280 (d) ` 400 48. The intersection point of the diagonals is (a) (5, 4) (b) (0, 0) (c) (4, 2) (d) (–4, 6) (d) (–6, 8) 49. If we interchange both the axes, then coordinates of C is given by (a) (8, 6) (b) (6, 8) (c) (–6, –8) 50. The image of the point D on the x-axis is given by (a) (–2, 6) (b) (–2, –6) (c) (2, –6) (d) (6, 2) NBSE 2021 7 [P.T.O.

ROUGH WORK NBSE 2021 8