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

Class 10  TERM-I SET-1 Series NBSE/X/2021 Code No. 241/10/1 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–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. If ∆ABC is right angled at C, then the value of cos (A + B) is 1 (a) 0 (b) 1 13 (c) 2 (d) 2 4. 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 5. 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 6. 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 7. The value of (1 – sin2 q) sec2 q is 1 (a) 1 (b) 0 (c) 2 (d) 3 8. The decimal expansion of the rational number 14587 will terminate after 1 1250 (a) One decimal place (b) Two decimal places (c) Three decimal places (d) Four decimal places 9. If the product of two numbers is 1575 and HCF of these numbers is 5, the LCM of two numbers is 1 (a) 415 (b) 305 (c) 315 (d) 45 10. The prime factor of 250 is given by 1 (a) 22 × 52 (b) 22 × 53 (c) 2 × 52 (d) 2 × 53 11. In 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 NBSE 2021 2

12. 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 13. If 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 14. What will be the value of 1− tan 2 45° ? 1 1+ tan 2 45° 1 (a) tan 90° (b) 1 (c) sin 45° (d) 0 15. In the given figure, ABCD is a rectangle. The values of x and y, respectively are 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 16. 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 17. A quadratic polynomial whose zeroes are –3 and 4, is 1 (a) x2 – x + 12 (b) x2 + x + 12 (c) x2 − x – 6 (d) 2x2 + 2x – 24 2 2 18. Which of the following cannot be the probability of an event? 1 (a) 2 (b) –1.5 (c) 15% (d) 0.7 1 3 1 19. The mid point of the line segment joining the points (–5, 7) and (–1, 3) is (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 (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. 21. 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 22. The probability that a non-leap year selected at random will contain 53 Sundays is  1 (a) 1 (b) 2 (c) 3 (d) 5 7 7 7 7 NBSE 2021 3 [P.T.O.

23. 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° 24. For what value of k, do the equations 3x – y + 8 = 0 and 6x – ky = –16 represent coincident lines? 1 (a) 1 (b) – 1 (c) 2 (d) –2 2 2 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. Area of the largest triangle that can be inscribed in a semicircle of radius r units is 1 (a) r2 sq. units (b) 1 r2 sq. units (c) 2r2 sq. units (d) 2r2 sq. units 2 29. 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 30. The LCM of two numbers is 1200. Which of the following cannot be their HCF?  1 (a) 600 (b) 500 (c) 400 (d) 200 31. 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 32. The value of (sin 30° + cos 30°) – (sin 60° + cos 60°) is 1 (a) –1 (b) 0 (c) 1 (d) 2 NBSE 2021 4

33. It is given that ∆ABC ~ ∆PQR, with BC = 1 . Then ar ∆PRQ is equal to 1 QR 4 ar ∆ABC 1 1 (a) 16 (b) 3 (c) 1 (d) 1 3 9 34. The pair of equations y = 0 and y = –7 has (a) One solution (b) Two solutions (c) Infinitely many solutions (d) No solution 35. 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 them 36. 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° 37. Someone is asked to take a number from 1 to 100. The probability that it is a prime number is 1 (a) 1 (b) 6 (c) 1 (d) 13 5 25 4 50 38. Area of a sector of angle p (in degrees) of a circle with the radius R is: 1 (a) p × 2πR (b) p × 2πR 2 180° 180° (c) p × 2πR (d) p × 2πR 2 190° 720° 39. The shadow of a 5 m long pole is 2 m long. At the same time the length of the shadow of a 12.5 m high building (in m) is 1 (a) 3.0 (b) 5.0 (c) 4.5 (d) 3.5 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 Students of residential society undertook to work for the campaign ‘Say no to plastics’in a city. They took the map of city and formed coordinate plane on it to divide their areas. Group A took the region under the coordinates (3, 3), (6, y), (x, 7) and (5, 6) and group B took the region under the coordinates (1, 3), (2, 6), (5, 7) and (4, 4). NBSE 2021 6

Based on the above information, answer the following questions: 46. If region covered by group A forms a parallelogram, where the coordinates are taken in the given order, then  1 (a) x = 8, y = 4 (b) x = 4, y = 8 (c) x = 2, y = 4 (d) x = 4, y = 2 47. Perimeter of the region covered by group A is  1 (a) 10 units (b) 13 units (c) 10 + 13 units (d) None of these 48. If the coordinates of region covered by group B, taken in the same order forms a quadrilateral, then the length of each of its diagonals is 1 (a) 4 2 units, 2 2 units (b) 6 2 units, 2 units (c) 3 2 units, 2 2 units (d) None of these 49. If region covered by group B forms a rhombus, where the coordinates are taken in given order, then the perimeter of this region is  1 (a) 10 units (b) 2 10 units (c) 3 10 units (d) 4 10 units 50. The coordinates of the point which divides the join of points P(x1, y1) and Q(x2, y2) internally in the ratio m : n is 1 (a)  mx2 + ny2 , mx1 + ny1  (b)  mx1 + ny1 , mx2 + ny2   m + n m + n   m + n m + n  (c)  mx2 + nx1 , my2 + ny1  (d) None of these  m + n m + n  NBSE 2021 7 [P.T.O.

ROUGH WORK NBSE 2021 8