SAS
Bongaigaon
Academic Session 2024-2025
Roll No........................ Date........................
MCQ Practice Paper
Total Time: 1 Hrs 30 Mins Max Marks: 70
General Instructions
This Question Paper is Divided into 1 Sections
Section A Consists of 70 Questions
Standard/Class: 10th Subject: MATHEMATICS
Section A
State True/False - (1 Marks)
1. tanθ increases faster than sinθ as θ increases. [1]
2. Two identical solid hemispheres of equal base radius r cm are stuck together along [1]
their bases. The total surface area of the combination is 6𝝅r2
3. BOA is a diameter of a circle and the tangent at a point P meets BA extended at T. If [1]
∠PBO = 30°, then ∠PTA is equal to
a) 40⁰ b) 30⁰ c) 60⁰ d) 45⁰
Objective(MCQ) - (1 Marks)
4. Which of the following is not irrational? [1]
(a) (2 – √3)²
(b) (√2 + √3)²
(c) (√2 -√3)(√2 + √3)
(d) √5
5. The distance of the point (-1, 7) from x-axis is [1]
(a) -1 (b) 7 (c) 6 (d) √50
6. The number of solutions of 3x + y = 243 and 243x - y = 3 is [1]
(a) 0 (b) 1 (c) 2 (d) infinite
Page 1 of 8
7. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is [1]
a) 2520 b) 10 c) 100 d) 564
8. If ABC and DEF are similar triangles such that ∠A = 47° and ∠E = 83°, then ∠C= [1]
(a) 50° (b) 60° (c) 70° (d) 80°
9. If the common difference of an AP is 3, then a20 - a15 is [1]
(A) 5 (B) 3 (C) 15 (D) 20
10. How many parallel tangents can a circle have? [1]
(a) 1 (b) 2 (c) infinite (d) none of these
11. IF ∆ABC ~ ∆DEF such that AB = 9.1 cm and DE = 6.5 cm. If the perimeter of ∆DEF is [1]
25 cm, then the perimeter of ∆ABC is
(a) 36 cm (b) 30 cm (c) 34 cm (d) 35 cm
12. For the following distribution : [1]
the sum of lower limits of the median class and modal class is
(a) 15 (b) 25 (c) 30 (d) 35
13. Show in the given figure, APB is a tangent to a circle with centre O at point P. If [1]
∠QPB = 50°, then the measure of ∠POQ is
(a) 100° (b) 120° (c) 140° (d) 150°
14. Consider the following distribution : [1]
the frequency of the class 30-40 is
(a) 3 (b) 4 (c) 48 (d) 51
15. If c and d are roots of the equation (x - a)(x - b) - k = 0, then a, b are roots of the [1]
equation
(a) (x - c)(x - d) - k = 0 (b) (x - c)(x - d) + k = 0
(c) (x - a)(x - c) + k = 0 (d) (x - b)(x - d) + k = 0
16. If Sr denotes the sum of the first r terms of an A.P. Then, S3n : (S2n - Sn) is [1]
(a) n (b) 3n (c) 3 (d) none of these
Page 2 of 8
17. The graph of y = 5 is a line parallel to the [1]
(a) x-axis (b) y-axis (c) both axis (d) none of these
18. The sum of the length, breadth and height of a cuboid is 6√3 cm and the length of its [1]
diagonal is 2√3 cm. The total surface area of the cuboid is
(a) 48 cm2 (b) 72 cm2 (c) 96 cm2 (d) 108 cm2
19. Assertion (A): The given figure represents a hemisphere surmounted by a conical [1]
block of wood. The diameter of their bases is 6cm each and the slant height of the
cone is 5cm. The volume of the solid is 196cm³
Reason (R): The volume hemisphere is given by ⅔πr³
a) Both A and R are correct and R is the correct explanation of A.
b) Both A and R are correct but R is not the correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
20. 3 chairs and 1 table cost ₹900; where as 5 chairs and 3 tables cost ₹2,100. If the [1]
cost of 1chairs is ₹x and 1 table is ₹y, then the situation can be represented
algebraically as
(a) 3x + y = 900 3x + 5y = 2100 (b) x + 3y = 900, 3x + 5y = 2100
(c) 3x + y = 900 5x + 3y = 2100 (d) x + 3y = 900 5x + 3y = 2100
21. The positive value of k for which the equation x2 + kx + 64 = 0 and x2 - 8x + k = 0 will [1]
both have real roots, is
(a) 4 (b) 8 (c) 12 (d) 16
22. D and E are respectively the points on the sides AB and AC of a triangle ABC such [1]
that AD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE || BC. Then, length of DE (in cm) is
(a) 2.5 (b) 3 (c) 5 (d) 6
23. Assertion (A): A constant polynomial always cuts the x-axis at only one point. [1]
Reason (R): Constant polynomial does not have any zero.
a) Both A and R are true and R is the correct explanation of A.
b) Both A and R are true but R is not the correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
24. Two concentric circles of radii 3 cm and 5 cm are given. The length of chord BC [1]
which touches the inner circle at P is equal to
Page 3 of 8
a) 4 cm. b) 8 cm c) 6 cm. d) 10 cm
25. The zeroes of the quadratic polynomial x2 + 99x + 127 are [1]
(a) both positive (b) both negative
(c) both equal (d) one positive and one negative
26. AOBC is a rectangle whose three vertices are vertices A (0, 3), O (0, 0) and B (5, 0). [1]
The length of its diagonal is
(a) 5 (b) 3 (c) √34 (d) 4
27. The largest number which divides 70 and 125, leaving remainders 5 and 8, [1]
respectively, is
(a) 13 (b) 65 (c) 875 (d) 1750
28. If the area of a circle is 64π cm2, then its circumference is [1]
(a) 7π cm (b) 16π cm (c) 14π cm (d) 21π cm
29. Assertion (A): The sum of the series with the nth term. tn = (9 - 5n) is (465), when no. [1]
of terms n = 15.
Reason (R): Given series is in A.P. and sum of n terms of an A.P. is
a) Both A and R are correct and R is the correct explanation of A.
b) Both A and R are correct but R is not the correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
30. The quadratic equation whose roots are 1 and [1]
(a) 2x² + x – 1 = 0 (b) 2x² – x – 1 = 0
(c) 2x² + x + 1 = 0 (d) 2x² – x + 1 = 0
31. The roots of the equation x2 + 3x - 10 = 0 are: [1]
(a) 2, -5 (b) -2, 5 (c) 2, 5 (d) -2, -5
32. Show in the given figure, AB is a chord of the circle and AOC is its diameter such that [1]
∠ACB = 50°. If AT is the tangent to the circle at the point A, then ∠BAT is equal to
(a) 65° (b) 60° (c) 50° (d) 40°
Page 4 of 8
33. The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have [1]
infinitely many solutions is
(a) 3 (b) – 3 (c) –12 (d) no value
34. Show in the given figure, ABCD is a square of side 14 cm with E, F, G and H as the [1]
mid-points of sides AB, BC, CD and DA respectively. The area of the shaded portion
is
(a) 44 cm2 (b) 49 cm2 (c) 98 cm2 (d) 49/2π cm2
35. In a right triangle ABC, right angled at B, BC = 12 cm and AB = 5cm The radius of the [1]
circle inscribed in the triangle (in cm) is
(a) 4 (b) 3 (c) 2 (d) 1
36. If the point P (2, 1) lies on the line joining points A (4, 2) and B (8, 4), then [1]
(a) AP = ⅓ AB (b) AP = BP (c) PB = ⅓ AB (d) AP = ½ AB
37. The product of the zeros of the polynomial x3 + 4x2 + x - 6 is [1]
(a) - 4 (b) 4 (c) 6 (d) -6
38. Show in the given figure, tan A - cot C is equal to [1]
(a) 0 (b) 5/12 (c) 7/13 (d) -7/13
39. Which of the following can not be determined graphically? [1]
(a) Mean (b) Median (c) Mode (d) None of these
40. The HCF and the LCM of 12, 21, 15 respectively are [1]
(a) 3, 140 (b) 12, 420 (c) 3, 420 (d) 420, 3
41. The number of polynomials having zeroes as 4 and 7 is [1]
(a) 2 (b) 3 (c) 4 (d) more than 4
42. Which of the following is not the graph of a quadratic polynomial? [1]
Page 5 of 8
43. The number of real roots of the equation (x - 1)2 + (x - 2)2 + (x - 3)2 = 0, is [1]
(a) 1 (b) 2 (c) 3 (d) none of these
44. It is found that on walking x meters towards a chimney in a horizontal line through [1]
its base, the elevation of its top changes from 30° to 60°. The height of the chimney
is
45. sin 2A = 2 sin A is true when A = [1]
(A) 0° (B) 30° (C) 45° (D) 60°
46. In an AP if a = –7.2, d = 3.6, an = 7.2, then n is [1]
(a) 1 (b) 3 (c) 4 (d) 5
47. If the mean of observations x1, x2,.........,xn is x̄, then the mean of x1 + a, x2 + a,........., [1]
xn + a is
48. [1]
If 2tan A = 3, then the value of is
(a) 7√13 (b) 1√13 (c) 3 (d) does not exist
49. The area of the triangle formed by the lines y = x, x = 6 and y = 0 is [1]
(a) 36 sq. units (b) 18 sq. units (c) 9 sq. units (d) 72 sq. units
50. [1]
If 5 tanθ - 4 = 0, then the value of is
(a) ⅝ (b) ⅚ (c) 0 (d) ⅙
51. If the mean of first a natural numbers is 5n/9, then n = [1]
(a) 5 (b) 4 (c) 9 (d) 10
52. A plumbline (sahul) is the combination of (show in the given figure). [1]
(a) a cone and a cylinder (b) a hemisphere and a cone
(c) frustum of a cone and a cylinder (d) sphere and cylinder
53. If A(5, 3), B(11, -5) and P(12, y) are the vertices of a right triangle right angled at [1]
P, then y =
Page 6 of 8
(a) -2, 4 (b) -2, 4 (c) 2, -4 (d) 2, 4
54. If x tan 45° sin 30° = cos 30° tan 30°, then x is equal to [1]
(a) √3 (b) ⅓ (c) ½ (d) 1
55. In ∆ABC, PQ || BC. If PB = 6 cm, AP = 4 cm, AQ = 8 cm, then the length of AC is [1]
(a) 12 cm (b) 20 cm (c) 6 cm (d) 14 cm
56. Assertion (A): The point (0, 4) lies on y-axis. [1]
Reason (R): The x coordinate on the point on y-axis is zero.
a) Both A and R are correct and R is the correct explanation of A.
b) Both A and R are correct but R is not the correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
57. If angle between two radii of a circle is 130º, the angle between the tangents at the [1]
ends of the radii is :
(a) 90º (b) 50º (c) 70º (d) 40º
58. Two dice are thrown simultaneously. The probability that the product of the numbers [1]
appearing on the dice is 7 is
a) 7 b) 2 c) 0 d) 1
59. If angles A, B, C of a ∆ABC form an increasing AP, then sin B = [1]
(a) 1/2 (b) √3/2 (c) 1 (d) 1/√2
60. Assertion (A): Two similar triangles are always congruent. [1]
Reason (R): If the areas of two similar triangles are equal then the triangles are
congruent.
a) Both A and R are correct and R is the correct explanation of A.
b) Both A and R are correct but R is not the correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
61. If A is an acute angle in a right triangle ABC, right angled at B, then the value of sin A [1]
+ cos A is
(a) equal to 1 (b) greater than 1 (c) Less than 1 (d) 2
62. Assertion (A): If (0, 3), (1, 1), and (-1, 2) be the midpoints of the sides of a triangle, [1]
then the centroid of the original triangle is (0, 2)
Reason (R): The centroids of the triangle and joins the midpoints of the sides of
triangle are same.
a) Both A and R are correct and R is the correct explanation of A.
b) Both A and R are correct but R is not the correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
63. Assertion (A): Tossing a coin 50 times is called an event. [1]
Reason (R): The possible outcomes of an experiment are called events.
a) Both A and R are correct and R is the correct explanation of A.
b) Both A and R are correct but R is not the correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
64. The surface area of a cube is 216 cm2, its volume is [1]
(a) 144 cm3 (b) 196 cm3 (c) 212 cm3 (d) 216 cm3
Page 7 of 8
65. Three vertices of a parallelogram ABCD are A(1, 4), B(-2, 3) and C(5, 8). The ordinate [1]
of the fourth vertex D is
(a) 8 (b) 9 (c) 7 (d) 6
66. If two positive integers p and q can be expressed as p = ab2 and q = a3 b; a, b being [1]
prime numbers, then LCM (p, q) is
(a) ab (b) a2 b2 (c) a3 b2 (d) a3 b3
67. 9 sec² A – 9 tan² A = [1]
(A) 1 (B) 9 (C) 8 (D) 0
68. (sec A + tan A) (1 – sin A) = [1]
(A) sec A (B) sin A (C) cosec A (D) cos A
69. sin 2B = 2 sin B is true when B is equal to [1]
(a) 90° (b) 60° (c) 30° (d) 0°
70. If A and (2A – 45°) are acute angles such that sin A = cos (2A – 45°), then tan A is [1]
equal to
(a) 0
(b) ½
(c) 1
(d) √3
Page 8 of 8
Answers
1. True 2. False 3. True
4. C 5. b 6. b
7. A 8. a 9. C
10. c 11. d 12. b
13. a 14. a 15. b
16. c 18. c 20. c
21. d 22. b 24. b
25. b 26. c 27. a
28. b 30. B 31. a
32. c 33. d 34. c
35. c 36. d 37. c
38. a 39. A 40. c
41. D 42. d 43. d
44. d 46. d 47. c
48. c 49. B 50. c
51. c 52. b 53. c
54. D 55. b 57. b
58. c 59. b 61. b
64. d 65. B 66. c
67. B 68. D 69. D
70. C
