Top 50 MCQs – CBSE Class 10 Maths (2026)

1. If HCF(336, 54) = 6, then LCM(336, 54) is:

(a) 3024
(b) 1008
(c) 1512
(d) 2016

✅ Answer: (a) 3024

We use \( \text{HCF} \times \text{LCM} = a \times b \). So, \( \text{LCM} = \frac{336 \times 54}{6} = 3024 \).

2. The zeroes of the polynomial \( x^2 - 3 \) are:

(a) \( \sqrt{3}, -\sqrt{3} \)
(b) \( 3, -3 \)
(c) \( 0, 3 \)
(d) \( 1, -1 \)

✅ Answer: (a) \( \sqrt{3}, -\sqrt{3} \)

Solve \( x^2 - 3 = 0 \Rightarrow x = \pm \sqrt{3} \).

3. The pair of equations \( 2x + 3y = 5 \) and \( 4x + 6y = 10 \) has:

(a) Unique solution
(b) No solution
(c) Infinitely many solutions
(d) None of these

✅ Answer: (c) Infinitely many solutions

The second equation is exactly twice the first ⇒ coincident lines.

4. In an AP, if \( a = 5 \), \( d = 3 \), then \( a_{10} \) is:

(a) 30
(b) 32
(c) 35
(d) 28

✅ Answer: (b) 32

\( a_n = a + (n-1)d = 5 + 9 \times 3 = 32 \).

5. If \( \sin A = \frac{1}{2} \), then \( \cos A = \)?

(a) \( \frac{\sqrt{3}}{2} \)
(b) \( \frac{1}{\sqrt{2}} \)
(c) \( \frac{1}{2} \)
(d) \( \frac{\sqrt{2}}{2} \)

✅ Answer: (a) \( \frac{\sqrt{3}}{2} \)

If \( \sin A = \frac{1}{2} \), then \( A = 30^\circ \), so \( \cos 30^\circ = \frac{\sqrt{3}}{2} \).

6. The distance between points (2, 3) and (5, 7) is:

(a) 5 units
(b) \( \sqrt{13} \)
(c) \( \sqrt{25} \)
(d) 6 units

✅ Answer: (a) 5 units

Distance = \( \sqrt{(5-2)^2 + (7-3)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \).

7. A tangent PQ at point P of a circle of radius 5 cm meets a line through the centre O at Q such that OQ = 13 cm. Length PQ is:

(a) 12 cm
(b) 13 cm
(c) 8 cm
(d) \( \sqrt{119} \) cm

✅ Answer: (a) 12 cm

OP ⊥ PQ ⇒ \( OP^2 + PQ^2 = OQ^2 \) ⇒ \( 5^2 + PQ^2 = 13^2 \) ⇒ \( PQ = \sqrt{169 - 25} = \sqrt{144} = 12 \).

8. If the probability of winning a game is 0.6, then the probability of losing it is:

(a) 1
(b) 0.4
(c) 0.6
(d) 0

✅ Answer: (b) 0.4

P(lose) = 1 – P(win) = 1 – 0.6 = 0.4.

9. The median of the data: 13, 15, 16, 18, 20 is:

(a) 16
(b) 15
(c) 18
(d) 17

✅ Answer: (a) 16

Odd number of terms ⇒ median = middle term = 3rd term = 16.

10. The volume of a sphere of radius 3 cm is:

(a) \( 36\pi \text{cm}^3 \)
(b) \( 12\pi \text{cm}^3 \)
(c) \( 27\pi \text{cm}^3 \)
(d) \( 9\pi \text{cm}^3 \)

✅ Answer: (a) \( 36\pi \text{cm}^3 \)

Volume = \( \frac{4}{3}\pi r^3 = \frac{4}{3}\pi (27) = 36\pi \).

11. The decimal expansion of \( \frac{17}{8} \) will terminate after how many places?

(a) 1
(b) 2
(c) 3
(d) 4

✅ Answer: (c) 3

\( \frac{17}{8} = \frac{17}{2^3} \). Denominator is of the form \( 2^m5^n \) ⇒ terminates after max(m,n) = 3 places.

12. If one zero of \( 2x^2 - 3x + k \) is reciprocal of the other, then \( k = \)?

(a) 2
(b) -2
(c) \( \frac{3}{2} \)
(d) \( -\frac{3}{2} \)

✅ Answer: (a) 2

Let zeroes be \( \alpha \) and \( \frac{1}{\alpha} \). Then product = \( \alpha \cdot \frac{1}{\alpha} = 1 = \frac{k}{2} \) ⇒ \( k = 2 \).

13. The value of \( \tan 48^\circ \tan 23^\circ \tan 42^\circ \tan 67^\circ \) is:

(a) 0
(b) 1
(c) -1
(d) 2

✅ Answer: (b) 1

Use \( \tan(90^\circ - \theta) = \cot \theta \). So, \( \tan 48^\circ = \cot 42^\circ \), \( \tan 23^\circ = \cot 67^\circ \). Product = \( \cot 42^\circ \tan 42^\circ \cdot \cot 67^\circ \tan 67^\circ = 1 \cdot 1 = 1 \).

14. The ratio of the areas of two similar triangles is 9 : 16. The ratio of their corresponding sides is:

(a) 3 : 4
(b) 4 : 3
(c) 81 : 256
(d) 16 : 9

✅ Answer: (a) 3 : 4

Area ratio = (side ratio)\(^2\) ⇒ side ratio = \( \sqrt{9/16} = 3/4 \).

15. If the roots of \( x^2 + 4x + k = 0 \) are real and equal, then \( k = \)?

(a) 4
(b) -4
(c) 16
(d) -16

✅ Answer: (a) 4

Discriminant \( D = b^2 - 4ac = 16 - 4k = 0 \) ⇒ \( k = 4 \).

16. The coordinates of the point which divides the line segment joining (4, –3) and (8, 5) in the ratio 3:1 internally are:

(a) (7, 3)
(b) (6, 1)
(c) (5, –1)
(d) (8, 2)

✅ Answer: (a) (7, 3)

Section formula: \( \left( \frac{3 \cdot 8 + 1 \cdot 4}{4}, \frac{3 \cdot 5 + 1 \cdot (-3)}{4} \right) = \left( \frac{28}{4}, \frac{12}{4} \right) = (7, 3) \).

17. The value of \( \frac{1 + \tan^2 A}{1 + \cot^2 A} \) is:

(a) \( \sec^2 A \)
(b) \( \tan^2 A \)
(c) \( \cot^2 A \)
(d) \( \cos^2 A \)

✅ Answer: (b) \( \tan^2 A \)

Numerator = \( \sec^2 A \), denominator = \( \csc^2 A \). So, \( \frac{\sec^2 A}{\csc^2 A} = \frac{1/\cos^2 A}{1/\sin^2 A} = \tan^2 A \).

18. A die is thrown once. The probability of getting a prime number is:

(a) \( \frac{1}{2} \)
(b) \( \frac{1}{3} \)
(c) \( \frac{2}{3} \)
(d) \( \frac{1}{6} \)

✅ Answer: (a) \( \frac{1}{2} \)

Prime numbers on a die: 2, 3, 5 ⇒ 3 outcomes. Total = 6 ⇒ P = \( \frac{3}{6} = \frac{1}{2} \).

19. The sum of first 10 natural numbers is:

(a) 45
(b) 55
(c) 65
(d) 100

✅ Answer: (b) 55

Sum = \( \frac{n(n+1)}{2} = \frac{10 \times 11}{2} = 55 \).

20. The angle of elevation of the top of a tower from a point 30 m away from its foot is \( 30^\circ \). Height of the tower is:

(a) \( 10\sqrt{3} \) m
(b) \( 30\sqrt{3} \) m
(c) \( \frac{30}{\sqrt{3}} \) m
(d) 15 m

✅ Answer: (c) \( \frac{30}{\sqrt{3}} \) m

\( \tan 30^\circ = \frac{h}{30} \Rightarrow \frac{1}{\sqrt{3}} = \frac{h}{30} \Rightarrow h = \frac{30}{\sqrt{3}} \).

21. The product of the zeroes of \( 3x^2 - 5x + 2 \) is:

(a) \( \frac{2}{3} \) (b) \( -\frac{5}{3} \) (c) \( \frac{5}{3} \) (d) \( -\frac{2}{3} \)

✅ Answer: (a) \( \frac{2}{3} \)

Product = \( \frac{c}{a} = \frac{2}{3} \).

22. If \( \cos \theta = \frac{12}{13} \), then \( \sin \theta = \)?

(a) \( \frac{5}{13} \) (b) \( \frac{13}{5} \) (c) \( \frac{12}{5} \) (d) \( \frac{1}{13} \)

✅ Answer: (a) \( \frac{5}{13} \)

\( \sin \theta = \sqrt{1 - \cos^2 \theta} = \sqrt{1 - \frac{144}{169}} = \sqrt{\frac{25}{169}} = \frac{5}{13} \).

23. The perimeter of a quadrant of a circle of radius 7 cm is:

(a) 25 cm (b) 36 cm (c) 22 cm (d) 11 cm

✅ Answer: (a) 25 cm

Perimeter = \( \frac{1}{4}(2\pi r) + 2r = \frac{1}{2} \pi r + 2r = \frac{22}{7} \cdot \frac{7}{2} + 14 = 11 + 14 = 25 \) cm.

24. The mode of 5, 7, 6, 5, 9, 5, 8 is:

(a) 5 (b) 6 (c) 7 (d) 8

✅ Answer: (a) 5

5 occurs most frequently (3 times).

25. The value of \( \sin^2 \theta + \cos^2 \theta = \)?

(a) 0 (b) 1 (c) -1 (d) 2

✅ Answer: (b) 1

Fundamental identity.

26. The discriminant of \( 2x^2 - 4x + 3 = 0 \) is:

(a) 8 (b) -8 (c) 4 (d) -4

✅ Answer: (b) -8

\( D = (-4)^2 - 4(2)(3) = 16 - 24 = -8 \).

27. The 10th term of the AP: 2, 7, 12, ... is:

(a) 45 (b) 47 (c) 50 (d) 52

✅ Answer: (b) 47

\( a = 2, d = 5 \), \( a_{10} = 2 + 9 \times 5 = 47 \).

28. If two tangents inclined at \( 60^\circ \) are drawn to a circle of radius 3 cm, then length of each tangent is:

(a) \( 3\sqrt{3} \) cm (b) 6 cm (c) \( 2\sqrt{3} \) cm (d) 3 cm

✅ Answer: (a) \( 3\sqrt{3} \) cm

Angle between tangents = \( 60^\circ \) ⇒ angle between radius and tangent = \( 30^\circ \). So, \( \tan 30^\circ = \frac{3}{l} \Rightarrow l = \frac{3}{\tan 30^\circ} = 3\sqrt{3} \).

29. The mean of first five multiples of 3 is:

(a) 9 (b) 10 (c) 12 (d) 15

✅ Answer: (a) 9

Numbers: 3, 6, 9, 12, 15. Mean = \( \frac{45}{5} = 9 \).

30. The value of \( \cot (90^\circ - \theta) = \)?

(a) \( \tan \theta \) (b) \( \cot \theta \) (c) \( \sec \theta \) (d) \( \csc \theta \)

✅ Answer: (a) \( \tan \theta \)

Co-function identity.

31. The HCF of two consecutive even numbers is:

(a) 1 (b) 2 (c) 0 (d) 4

✅ Answer: (b) 2

Example: 4 and 6 → HCF = 2.

32. The graph of \( y = x^2 - 4 \) intersects x-axis at:

(a) (2, 0) and (–2, 0) (b) (0, 2) (c) (4, 0) (d) (0, –4)

✅ Answer: (a) (2, 0) and (–2, 0)

Set \( y = 0 \): \( x^2 = 4 \Rightarrow x = \pm 2 \).

33. The area of a circle is \( 154 \text{cm}^2 \). Its diameter is:

(a) 7 cm (b) 14 cm (c) 21 cm (d) 28 cm

✅ Answer: (b) 14 cm

\( \pi r^2 = 154 \Rightarrow r^2 = 49 \Rightarrow r = 7 \Rightarrow d = 14 \).

34. If \( P(E) = 0.05 \), then \( P(\text{not } E) = \)?

(a) 0.95 (b) 0.5 (c) 1.05 (d) 0

✅ Answer: (a) 0.95

\( P(\text{not } E) = 1 - P(E) = 0.95 \).

35. The common difference of the AP whose nth term is \( 3n + 5 \) is:

(a) 3 (b) 5 (c) 8 (d) 2

✅ Answer: (a) 3

\( a_n = 3n + 5 \), so \( a_1 = 8, a_2 = 11 \), d = 3.

36. The value of \( \frac{\tan 25^\circ}{\cot 65^\circ} = \)?

(a) 0 (b) 1 (c) -1 (d) \( \tan 25^\circ \)

✅ Answer: (b) 1

\( \cot 65^\circ = \tan(90^\circ - 65^\circ) = \tan 25^\circ \), so ratio = 1.

37. The curved surface area of a hemisphere of radius r is:

(a) \( 2\pi r^2 \) (b) \( 3\pi r^2 \) (c) \( \pi r^2 \) (d) \( \frac{2}{3}\pi r^3 \)

✅ Answer: (a) \( 2\pi r^2 \)

CSA of hemisphere = half of sphere = \( \frac{1}{2} \times 4\pi r^2 = 2\pi r^2 \).

38. The pair of equations \( x + 2y + 5 = 0 \) and \( -3x - 6y + 1 = 0 \) has:

(a) Unique solution (b) No solution (c) Infinitely many (d) None

✅ Answer: (b) No solution

Ratios: \( \frac{1}{-3} = \frac{2}{-6} \ne \frac{5}{1} \) ⇒ parallel lines.

39. The probability of an impossible event is:

(a) 1 (b) 0 (c) 0.5 (d) –1

✅ Answer: (b) 0

40. If \( \alpha, \beta \) are roots of \( x^2 - 5x + 6 = 0 \), then \( \alpha + \beta = \)?

(a) 5 (b) 6 (c) –5 (d) –6

✅ Answer: (a) 5

Sum of roots = \( -\frac{b}{a} = 5 \).

41. The distance of point (–3, 4) from origin is:

(a) 5 (b) 7 (c) 1 (d) \( \sqrt{7} \)

✅ Answer: (a) 5

\( \sqrt{(-3)^2 + 4^2} = \sqrt{9 + 16} = 5 \).

42. The value of \( \sin 60^\circ \cos 30^\circ + \cos 60^\circ \sin 30^\circ = \)?

(a) 0 (b) 1 (c) \( \frac{1}{2} \) (d) \( \frac{\sqrt{3}}{2} \)

✅ Answer: (b) 1

This is \( \sin(A+B) = \sin 90^\circ = 1 \).

43. The total surface area of a cube of side 5 cm is:

(a) 125 cm² (b) 150 cm² (c) 25 cm² (d) 100 cm²

✅ Answer: (b) 150 cm²

TSA = \( 6a^2 = 6 \times 25 = 150 \).

44. The empirical relationship between mean, median, and mode is:

(a) Mode = 3 Median – 2 Mean (b) Mean = 3 Mode – 2 Median (c) Median = 2 Mode – Mean (d) None

✅ Answer: (a) Mode = 3 Median – 2 Mean

45. The value of \( \cos 0^\circ + \sin 90^\circ = \)?

(a) 0 (b) 1 (c) 2 (d) –1

✅ Answer: (c) 2

\( \cos 0^\circ = 1, \sin 90^\circ = 1 \), sum = 2.

46. The number of tangents that can be drawn from an external point to a circle is:

(a) 1 (b) 2 (c) 3 (d) infinite

✅ Answer: (b) 2

47. The mid-point of line segment joining (–1, 7) and (4, –3) is:

(a) (1.5, 2) (b) (2, 2) (c) (3, 4) (d) (1, 2)

✅ Answer: (a) (1.5, 2)

Midpoint = \( \left( \frac{-1+4}{2}, \frac{7 + (-3)}{2} \right) = (1.5, 2) \).

48. The value of \( \frac{1 - \tan^2 45^\circ}{1 + \tan^2 45^\circ} = \)?

(a) 0 (b) 1 (c) –1 (d) 2

✅ Answer: (a) 0

\( \tan 45^\circ = 1 \), so \( \frac{1 - 1}{1 + 1} = 0 \).

49. The probability of getting a number less than 3 when a die is thrown is:

(a) \( \frac{1}{3} \) (b) \( \frac{1}{2} \) (c) \( \frac{2}{3} \) (d) \( \frac{1}{6} \)

✅ Answer: (a) \( \frac{1}{3} \)

Favorable: 1, 2 ⇒ 2 outcomes. P = \( \frac{2}{6} = \frac{1}{3} \).

50. The height of a cone with radius 3 cm and volume \( 12\pi \text{cm}^3 \) is:

(a) 4 cm (b) 3 cm (c) 6 cm (d) 12 cm

✅ Answer: (a) 4 cm

Volume = \( \frac{1}{3}\pi r^2 h = 12\pi \Rightarrow \frac{1}{3} \pi (9) h = 12\pi \Rightarrow 3h = 12 \Rightarrow h = 4 \).