SET 1 30 MATHS MCQs for Class 10 based on NCERT PATTERN

Class 10 Maths MCQs

Class 10 Maths MCQs

Here are 30 Multiple Choice Questions (MCQs) for Class 10 Mathematics based on the NCERT syllabus. These questions cover topics from all chapters.

Real Numbers

1. The HCF of 96 and 404 is:

a) 4

b) 6

c) 8

d) 12

2. Which of the following is an irrational number?

a) √9

b) √25

c) √2

d) √16

3. The decimal expansion of 13/625 will terminate after how many decimal places?

a) 1

b) 2

c) 3

d) 4

Polynomials

4. The zeroes of the polynomial \( x^2 - 3x - 4 \) are:

a) 1, -4

b) -1, 4

c) 3, -4

d) -3, 4

5. If one zero of the quadratic polynomial \( x^2 + 3x + k \) is 2, then the value of \( k \) is:

a) -10

b) 10

c) -5

d) 5

6. The number of zeroes of the polynomial \( x^3 - 4x^2 + 5x - 2 \) is:

a) 1

b) 2

c) 3

d) 4

Pair of Linear Equations in Two Variables

7. The pair of equations \( x + 2y = 5 \) and \( 3x + 6y = 15 \) has:

a) A unique solution

b) No solution

c) Infinitely many solutions

d) Two solutions

8. The value of \( k \) for which the system of equations \( x + 2y = 3 \) and \( 5x + ky = 15 \) has infinitely many solutions is:

a) 5

b) 10

c) 15

d) 20

9. The solution of the equations \( 2x + 3y = 12 \) and \( x - y = 1 \) is:

a) \( x = 3, y = 2 \)

b) \( x = 2, y = 3 \)

c) \( x = 3, y = 3 \)

d) \( x = 2, y = 2 \)

Quadratic Equations

10. The roots of the quadratic equation \( x^2 - 5x + 6 = 0 \) are:

a) 2, 3

b) -2, -3

c) 1, 6

d) -1, -6

11. The quadratic equation whose roots are 2 and -3 is:

a) \( x^2 + x - 6 = 0 \)

b) \( x^2 - x - 6 = 0 \)

c) \( x^2 + 5x + 6 = 0 \)

d) \( x^2 - 5x + 6 = 0 \)

12. The discriminant of the quadratic equation \( 2x^2 - 4x + 3 = 0 \) is:

a) 8

b) -8

c) 16

d) -16

Arithmetic Progressions

13. The 10th term of the AP: 5, 8, 11, 14, ... is:

a) 32

b) 35

c) 38

d) 40

14. The sum of the first 20 terms of the AP: 1, 4, 7, 10, ... is:

a) 590

b) 600

c) 610

d) 620

15. If the 3rd term of an AP is 5 and the 7th term is 17, then the common difference is:

a) 2

b) 3

c) 4

d) 5

Triangles

16. In two similar triangles, the ratio of their corresponding sides is 3:5. What is the ratio of their areas?

a) 3:5

b) 9:25

c) 6:10

d) 27:125

17. In a right-angled triangle, the lengths of the two perpendicular sides are 6 cm and 8 cm. The length of the hypotenuse is:

a) 10 cm

b) 12 cm

c) 14 cm

d) 16 cm

18. If the areas of two similar triangles are in the ratio 16:25, then the ratio of their corresponding sides is:

a) 4:5

b) 5:4

c) 16:25

d) 25:16

Coordinate Geometry

19. The distance between the points \( A(2, 3) \) and \( B(5, 7) \) is:

a) 5

b) 6

c) 7

d) 8

20. The midpoint of the line segment joining the points \( (4, 5) \) and \( (-2, 3) \) is:

a) \( (1, 4) \)

b) \( (2, 4) \)

c) \( (3, 4) \)

d) \( (4, 4) \)

21. The coordinates of the point which divides the line segment joining \( (1, 2) \) and \( (4, 5) \) in the ratio 2:1 are:

a) \( (3, 4) \)

b) \( (4, 3) \)

c) \( (5, 4) \)

d) \( (4, 5) \)

Trigonometry

22. If \( \sin \theta = \frac{3}{5} \), then \( \cos \theta \) is:

a) \( \frac{4}{5} \)

b) \( \frac{3}{4} \)

c) \( \frac{5}{4} \)

d) \( \frac{5}{3} \)

23. The value of \( \tan 45^\circ \) is:

a) 0

b) 1

c) \( \frac{1}{\sqrt{2}} \)

d) \( \sqrt{3} \)

24. If \( \tan \theta = \frac{1}{\sqrt{3}} \), then \( \theta \) is:

a) 30°

b) 45°

c) 60°

d) 90°

Circles

25. The length of the tangent from a point \( P \) to a circle of radius 5 cm is 12 cm. The distance of \( P \) from the center of the circle is:

a) 13 cm

b) 14 cm

c) 15 cm

d) 16 cm

26. If two tangents inclined at an angle of 60° are drawn to a circle of radius 3 cm, then the length of each tangent is:

a) \( 3\sqrt{3} \) cm

b) 6 cm

c) 3 cm

d) \( 2\sqrt{3} \) cm

Statistics

27. The mean of the first 10 natural numbers is:

a) 5

b) 5.5

c) 6

d) 6.5

28. The median of the data 3, 5, 7, 9, 11 is:

a) 5

b) 7

c) 9

d) 11

Probability

29. The probability of getting a head when a coin is tossed once is:

a) 0

b) 0.5

c) 1

d) 2

30. A bag contains 5 red balls and 3 blue balls. The probability of drawing a red ball is:

a) \( \frac{3}{8} \)

b) \( \frac{5}{8} \)

c) \( \frac{1}{2} \)

d) \( \frac{2}{5} \)

Answers

1. a) 4

2. c) √2

3. d) 4

4. b) -1, 4

5. a) -10

6. c) 3

7. c) Infinitely many solutions

8. b) 10

9. a) \( x = 3, y = 2 \)

10. a) 2, 3

11. a) \( x^2 + x - 6 = 0 \)

12. b) -8

13. a) 32

14. a) 590

15. b) 3

16. b) 9:25

17. a) 10 cm

18. a) 4:5

19. a) 5

20. a) \( (1, 4) \)

21. a) \( (3, 4) \)

22. a) \( \frac{4}{5} \)

23. b) 1

24. a) 30°

25. a) 13 cm

26. a) \( 3\sqrt{3} \) cm

27. b) 5.5

28. b) 7

29. b) 0.5

30. b) \( \frac{5}{8} \)

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