Class 10 Mathematics (NCERT)

1. The area of a circle with radius r is given by:

• A. 2πr
• B. πr²
• C. πr
• D. 2πr²

2. The circumference of a circle of radius r is given by:

• A. πr²
• B. 2πr
• C. πr
• D. 2πr²

3. Area of a sector of angle θ of a circle with radius r is:

• A. (θ / 360°) × 2πr
• B. (θ / 180°) × πr²
• C. (θ / 360°) × πr²
• D. (θ / 180°) × 2πr

4. The length of an arc of a sector of angle θ of a circle with radius r is:

• A. (θ / 360°) × πr²
• B. (θ / 360°) × 2πr
• C. (θ / 180°) × πr²
• D. (θ / 720°) × 2πr

5. If the perimeter and area of a circle are numerically equal, then the radius of the circle is:

• A. 2 units
• B. π units
• C. 4 units
• D. 7 units

6. If the radius of a circle is 7 cm, its area is (take π = 22/7):

• A. 44 cm²
• B. 154 cm²
• C. 308 cm²
• D. 77 cm²

7. The perimeter of a quadrant of a circle of radius r is:

• A. (πr / 2) + 2r
• B. (πr / 2)
• C. πr + 2r
• D. 2πr + r

8. Area of a sector of central angle 60° in a circle of radius 6 cm is:

• A. 132/7 cm²
• B. 66/7 cm²
• C. 11/7 cm²
• D. 154/7 cm²

9. If the area of a circle is 154 cm², then its perimeter is:

• A. 22 cm
• B. 44 cm
• C. 88 cm
• D. 66 cm

10. The area of a quadrant of a circle whose circumference is 22 cm is:

• A. 77/8 cm²
• B. 77/4 cm²
• C. 77/2 cm²
• D. 154 cm²

11. Angle subtended by minute hand of a clock in 5 minutes is:

• A. 5°
• B. 15°
• C. 30°
• D. 60°

12. Area swept by 14 cm long minute hand of a clock in 5 minutes is:

• A. 154/3 cm²
• B. 154/6 cm²
• C. 308/3 cm²
• D. 77/3 cm²

13. Area of segment of a circle is calculated by subtracting area of corresponding triangle from area of corresponding:

• A. Circle
• B. Sector
• C. Quadrant
• D. Diameter

14. If ratio of areas of two circles is 4 : 9, then ratio of their radii is:

• A. 2 : 3
• B. 16 : 81
• C. 4 : 9
• D. 1 : 2

15. If ratio of circumferences of two circles is 3 : 4, then ratio of their areas is:

• A. 3 : 4
• B. 9 : 16
• C. 16 : 9
• D. √3 : 2

16. If diameter of a circle is increased by 100%, its area increases by:

• A. 100%
• B. 200%
• C. 300%
• D. 400%

17. A chord of a circle of radius 10 cm subtends a right angle at centre. Area of minor sector is (use π = 3.14):

• A. 78.5 cm²
• B. 314 cm²
• C. 157 cm²
• D. 39.25 cm²

18. Perimeter of a semicircle with radius r including its diameter is:

• A. πr
• B. πr + r
• C. πr + 2r
• D. 2πr + 2r

19. The area of the largest triangle that can be inscribed in a semicircle of radius r is:

• A. r²
• B. 2r²
• C. r²/2
• D. 1/2 r²

20. Area of a square inscribed in a circle of radius r is:

• A. r²
• B. 2r²
• C. 4r²
• D. πr²

21. The wheel of a car makes 1000 revolutions in moving 88 km. Diameter of the wheel is:

• A. 14 m
• B. 28 m
• C. 7 m
• D. 28 cm

22. Area of ring bounded by two concentric circles of radii R and r (R > r) is:

• A. π(R - r)
• B. π(R² - r²)
• C. π(R² + r²)
• D. 2π(R - r)

23. Area of a sector of angle p (in degrees) of a circle with radius R is:

• A. (p / 180°) × 2πR
• B. (p / 180°) × πR²
• C. (p / 360°) × 2πR
• D. (p / 720°) × 2πR²

24. If circumference of a circle is 44 cm, then area of circle is:

• A. 154 cm²
• B. 308 cm²
• C. 44 cm²
• D. 88 cm²

25. Number of revolutions made by a wheel of diameter 0.7 m to cover distance of 1.1 km is:

• A. 500
• B. 1000
• C. 250
• D. 100

26. If sum of areas of two circles with radii R1 and R2 is equal to area of circle of radius R, then:

• A. R1 + R2 = R
• B. R1² + R2² = R²
• C. R1 + R2 < R
• D. R1² + R2² < R²

27. If sum of circumferences of two circles with radii R1 and R2 is equal to circumference of circle of radius R, then:

• A. R1 + R2 = R
• B. R1 + R2 > R
• C. R1 + R2 < R
• D. R1² + R2² = R²

28. A horse is tied to a peg at one corner of a square grass field of side 15 m by a 5 m long rope. Area of field horse can graze is:

• A. 19.625 m²
• B. 78.5 m²
• C. 154 m²
• D. 225 m²

29. Area of an equilateral triangle of side 2a is:

• A. √3 a²
• B. (√3/4) a²
• C. 2√3 a²
• D. √3/2 a²

30. Distance travelled by a circular wheel of diameter d in 1 revolution is:

• A. πd
• B. 2πd
• C. πd²
• D. πd/2