NCERT Exemplar Problems – Class 10 Mathematics
Chapter 11: Areas Related to Circles
Multiple Choice Questions (Exercise 11.1) with Correct Answers
Source: NCERT Exemplar Problems Class 10 Mathematics (Official Answer Key)
1. If the sum of the areas of two circles with radii \(R_1\) and \(R_2\) is equal to the area of a circle of radius \(R\), then
(A) \(R_1 + R_2 = R\)
(B) \(R_1^{2} + R_2^{2} = R^{2}\)
(C) \(R_1 + R_2 < R\)
(D) \(R_1^{2} + R_2^{2} < R^{2}\)
Correct Answer: (B)
2. If the sum of the circumferences of two circles with radii \(R_1\) and \(R_2\) is equal to the circumference of a circle of radius \(R\), then
(A) \(R_1 + R_2 = R\)
(B) \(R_1 + R_2 > R\)
(C) \(R_1 + R_2 < R\)
(D) Nothing definite can be said about the relation among \(R_1\), \(R_2\) and \(R\)
Correct Answer: (A)
3. If the circumference of a circle and the perimeter of a square are equal, then
(A) Area of the circle = Area of the square
(B) Area of the circle > Area of the square
(C) Area of the circle < Area of the square
(D) Nothing definite can be said about the relation between the areas of the circle and square
Correct Answer: (B)
4. Area of the largest triangle that can be inscribed in a semi-circle of radius \(r\) units is
(A) \(r^{2}\) sq. units
(B) \(\dfrac{1}{2} r^{2}\) sq. units
(C) \(2r^{2}\) sq. units
(D) \(\sqrt{2}\, r^{2}\) sq. units
Correct Answer: (A)
5. If the perimeter of a circle is equal to that of a square, then the ratio of their areas is
(A) \(22:7\) (B) \(14:11\) (C) \(7:22\) (D) \(11:14\)
Correct Answer: (B)
6. It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would be
(A) 10 m (B) 15 m (C) 20 m (D) 24 m
Correct Answer: (A)
7. The area of the circle that can be inscribed in a square of side 6 cm is
(A) \(36\pi\) cm² (B) \(18\pi\) cm² (C) \(12\pi\) cm² (D) \(9\pi\) cm²
Correct Answer: (D)
8. The area of the square that can be inscribed in a circle of radius 8 cm is
(A) 256 cm² (B) 128 cm² (C) \(64\sqrt{2}\) cm² (D) 64 cm²
Correct Answer: (B)
9. The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is
(A) 56 cm (B) 42 cm (C) 28 cm (D) 16 cm
Correct Answer: (C)
10. The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is
(A) 31 cm (B) 25 cm (C) 62 cm (D) 50 cm
Correct Answer: (D)
Answers taken from the official NCERT Exemplar answer key.