Q.1. If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
(A) 3 units
(B) 4 units
(C) π units
(D) 2 units
AnswerAnswer: (D) 2 units
Q.2. A pendulum swings through on angle of 30∘ and describes an arc 8.8 cm in length. Find the length of pendulum in cm.
AnswerAnswer: (A) 16.8
Q.3. In the figure, the area of the portion in orange color is
(A) Area of outer circle + Area of inner circle
(B) Area of outer circle – Area of inner circle
(C) Area of inner circle – Area of outer circle
(D) Area of outer circle
AnswerAnswer: (B) Area of outer circle – Area of inner circle
Q.4. Given below is a combination figure of square ABCD of side 26cm and four circles. Find the area of the shaded region.
(A) 530.64 cm2
(B) 402.83 cm2
(C) 360 cm2
(D) 480.53 cm2
AnswerAnswer: (A) 530.64 cm2
Q.5. In the given figure, a circle is inscribed in a trapezium of height 14 cm and lengths of parallel sides are equal to 25 cm and 40 cm. What is the area of the shaded region?
(A) 455 sq cm
(B) 154 sq cm
(C) 509 sq cm
(D) 301 sq cm
AnswerAnswer: (D) 301 sq cm
Q.6. Radius of the outer circle is 18 cm and the radius of the inner circle is 7 cm. What is the area of the region between the outer and the inner circles?
(A) 361 π cm2
(B) 133 cm2
(C) 192.5 cm2
(D) 275 π cm2
AnswerAnswer: (D) 275 πcm2
Q.7. There is a circular swimming pool with center O. The radius of pool is 5 m. There are 2 points on the wall of the pool separated by distance of 7 m. These 2 points are named A and B. A rope is attached between A and B. This rope separates the shallow section of pool from deep section of pool. The shallow section is the smaller section. Which of following statements are true?
(A) The shallow section is an arc.
(B) The area of circle between OA and OB is an arc.
(C) The shallow section is a segment
(D) The shallow section is a sector
AnswerAnswer: (C) The shallow section is a segment
Q.8. A stadium is in circular shape. Within the stadium some areas have been allotted for a hockey court and a javelin range, as given in the figure. Assume the shape of the hockey court and the javelin range to be square and triangle, resp. The curators would like to accommodate a few more sports in the stadium. Help them by measuring the unallocated region within the stadium. (the radius of the stadium is 200 mts.)
(A) 40000π m2
(B) 40000(π−1) m2
(C) 20000(π−1) m2
(D) 20000π m2
AnswerAnswer: (B) 40000(π−1) m2
Q.9. Find the area of the shaded region where ABC is a quadrant of radius 5cm and a semicircle is drawn with BC as diameter.
(A) 8.8 cm2
(B) 7.14 cm2
(C) 12.5 cm2
(D) 19.64 cm2
AnswerAnswer: (C) 12.5 cm2
Q.10. Area of the shaded portion in the following figure is equal to area of.
(A) sector OADBO – segment ADBA
(B) segment AEBA
(C) segment ADBA
(D) segments ADBA and AEBA
AnswerAnswer: (D) segments ADBA and AEBA
Q.11. Consider a point A on the circle of radius 7/π cm as shown in the figure. A ball on point A moves along the circumference until it reaches a point B. The tangent at B is parallel to the tangent at A. What is the distance travelled by the ball? (Consider the ball to be a point object)
Note: The point B in the diagram may not represent its actual position.
AnswerAnswer: (B) 7cm
Q.12. There is a circle of diameter 10 cm. A chord of length 6 cm is drawn inside the circle. What is the distance between the centre and this chord in cm?
AnswerAnswer: (C) 4
Q.13. Find the area of the shaded region
(A) 24 cm2
AnswerAnswer: (C) 28cm2
Q.14. Find the area of the shaded region
AnswerAnswer: (C) 43cm2
Q.15. If a square with side ‘a’ is inserted within a circle such that the corners coincide with the
circumference of the circle with diameter ‘d’. Find the relation between ‘a’ and ‘d’.
(A) a = d/√2
AnswerAnswer: (A) a = d/√2
Q.16. The shaded area in the adjoining figure, between the circumferences of two concentric circles is 346.5 cm2. The circumference of the inner circle is 88 cm. Calculate the radius of the outer circle. [Take π=22/7]
(A) 35 cm
(B) 32 cm
AnswerAnswer: (C) 17.5cm
Q.17. A wire is bent to form a circle of radius 7 cm. From the resulting shape, a chunk of the wire is cut off, and the wire cut off measures 4 cm in length. The length of the remaining wire is
AnswerAnswer: (C) 40cm
Q.18. In the given figure below, OACB is a quadrant of a circle. The radius OA = 3.5 cm, OD = 2 cm. Calculate the area of the shaded region.
AnswerAnswer: (D) 6.125cm2
Q.19. In the figure below, AB and CD are two diameters of a circle (with center O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.
(A) 65.5 cm2
(B) 66.5 cm2
(C) 67.5 cm2
(D) 68.5 cm2