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

1

(a)

2 units

(b)

7 units

(c)

4 units

(d)

π units

If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, then the diameter of the larger circle (in cm) is

1

(a)

34

(b)

17

(c)

26

(d)

14

The ratio of radii of two circles is in the ratio of 1:5. Calculate the ratio of their perimeters

1

(a)

1:8

(b)

1:2

(c)

1:6

(d)

1:5

The area of a sector of a circle of radius 5 cm is 5 cm2. The angle contained by the sector will be

1

(a)

90°

(b)

45°

(c)

72°

(d)

60°

The inner circumference of a circular track is 440m, and the track is 14m wide. The cost of levelling the track at 25 paise/m2 will be

1

(a)

Rs. 1250

(b)

Rs. 1694

(c)

Rs. 1684

(d)

Rs. 1400

Find the circumference of the circle, whose area is 144 cm²

1

(a)

46 πcm

(b)

24 πcm

(c)

72 πcm

(d)

12 πcm

A pendulum swings through an angle of 300 and describes an arc 8.8cm in length. The length of the pendulum is

1

(a)

17 cm

(b)

8.8 cm

(c)

15.8 cm

(d)

16.8 cm

From a circular sheet of paper with a radius 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion?

1

(a)

4:3

(b)

3:1

(c)

1:3

(d)

4:1

What is the area of a regular hexagon inscribed in a circle of radius r units?

1

(a)

\(\frac { 2 }{ \sqrt { 3 } } { r }^{ 2 }\)sq. units

(b)

\(\frac { 3\sqrt { 3 } }{ 2 } { r }^{ 2 }\)sq. units

(c)

\(2\sqrt { 3 } \quad { r }^{ 2 }\)sq. units

(d)

\(\frac { \sqrt { 3 } }{ 2 } { r }^{ 2 }\)sq. units

The sum of the diameters of two circles is 280 cm and the difference of their circumferences is 88 cm. Then the larger of the two radii is

1

(a)

63 cm

(b)

44 cm

(c)

77 cm

(d)

cannot be determined

ABCD is a square of side 10 cm. The area of the shaded region will be

1

(a)

80 cm²

(b)

57 cm²

(c)

75 cm²

(d)

60 cm²

The radius of a circle if its perimeter and area are numerically equal is

1

(a)

2 units

(b)

8 units

(c)

5 units

(d)

4 units

In the given figure, ABCPA is a quadrant of a circle of radius 14cm. With AC as diameter, a semi-circle is drawn. Then the area of the shaded region will be

1

(a)

72 cm²

(b)

98 cm²

(c)

102 cm²

(d)

35 cm²

We have a circle with centre O and two radii OA and OB. If the perimeter of minor sector OAB is 55 cm, and the radius of the circle is 7cm, the value of ∠AOB is

1

(a)

450^o

(b)

45^o

(c)

180^o

(d)

110^o

A wire is bent in the form of a circle of radius 28 cm. It is rebent to form a square. The length of the side of the square will be

1

(a)

30 cm

(b)

88 cm

(c)

44 cm

(d)

40 cm

The area swept by the minute hand of a circular clock in 5 minutes forms a

1

(a)

Circle

(b)

Segment

(c)

Cone

(d)

Sector

A garden roller has a circumference of 4 m. The number of revolutions it makes in moving 40 metres are:

1

(a)

10

(b)

12

(c)

8

(d)

16

What is the area of the square inscribed in a circle with a circumference of 18.84 cm?

1

(a)

20 cm²

(b)

15 cm²

(c)

16 cm²

(d)

18 cm²

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

1

(a)

71/8 cm²

(b)

77/8 cm²

(c)

75/8 cm²

(d)

73/8 cm²

A square ABCD is inscribed in a circle of 10 units. The area of the circle not included in the square is

1

(a)

100 sq. units

(b)

250 sq. units

(c)

114 sq. units

(d)

112 sq. units

The perimeter of the given figure is

1

(a)

132 cm

(b)

42 cm

(c)

45 cm

(d)

150 cm

The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 40 cm and 9 cm is:

1

(a)

62 cm

(b)

49 cm

(c)

41 cm

(d)

82 cm

The area and circumference of a circle are numerically equal. What is the diameter of the circle?

1

(a)

4 units

(b)

20 units

(c)

2 units

(d)

40 units

The diameter of a cycle wheel is 28 cm. The number of revolutions it makes in moving 13.2 km is

1

(a)

1500

(b)

15000

(c)

500

(d)

8000

A circular disc of radius 6 cm is divided into three sectors with central angles 90o, 120o and 150o. The ratio of the areas of the three sectors is

1

(a)

4: 5: 6

(b)

1: 5: 6

(c)

3: 4: 5

(d)

2: 3: 4

If the circumference of a circle increases from 2π to 4π then its area is

1

(a)

Tripled

(b)

Doubled

(c)

Four times

(d)

Halved

A momento is made as shown in the figure. Its base shade is to be silver plated from the front at the rate of 20 per cm². what  is the total coast of silver plating?

1

(a)

230

(b)

260

(c)

240

(d)

250

If C is the circumference of a circle of radius r, then perimeter of one of the quadrants will be

1

(a)

\(\frac { C }{ 2 } \)

(b)

\(\frac { C }{ 4 } +r\)

(c)

\(\frac { C }{ 4 } \)

(d)

\(\frac { C }{ 4 } +2r\)

The perimeter (in cm) of a square circumscribing a circle of radius a cm, is

1

(a)

4 a

(b)

8 a

(c)

16 a

(d)

2 a

The angle of the major sector and the corresponding minor sector of a circle are

1

(a)

supplementary angles

(b)

complementary angles

(c)

conjugate angles

(d)

Reflex angles

The length of a minute hand of a wall clock is 7 cm. What is the area swept by it is 30 minutes?

1

(a)

2.308

(b)

3.608

(c)

-3.208

(d)

3.208

The minute hand of a clock is 10 cm long. The area of the face of the clock described by the minute hand between 8 A.M and 8.25 A.M is

1

(a)

100 cm²

(b)

125.5 cm²

(c)

120 cm²

(d)

130.95 cm²

The shaded part of the circle in the given figure represents a

1

(a)

Segment

(b)

semi-circle

(c)

Sector

(d)

Chord

In the figure, OACB represents a Quadrant of a circle of radius 3.5 cm with centre O. The area of the shaded region is

1

(a)

9.625 sq. cm

(b)

8.675 sq. cm

(c)

5.5 sq. cm

(d)

6.125 sq. cm

If the difference between the circumference and the radius of a circle is 37 cm,If the difference between the circumference and the radius of a circle is 37 cm, then using \(\pi =\frac { 22 }{ 7 } \)the circumference (in cm) of the circle is:

1

(a)

44

(b)

154

(c)

14

(d)

7

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

1

(a)

\({ R }_{ 1 }^{ 2 }+{ R }_{ 2 }^{ 2 }={ R }^{ 2 }\)

(b)

R₁ + R₂ < R

(c)

R₁ + R₂ = R

(d)

\({ R }_{ 1 }^{ 2 }+{ R }_{ 2 }^{ 2 }={ <R }^{ 2 }\)

The area of a circle with diameter 6 m exceeds the combined areas of circles with diameters 4m and 2 m by

1

(a)

0 m²

(b)

4π m²

(c)

π m²

(d)

5π m²

The value of π is

1

(a)

4.13

(b)

11/7

(c)

33/6

(d)

3.14

To warn ships of underwater rocks, a light house spreads a red colored light over a sector of angle 80o to a distance of 16.5 km. The area of the sea over which the ships are warned is

1

(a)

135.7 km²

(b)

200 km²

(c)

180.5 km²

(d)

190.14 km²

In given figure, a circle of radius 7.5cm is inscribed in a square, the remaining area of the square is

1

(a)

46 cm sq.

(b)

48.91 cm sq

(c)

52.32 cm sq

(d)

48.375 cm sq

The radii of two circles are 19 cm and 9 cm respectively. The radius of the circle which has its circumference equal to the sum of the circumferences of the two circles is:

1

(a)

30 cm

(b)

26 cm

(c)

32 cm

(d)

28 cm

In fig, area of shaded region is

1

(a)

\(\pi \left( { r }_{ 1 }^{ 2 }+{ r }_{ 2 }^{ 2 } \right) \)

(b)

\(\pi \left( { r }_{ 1 }+{ r }_{ 2 } \right) \)

(c)

\(\pi \left( { r }_{ 1 }-{ r }_{ 2 } \right) \)

(d)

\(\pi \left( { r }_{ 2 }^{ 2 }+{ r }_{ 1 }^{ 2 } \right) \)

If the side of an equilateral triangle and the radius of a circle are equal, find the ratio of their areas.

1

(a)

\(\pi :\sqrt { 2 } \)

(b)

\(\sqrt { 2 } :\pi \)

(c)

\(\sqrt { 3 } :4\pi \)

(d)

\(\sqrt { 3\pi } :4\)

The area of a circular plot is 9856 sq. m. The cost of fencing the plot at the rate of Rs. 6 per meter will be

1

(a)

Rs. 3456

(b)

Rs. 2211

(c)

Rs. 2112

(d)

Rs. 2000

A wire in the shape of square of perimeter 88 cm is bent so as to form a circular ring. Find the radius of the ring.

1

(a)

28 cm

(b)

7 cm

(c)

14 cm

(d)

22 cm

The outer and inner diameters of a circular ring are 34 cm and 32 cm respectively. The area of the ring is:

1

(a)

33π cm²

(b)

60π cm²

(c)

66π cm²

(d)

29π cm²

If the diameter of semicircular protractor is 14 cm, then its perimeter is:

1

(a)

30 cm

(b)

44 cm

(c)

36 cm

(d)

40 cm

If the ratio of the arc AB to the circumference of a circle is 1:3,then measure of the angle subtended by the arc at the centre is

1

(a)

120°

(b)

172°

(c)

72°

(d)

65°

If O is the centre of the circle, and OA and OB are two radii, find the ratio of the area of the sector AOB to the area of the circle, if ㄥAOB = 60^o

1

(a)

1:4

(b)

4:1

(c)

1:6

(d)

6:1

park is in the form of a rectangle 120m by 90 m. At the centre of the park there is a circular lawn as shown in the figure. If the area of the park excluding the lawn is 2950 m², then the radius of the circular lawn will be

1

(a)

50 m

(b)

60 m

(c)

35 m

(d)

40 m