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51). If the radius of a circle is increased by 6%, find the percentage increase in its area.
A). 15%
B). 12.36%
C). 8.39%
D). 17%
52). The area of a sector of a circle is 77 sq cm and the angle of the sector is 45 degree. Find the radius of the circle.
A). 7 cm
B). 14 cm
C). 21 cm
D). 28 cm
53). The wheel of an engine turns 350 times round its axle to cover a distance of 1.76 km. The diameter of the wheel is
A). 3 cm
B). \( \Large 3\sqrt{3} \) cm
C). 9 cm
D). \( \Large \sqrt{3} \) cm
54). The ratio of the areas of the circumcircle and the incircle of a square is
A). 2 : 1
B). 1 : 2
C). \( \Large \sqrt{2}:1 \)
D). \( \Large 1:\sqrt{2} \)
55). The circumferences of two circles are in the ratio 2 : 3. What is the ratio of their areas?
A). 2 : 3
B). 4 : 9
C). 1 : 3
D). 8 : 27


56). Consider the following statements
Area of segment of a circle is less than area of its corresponding sector.
Distance travelled by a circular Wheel of diameter 2d cm in one revolution is greater than 6d cm.
Which of the above statements is/are correct?

A). Only I
B). Only II
C). Both I and II
D). Neither I nor II
57). The radius of a circle is so increased that its circumference increased by 5%. The area of the circle, then increases by
A). 12.5%
B). 10.25%
C). 10.5%
D). 11.25%
58). The area of a circle is increased by 22 sq cm when its radius is increased by 1 cm. Find the original radius of the Circle.
A). 6 cm
B). 3.2 cm
C). 3 cm
D). 3.5 cm
59). What is the area of the larger segment circle formed by a chord of, length 5 cm subtending an angle of 90 degree at the centre?
A). \( \Large \frac{25}{4}\left(\frac{\pi}{2}+1\right)cm^{2} \)
B). \( \Large \frac{25}{4}\left(\frac{\pi}{2}-1\right)cm^{2} \)
C). \( \Large \frac{25}{4}\left(\frac{3\pi}{2}+1\right)cm^{2} \)
D). None of the above
60). A person observed that he required 30 s time to cross a circular ground along its diameter than to cover it once along the boundary. If his speed was 30m/min, then the radius of the circular ground is \( \Large (take \  \pi = 22/7) \)
A). 10.5 m
B). 3.5 m
C). 5.5 m
D). 7.5 m
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