The ratio of the areas of a circle and an equilateral triangle whose diameter and a side are respectively equal, is (a) `pi\ :sqrt(2)` (b) `pi\ :sqrt(3)` (c) `sqrt(3)\ :pi` (d) `sqrt(2)\ :pi`

The ratio of the area of a square of side a and that of an equilateral triangle of side a , is (a) 2:1\ (b) 2:sqrt(3)\ (c) 4:3 (d) 4:sqrt(3)

If area of a circle inscribed in an equilateral triangle is 48pi square units, then perimeter of the triangle is (a) 17sqrt(3) units (b) 36 units (c) 72 units (d) 48sqrt(3) units

If the area of a square is same as the area of the circle, then the ratio of their perimeters, in terms of pi , is (a) pi\ :sqrt(3) (b) 2\ :sqrt(pi) (c) 3\ :pi (d) pi\ :sqrt(2)

The area of a circle inscribed in an equilateral triangle is 154\ c m^2 . Find the perimeter of the triangle. [U s e\ \ pi=22//7a n d\ sqrt(3)=1. 73]

A rectangle is inscribed in an equilateral triangle of side length 2a units. The maximum area of this rectangle can be (a) sqrt(3)a^2 (b) (sqrt(3)a^2)/4 a^2 (d) (sqrt(3)a^2)/2

The value of the definite integral int_0^(pi/2)sqrt(tanx)dx is sqrt(2)pi (b) pi/(sqrt(2)) 2sqrt(2)pi (d) pi/(2sqrt(2))

The area of a square is equal to the area of a circle. The ratio between the side of the square and the radius of the circle is (a) sqrt(pi):1 (b) 1:sqrt(pi) (c) 1:pi (d) pi:1

In Fig. 15.111, if A B C is an equilateral triangle, then shaded area is equal to (FIGURE) (a) (pi/3-(sqrt(3))/4)r^2 (b) (pi/3-(sqrt(3))/2)r^2 (c) (pi/3+(sqrt(3))/4)r^2 (d) (pi/3+sqrt(3))r^2

If the circumference and the area of a circle are numerically equal, then diameter of the circle is (a) pi/2 (b) 2pi (c) 2 (d) 4

A pair of tangents is drawn to a unit circle with center at the origin and these tangents intersect at A enclosing an angle of 60^0 . The area enclosed by these tangents and the arc of the circle is (a) 2/(sqrt(3))-pi/6 (b) sqrt(3)-pi/3 (c) pi/3-(sqrt(3))/6 (d) sqrt(3)(1-pi/6)