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`

In Fig. 15.109, the area of segment A C B is (FIGURE) (a) (pi/3-(sqrt(3))/2)\ r^2 (b) (pi/3+(sqrt(3))/2)\ r^2 (c) (pi/3-2/(sqrt(3)))\ r^2 (d) None of these

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

int_0^3(3x+1)/(x^2+9)dx = (pi^)/(12)+log(2sqrt(2)) (b) (pi^)/2+log(2sqrt(2)) (c) (pi^)/6+log(2sqrt(2)) (d) (pi^)/3+log(2sqrt(2))

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

Let A_n be the area that is outside a n-sided regular polygon and inside its circumscribeing circle. Also B_n is the area inside the polygon and outside the circle inscribed in the polygon. Let R be the radius of the circle circumscribing n-sided polygon. On the basis of above information, answer the equation If n=6\ then A_n is equal to R^2((pi-sqrt(3))/2) (b) R^2((2pi-6sqrt(3))/2) R^2(pi-sqrt(3)) (d) R^2((2pi-3sqrt(3))/2)

The height of an equilateral triangle is sqrt(6)\ c mdot Its area is (a) 3sqrt(3)\ c m^2 (b) 2sqrt(3)\ c m^2 (c) 2sqrt(2)\ c m^2 (d) 6sqrt(2)\ c m^2

If theta=pi/3, then the volume of pyramid is 1/(sqrt(3)) (b) 1/(3sqrt(2)) (c) 1/(2sqrt(3)) (d) 1/(sqrt(2))

If A is the area an equilateral triangle of height h , then (a) A=sqrt(3)\ h^2 (b) sqrt(3)A=h (c) sqrt(3)A=h^2 (d) 3A=h^2

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)

In triangle ABC,angleA=pi/2b=4,c=3 ,then the value of R/r is equal to