Area of circle inscribed in the equilateral`/_\ABC` is (A) `2/3 piR^2` (B) `1/4 pi R^2` (C) `1/3 pi R^2` (D) none of these

int_-pi^(3pi) cot^-1(cotx)dx= (A) pi^2 (B) 2pi^2 (C) 3pi^2 (D) none of these

sqrt(3)int_0^pi dx/(1+2sin^2x)= (A) -pi (B) 0 (C) pi (D) none of these

sin^-1 (cos(sin^-1(sqrt(3)/2))= (A) pi/3 (B) pi/6 (C) - pi/6 (D) none of these

sin^-1 (-1/2)+tan^-1 (sqrt(3))= (A) -pi/6 (B) pi/3 (C) pi/6 (D) none of these

Which of the following expresses the circumference of a circle inscribed in a sector OAB with radius RandAB=2a?(a)2 pi(Ra)/(R+a) (b) (2 pi R^(2))/(a)2 pi(r-a)^(2)(d)2 pi(R)/(R-a)

The area of a circle inscribed in an equilateral triangle is 154cm^(2). Find the perimeter of the triangle.[Use pi=22/7and sqrt(3)=1.73]

int_0^pi dx/(1-2acosx+a^2), alt1 is equal to (A) (pialog2)/4 (B) (4pi)/(2-a^2) (C) pi/(1-a^2) (D) none of these

int_-(pi/3)^(pi/3) (x^3cosx)/sin^2xdx= (A) 0 (B) 1 (C) -1 (D) none of these

If the sum of the areas of two circles with radii r_1 and r_2 is equal to the area of a circle of radius r , then r_1^2 +r_2^2 (a) > r^2 (b) =r^2 (c)