In a ` triangleA B C ,/_B=90^0 and b+a=4.` The area of the triangle is maximum when `/_C` is (a)`pi/4` (b) `pi/6` (c)`pi/3` (d) none of these

If an a triangle A B C , b=3 c, a n d C-B=90^0, then find the value of tanB

If cot^(-1)n/pi>pi/6,n in N , then the maximum value of n is (a) 6 (b) 7 (c) 5 (d) none of these

The range of f(x)=sin^(-1)((x^2+1)/(x^2+2)) is (a) [0,pi/2] (b) (0,pi/6) (c) [pi/6,pi/2] (d) none of these

In any triangle A B C ,(a^2+b^2+c^2)/(R^2) has the maximum value of 3 (b) 6 (c) 9 (d) none of these

The value of c in Lagranges theorem for the function f(x)=logsinx in the interval [pi/6,(5pi)/6] is (a) pi/4 (b) pi/2 (c) (2pi)/3 (d) none of these

If in a triangle ABC, a=5, b=4 and A=pi/2 +B, then the value of tan ""C/2 is-

Area enclosed between the curves |y|=1-x^2 and x^2+y^2=1 is (a) (3pi-8)/3 (b) (pi-8)/3 (c) (2pi-8)/3 (d) None of these

Consider square A B C D of side length 1. Let P be the set of all segments of length 1 with endpoints on the adjacent sides of square A B C D . The midpoints of segments in P enclose a region with area Adot The value of A is (a) pi/4 (b) 1-pi/4 (c) 4-pi/4 (d) none of these

The principal value of sin^(-1)(sin((2pi)/3)) is (a) -(2pi)/3 (b) (pi)/3 (c) (4pi)/3 (d) (5pi)/3 (e) none of these

int_0^oo(x dx)/((1+x)(1+x^2)) is equal to (A) pi/4 (B) pi/2 (C) pi (D) none of these"