In a ` A 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

In any triangle A B C ,(a^2+b^2+c^2)/(R^2) has the maximum value of (a) 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 cot^(-1)n/pi>pi/6,n in N , then the maximum value of n is 6 (b) 7 (c) 5 (d) none of these

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

The value of integral int_0^(1/sqrt3) (dx)/((1+x^2)sqrt(1-x^2)) must be (a) 3+2pi (b) 4-pi (c) 2+pi (d) none of these

If x , y in [0,2pi]a n dsinx+siny=2, then the value of x+y is pi (b) pi/2 (c) 3pi (d) none of these

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

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

If 3tan(theta-15^0)=tan(theta+15^0), then theta is equal to n in Z) n pi+pi/4 (b) npi+pi/8 npi+pi/3 (d) 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"