if `Agt0,Bgt0` and `A+B=pi/3` then the maximum value of` tanA*tanB` is (A) `1/3` (B) `1/6` (C) `1/2` (D) 1

If agt0,Bgt0 and A+B=pi/4 , then the minimum value of tanA+tanB is

If A>0,B>0, and A+B=(pi)/(3), then the maximum value of tan A tan B is (1)/(sqrt(3))(b)(1)/(3) (c) 3(d) sqrt(3)

If ab=2a+3b, agt0, b gt0 , then the minimum value of ab is

The maximum value of [x(x-1)+1]^(1/3),0lt=xlt=1 is (A) (1/3)^(1/3) (B) 1/2 (C) 1 (D) 0

If a,bgt0 then the maximum value of (a^(3)b)/((a+b)^(4)), is

If agt0, bgt0, cgt0 and the minimum value of a^2(b+c)+b^2(c+a)+c^2(a+b) is kabc, then k is (A) 1 (B) 3 (C) 6 (D) 4

If y=tan^(-1)(1)/(2)+tan^(-1)b,(0 =(pi)/(4) then the maximum value of b is (1)/(2)(b)-1 (c) (2)/(3)(d)

If lim_(x->0)[1+x1n(1+b^2)]^(1/x)=2bsin^2theta,b >0,where theta in (-pi,pi], then the value of theta is (a)+-pi/4 (b) +-pi/3 (c) +-pi/6 (d) +-pi/2