The minimum value of `2^(x^2-3)^(3+27)` is a)`2^(27)` (b) 2 (c) 1 (d) none of these

In any triangle, the minimum value of r_1r_2r_3//r^3 is equal to 1 (b) 9 (c) 27 (d) none of these

The minimum value of e^(2x^2-2x+1)sin^2x is e (b) 1/e (c) 1 (d) 0

Let alphaa n dbeta be any two positive values of x for which 2cosx ,|cosx|, and 1-3cos^2x are in G.P. The minimum value of |alpha-beta| is pi/3 (b) pi/4 (c) pi/2 (d) none of these

If a >0, then least value of (a^3+a^2+a+1)^2 is (a) 64 a^2 (b) 16 a^4 (c) 16 a^3 (d)d. none of these

The value of 3^((log)_4 5)-5^((log)_4 3) is 0 (b) 1 (c) 2 (d) none of these

Let f(x)=cospix+10x+3x^2+x^3,-2lt=xlt=3. The absolute minimum value of f(x) is 0 (b) -15 (c) 3-2pi none of these

The maximum slope of the curve y=-x^3+3x^2+9x-27 is 0 (b) 12 (c) 16 (d) 32

If a ,b ,c ,d in R^+-{1}, then the minimum value of (log)_d a+(log)_b d+(log)_a c+(log)_c b is (a) 4 (b) 2 (c) 1 (d)none of these

If 2^(x+y)=6^ya n d3^(x-1)=2^(y+1), then the value of (log3-log2)(x-y) is 1 (b) (log)_2 3-(log)_3 2 log(3/2) (d) none of these

In A B C , if the orthocentre is (0,0) and the circumcenter is (1,2), then centroid of A B C) is (a) (1/2,2/3) (b) (1/3,2/3) (c) (2/3,1) (d) none of these