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 tan[cos^(-1)(4/5)+tan^(-1)(2/3)] is 6/(17) (b) 7/(16) (c) (16)/7 (d) none of these

The least value of 2sin^2theta+3cos^2theta is 1 (b) 2 (c) 3 (d) 5

If a , b in [0,2pi] and the equation x^2+4+3sin(a x+b)-2x=0 has at least one solution, then the value of (a+b) can be (a) (7pi)/2 (b) (5pi)/2 (c) (9pi)/2 (d) none of these

The least natural number a for which x+a x^(-2)>2AAx in (0,oo) is 1 (b) 2 (c) 5 (d) none of these

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

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

The value of int_0^1e^(x^2-x)dx is (a) 1 (c) > e^(-1/4) (d) none of these

If the function f(x)=a x^3+b x^2+11 x-6 satisfies conditions of Rolles theorem in [1,3] and f'(2+1/(sqrt(3)))=0, then values of a and b , respectively, are (A) -3,2 (B) 2,-4 (C) 1,-6 (D) none of these

In triangle A B C ,tanA+tanB+tanC=6a n dtanAtanB=2, then the values of tanA ,tanB ,tanC are, respectively (a) 1,2,3 (b) 3,2//3,7//3 (c) 4,1//2 ,3//2 (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