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 least natural number a for which x+(a)/(x^(2))>=6,AA x in(0,oo); is

The smallest value of natural number n, for which 2n + 1 is not a prime number, is 3 (b) 4 (c) 5 (d) None of these

The least natural number satisfying the inequation (x-1)/(x)-(x+1)/(x-1)<2 is 0 (b) 1 (c) 2 (d) 3

Let f:R rarr[0,(pi)/(2)) be defined by f(x)=tan^(-1)(x^(2)+x+a)* Then the set of values of a for which f is onto is (a)(0,oo)(b)[2,1](c)[(1)/(4),oo](d) none of these

int_0^oo (xlogx)/(1+x^2)^2dx= (A) e (B) 1 (C) 0 (D) none of these

If a (A) x=0 (B) x=1 (C) x=2 (D) None of these.

The smallest natural number is (a) 0 (b) 1 (c) -1 (d) None of these

int_0^oo logx/(1+x^2)dx= (A) log2 (B) pi/2 (C) 0 (D) none of these

The number of real solutions of the log_(0.5)|x|=2|x| is 1 (b) 2(c)0(d) none of these

The number of points in (-oo,oo), for which x^(2)-x sin x-cos x=0, is 6(b)4(c)2(d)0