If `a=int_(1/2)^2 1/x cot^7(x-1/x)dx`, then (A) `a=0` (B) `0ltalt1` (C) `agt0` (D) none of these

If int_0^1 xe^(x^2) dx=k int_0^1 e^(x^2) dx , then (A) kgt1 (B) 0ltklt1 (C) k=1 (D) none of these

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

Let a=int_0^(pi/2) sinx/xdx , then (A) 0ltalt1 (B) agt2 (C) 1ltaltpi/2 (D) none of these

If [x] denotes the integral part of x and a=int_(-1)^0 (sin^2x)/([x/pi]+1/2)dx, b=int_0^1 (sin^2x)/([x/pi]+1/2)d (x-[x]) , then (A) a=b (B) a=-b (C) a=2b (D) none of these

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

int_0^pi sqrt((1+cos2x)/2)dx= (A) 0 (B) 1 (C) 2 (D) none of these

int_(0)^(1)(cot^(-1)x)/(1+x^(2))dx

int_(0)^(1)cot^(-1)(1-x+x^(2))dx

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

If I=int_(0)^((1)/(2))(1)/(sqrt(1-x^(2n)))dx, then (A) I =(1)/(2)(C)I>=0(D) none of these