If `n in N` and `int_0^1 e^x(x-1)^ndx=2e-5`, then `n=` (A) `1` (B) `2` (C) `3` (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

int_0^pi (sin((n+1)/2)x)/sinxdx= (A) 0 (B) pi/2 (C) pi (D) none of these

If n is a whole number such that n+n=n ,\ t h e n\ n=? (a) 1 (b) 2 (c) 3 (d) none of these

The value of the integral int_0^1e^x^2_dx lies in the interval (a) (0,1) (b) (-1,0) (c) (1, e) (d) none of these

The number of terms in the expansion of (x+1/x+1)^n is (A) 2n (B) 2n+1 (C) 2n-1 (D) none of these

If the coefficient of x^100 is in 1+(1+x)+(1+x)^2+(1+x)^3+………+(1+x)^n , (n >= 100) is ^201C_101 then n (A) 100 (B) 200 (C) 101 (D) none of these

The number of solution of equation sin^(-1)x+nsin^(-1)(1-x)=(mpi)/2,w h e r e n >0,m<=0, is 3 (b) 1 (c) 2 (d) None of these

f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim_(x->oo)f(x) is equal to (a) 1 (b) 1/2 (c) 2 (d) none of these

If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xf(x)= (a)1 (b) -1 (c) 0 (d) none of these

Lt_(nrarroo) {(n!)/(kn)^n}^(1/n), k!=0 , is equal to (A) k/e (B) e/k (C) 1/(ke) (D) none of these