The maximum value of `(logx)/x` is (a) `1` (b) `2/e` (c) `e` (d) `1/e`

The value of e^(2logx)= ……….

The value of e^(2logx) = …………..

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

The maximum value of x^4e^ (-x^2) is (A) e^2 (B) e^(-2) (C) 12 e^(-2) (D) 4e^(-2)

If f^(prime)(x)=f(x)+int_0^1f(x)dx ,gi v e nf(0)=1, then the value of f((log)_2 2) is (a) 1/(3+e) (b) (5-e)/(3-e) (c) (2+e)/(e-2) (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

The domain of f(x)i s(0,1)dot Then the domain of (f(e^x)+f(1n|x|) is (a) (-1, e) (b) (1, e) (c) (-e ,-1) (d) (-e ,1)

lim_(x->-1)1/(sqrt(|x|-{-x}))(w h e r e{x} denotes the fractional part of (x) ) is equal to (a)does not exist (b) 1 (c) oo (d) 1/2

In A B C with fixed length of B C , the internal bisector of angle C meets the side A Ba tD and the circumcircle at E . The maximum value of C D.D E is c^2 (b) (c^2)/2 (c) (c^2)/4 (d) none of these

The value of int_1^(e^(37))(pisin(piI nx))/xdx is (a)2 (b) 4 (c) e^(27) (d) e^(37)