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

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

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

The maximum value of the function x^(2)e^(-2x),xgt0 is

The value of lim_(x rarr 1)(2-x)^(tan((pix)/2)) is (a) e^(-2/pi) (b) e^(1/pi) (c) e^(2/pi) (d) e^(-1/pi)

The value of int_0^1e^(x^2-x)dx is (a) 1 (c) > e^(-1/4) (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)

Let f,g and h be real-valued functions defined on the interval [0,1] by f(x)=e^(x^2)+e^(-x^2) , g(x)=x e^(x^2)+e^(-x^2) and h(x)=x^2 e^(x^2)+e^(-x^2) . if a,b and c denote respectively, the absolute maximum of f,g and h on [0,1] then

The value of the integral int_(e^(-1))^(e^2)|((log)_e x)/x| dx is (A) 3/2 (B) 5/2 (C) 3 (D) 5

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

If A , B ,C are angles of a triangles, then the value of |[e^(2i A),e^(-i C),e^(-i B)],[e^(-i C),e^(2i B),e^(-i A)],[e^(-i B),e^(-i A),e^(2i C)]| is 1 b. -1 c. -2 d. -4