The function `x^x` decreases in the interval (a) `(0,e)` (b) `(0,1)` (c) `(0,1/e)` (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 curve given by x+y=e^(x y) has a tangent parallel to the y-axis at the point (a) (0,1) (b) (1,0) (c) (1,1) (d) none of these

The values of a for which the integral int_0^2|x-a|dxgeq1 is satisfied are (a) (2,oo) (b) (-oo,0) (c) (0,2) (d) none of these

The range of f(x)=[|sin x|+|cosx"|""]"dot Where [.] denotes the greatest integer function, is {0} (b) {0,1} (c) {1} (d) none of these

The range of f(x)=[|sin x|+|cosx"|""]"dot Where [ ] denotes the greatest integer function, is {0} (b) {0,1} (c) {1} (d) none of these

int_(-1)^2[([x])/(1+x^2)]dx ,w h e r e[dot] denotes the greater integer function, is equal to (a) -2 (b) -1 (c) 0 (d) none of these

Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-constant, and differentiable function such that f^(prime)(x)<2f(x) and f(1/2)=1 . Then the value of int f(x)dx lies in the interval for x:[1/2,1] (a) (2e-1,2e) (b) (3-1,2e-1) (c) ((e-1)/2,e-1) (d) (0,(e-1)/2)

lim_(x->0) {(1+x)^(2/x)} (where {.} denotes the fractional part of x (a) e^2−7 (b) e^2−8 (c) e^2−6 (d) none of these

If f(x) = x+ 1/x , x>0 then the greatest value of f(x) is (a) -2 (b)0 (c) 3 (d) none of these

If the function f(x)=((128 a+a x)^(1/8)-2)/((32+b x)^(1/5)-2) is continuous at x=0 , then the value of a/b is (A) 3/5f(0) (B) 2^(8/5)f(0) (C) (64)/5f(0) (D) none of these