The function `x^x` decreases in the interval `(0,e)` (b) `(0,1)` `(0,1/e)` (d) none of these

The function f(x)=x^(x) decreases on the interval (a) (0,e)(b)(0,1)(c)(0,1/e)(d)(1/e,e)

If a!=0 and log_(x)(a^(2)+1)<0 then x lies in the interval (A)(0,oo)(B)(0,1)(C)(0,a)(D) none of these

The values of x for which 1/(1+sqrt(x)), 1/(1-x), 1/(1-sqrt(x) are in A.P. lie in the interval (A) (0,oo) (B) (1,oo) (C) (0,1) (D) none of these

On which of the following intervals is the function x^(100)+sin x-1 decreasing? (a) (0,(pi)/(2))(b)(0,1)(c)((pi)/(2),pi)( d) none of these

Statement-1: The function f(x)\ =\ ln\ x is increasing in (0,10) and g(x) = 1/x is decreasing in (0,10) Statement-2: If a differentiable function increases in the interval (a , b) then its derivative function decreases in the interval (a , b) .

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

If x lies in the interval [0,1], then the least value of x^(2)+x+1 is (a) 3/4(c)1 (d) none of these

On which of the following intervals is the function f given by f(x)=x^(100)+sinx-1 strictly decreasing ? (A) (0, 1) (B) (pi/2,pi) (C) (0,pi/2) (D) None of these