`f(x)=|x log_e x|` monotonically decreases in (a)`(0,1/e)` (b) `(1/e ,1)` (c)`(1,oo)` (d) `(1/e ,oo)`

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

The function f(x)=cot^(-1)x+x increases in the interval (a)(1,oo)(b)(-1,oo)(c)(-oo,oo)(d)(0,oo)

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

The domain of f(x)=log|log x|is(0,oo)(b)(1,oo)(c)(0,1)uu(1,oo)(d)(-oo,1)

If f(x)=2e^(x)-c ln x monotonically increases for every x in(0,oo), then the true set of values of c is

If f(x)=(log)_(x^(2))(log x), then f'(x) at x=e is (a) 0(b)1(c)1/e (d) 1/2e

Range of the function f(x)=(ln x)/(sqrt(x)) is (a) (-oo,\ e) (b) (-oo,\ e^2) (c) (-oo,2/e) (d) (-oo,1/e)

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

Let f:(0,oo)vec R be given by f(x)=int_((1)/(x))^(x)(e^(-(t+(1)/(t)))dt)/(t), then (a)f(x) is monotonically increasing on [1,oo)(b)f(x) is monotonically decreasing on (1,oo)(b)f(x) is an odd function of x on R

The interval of increase of the function f(x)=x-e^(x)+tan(2 pi/7) is (a) (0,oo)(b)(-oo,0)(c)(1,oo)(d)(-oo,1)