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

Let f(x)=inte^x(x-1)(x-2)dxdot Then f decreases in the interval (a) (-oo,-2) (b) -2,-1) (c) (1,2) (d) (2,+oo)

The domain of f(x)="log"|logx|i s (a) (0,oo) (b) (1,oo) (c) (0,1)uu(1,oo) (d) (-oo,1)

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)a n df(1/2)=1 . Then the value of int_(1/2)^1f(x)dx lies in the interval (a) (2e-1,2e) (b) (3-1,2e-1) (c) ((e-1)/2,e-1) (d) (0,(e-1)/2)

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)

The domain of the following function is f(x)=(log)_2(-(log)_(1/2)(1+1/((x^(1/4)))-1) (a) (0,1) (b) (1,0) (1,oo) (d) (1,oo)

If f(x)=int_(x^2)^(x^2+1)e^-t^2dt , then f(x) increases in (0,2) (b) no value of x (0,oo) (d) (-oo,0)

For all x in (0,1) (a) e^x (b) (log)_e (x+1) (c) sinx>x (d) (log)_e x > x

Find the values of 1/x for the following values of x (2,5) (b ) [-5 ,-1] ( c) ( 3, oo) (d) (-3,oo) ( e) (-oo , 4)

The differential coefficient of f((log)_e x) with respect to x , where f(x)=(log)_e x , is (a) x/((log)_e x) (b) 1/x(log)_e x (c) 1/(x(log)_e x) (d) none of these