`f(x)=(x-2)|x-3|` is monotonically increasing in (a)`(-oo,5/2)uu(3,oo)` (b) `(5/2,oo)` (c)`(2,oo)` (d) `(-oo,3)`

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

Prove that f(x) = x^(2) -6x + 3 is strictly increasing in (3, 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)

The value of a for which the function f(x)=(4a-3)(x+log5)+2(a-7)cotx/2sin^2x/2 does not possess critical points is (a) (-oo,-4/3) (b) (-oo,-1) (c) [1,oo) (d) (2,oo)

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)

If (log)_3(x^2-6x+11)lt=1, then the exhaustive range of values of x is: (a) (-oo,2)uu(4,oo) (b) [2,4] (c) (-oo,1)uu(1,3)uu(4,oo) (d) none of these

The domain of the function f(x)=1/(sqrt(|x|-x)) is: (1) (-oo,oo) (2) (0,oo (3) (-oo,""0) (4) (-oo,oo)"-"{0}

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)

If (y+3)/(2y+5)=sin^2x+2cosx+1, then the value of y lies in the interval (-oo,-8/3) (b) (-(12)/5,oo) (-8/3,-(12)/5) (d) (-8/3,oo)

For x^2-(a+3)|x|+4=0 to have real solutions, the range of a is (-oo,-7]uu[1,oo) b. (-3,oo) c. (-oo,-7) d. [1,oo)