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)`

Evaluate: inte^x(1/x-1/(x^2))dxdot

f(x)=(x-1)|(x-2)(x-3)|dot Then f decreases in (a) (2-1/(sqrt(3)),2) (b) (2,2+1/(sqrt(3))) (c) (2+1/(sqrt(3)),4) (d) (3,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)

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: R ->[0,pi/2) be defined by f(x)=tan^(-1)(x^2+x+a)dot Then the set of values of a for which f is onto is (a) (0,oo) (b) [2,1] (c) [1/4,oo] (d) none of these

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)

Let f(x)=int x^2/((1+x^2)(1+sqrt(1+x^2)))dx and f(0)=0 then f(1) is

If f^(prime)(x)=|x|-{x}, where {x} denotes the fractional part of x , then f(x) is decreasing in (-1/2,0) (b) (-1/2,2) (-1/2,2) (d) (1/2,oo)

If f(x)=x^2+x+3/4 and g(x)=x^2+a x+1 be two real functions, then the range of a for which g(f(x))=0 has no real solution is (A) (-oo,-2) (B) (-2,2) (C) (-2,oo) (D) (2,oo)