Let `f:[-1, 10]->R ,w h e r ef(x)=sinx+[(x^2)/a],` be an odd function. Then the set of values of parameter `a` is/are `(-10 ,10)~{0}` (b) `(0, 10)` `(100 ,oo)` (d) `(100 ,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

The set of points where the function f(x)=x|x| is differentiable is (-oo,oo) (b) (-oo,0)uu(0,oo) (0,oo) (d) [0,oo)

If cos^2x-(c-1)cosx+2cgeq6 for every x in R , then the true set of values of c is (a) (2,oo) (b) (4,oo) (c) (-oo,-2) (d) (-oo,-4)

The solution set of the inequality max {1-x^2,|x-1|}<1 is (-oo,0)uu(1,oo) (b) (-oo,0)uu(2,oo) (0,2) (d) (0,2)

The set of points where the function f(x)=x|x| is differentiable is (a) (-oo,\ oo) (b) (-oo,\ 0)uu(0,\ oo) (c) (0,\ oo) (d) [0,\ oo]

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

Statement-1: Every function can be uniquely expressed as the sum of an even function and an odd function. Statement-2: The set of values of parameter a for which the functions f(x) defined as f(x)=tan(sinx)+[(x^(2))/(a)] on the set [-3,3] is an odd function is , (9,oo)

If e^x+e^(f(x))=e , then the range of f(x) is (-oo,1] (b) (-oo,1) (1, oo) (d) [1,oo)

Ifint_(sinx)^1t^2f(t)dt=1-sinx ,w h e r e .x in (0,pi/2), then find the value of f(1/(sqrt(3)))dot

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