The values of `a` for which the integral `int_0^2|x-a|dxgeq1` is satisfied are (a)`(2,oo)` (b) `(-oo,0)` (c)`(0,2)` (d) none of these

The exhaustive set of values of a for which inequation (a -1)x^2- (a+1)x+ a -1>=0 is true AA x >2 (a) (-oo,1) (b)[7/3,oo) (c) [3/7,oo) (d) none of these

Th range of k for which the inequaliity kcos^2x-kcosx+1>=0 AA x in(-oo,oo) is

The value of integral int_0^(1/sqrt3) (dx)/((1+x^2)sqrt(1-x^2)) must be (a) 3+2pi (b) 4-pi (c) 2+pi (d) none of these

The value of the integral int_0^1sqrt((1-x)/(1+x))dx is (a) pi/2+1 (b) pi/2-1 (c) -1 (d) 1

The value of the definite integral int_0^(pi/2)(sin5x)/(sinx)dxi s 0 (b) pi/2 (c) pi (d) 2pi

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

int_0^oo(pi/(1+pi^2x^2)-1/(1+x^2))logxdx is equal to (a) -pi/2lnpi (b) 0 (c) pi/2ln2 (d) none of these

The domain of the function f(x)=sqrt(x^2-[x]^2) , where [x] is the greatest integer less than or equal to x , is (a) R (b) [0,+oo) (c) (-oo,0) (d) none of these

Given that f'(x) > g'(x) for all real x, and f(0)=g(0) . Then f(x) < g(x) for all x belong to (a) (0,oo) (b) (-oo,0) (c) (-oo,oo) (d) none of these

The value of the integral int_0^oo(xlogx)/((1+x^2)^2)dxi s 0 (b) log 7 (c) 5 log 13 (d) none of these