The equation `cos^8x+bcos^4x+1=0` will have a solution if `b` belongs to (A) `(-oo,2]` (B) `[2,oo]` (C) `[-oo,-2]` (D) none of these

For the equation cos^(-1)x+cos^(-1)2x+pi=0 , the number of real solution is (A)1 (B) 2 (C) 0 (D) oo

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

int_0^oo(x dx)/((1+x)(1+x^2)) is equal to (A) pi/4 (B) pi/2 (C) pi (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

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 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

e^(|sinx|)+e^(-|sinx|)+4a=0 will have exactly four different solutions in [0,2pi] if. a in R (b) a in [-3/4,-1/4] a in [(-1-e^2)/(4e),oo] (d) none of these

If no solution of 3siny+12sin^3x=a lies on the line y=3x , then (a) a in (-oo,-9)uu(9,oo) (b) a in [-9,9] (c) a in {-9,9} (d) none of these

If b > a , then the equation (x-a)(x-b)-1=0 has (a) both roots in (a ,b) (b) both roots in (-oo,a) (c) both roots in (b ,+oo) (d)one root in (-oo,a) and the other in (b ,+oo)

Let f: R->R be a function such that f(x)=a x+3sinx+4cosxdot Then f(x) is invertible if (a) a in (-5,5) (b) a in (-oo,5) (c) a in (-5,+oo) (d) none of these