Range of `f(x) =sin^20x+cos^48x` is (A) `[0,1]` (B) `(0,1]` (C) `(0,oo)` (D) none of these

If expression x^2-4cx+b^2gt0 for all x epsilon R and a^2+c^2ltab then range of the function (x+a)/(x^2+bx+c^2) is (A) (0,oo) (B) (0,oo) (C) (-oo,oo) (D) none of these

If a!=0 and log_x (a^2+1)lt0 then x lies in the interval (A) (0,oo) (B) (0,1) (C) (0,a) (D) none of these

The values of x for which 1/(1+sqrt(x)), 1/(1-x), 1/(1-sqrt(x) are in A.P. lie in the interval (A) (0,oo) (B) (1,oo) (C) (0,1) (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 function x^x decreases in the interval (a) (0,e) (b) (0,1) (c) (0,1/e) (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

If intf(x)*cosxdx=1/2{f(x)}^2+c , then f(0)= (A) 1 (B) 0 (C) -1 (D) none of these

Let f(x)=(1+b^2)x^2+2b x+1 and let m(b) the minimum value of f(x) as b varies, the range of m(b) is (A) [0,1] (B) (0,1/2] (C) [1/2,1] (D) (0,1]

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

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