Let `f (x)=cos(pi/x)` and `D_+={x: f (x)>0}` . Then D_+ contains (a) (2/5,1/2) (b) (1/2,2/3) (c) (2/3,-1/2) (d) (-pi,-1/2)`

Let f(x)={1+(2x)/a ,0lt=x 1)f(x) exists ,then a is (a) 1 (b) -1 (c) 2 (d) -2

Let f(x)=cos^(-1)((x^2)/(1+x^2)) . The range of f is a) [0,pi/2] b) [-pi/2,pi/2] c) [-pi/2,0] d)None of these

If f(x)=cos[pi^2]x +cos[-pi^2]x , where [x] stands for the greatest integer function, then (a) f(pi/2)=-1 (b) f(pi)=1 (c) f(-pi)=0 (d) f(pi/4)=1

If the equation x^3+b x^2+c x+1=0,(b (a) -pi (b) -pi/2 (c) pi/2 (d) pi

Let f(x)=sin^(-1)x+|sin^(-1)x|+sin^(-1)|x| The range of f(x) is (a) [0,(pi)/(2)] (b) [0,(3pi)/(2)] (c) [0,(pi)/(4)] (d) [0,pi]

Let f(x)=sin^(-1)2x + cos^(-1)2x + sec^(-1)2x . Then the sum of the maximum and minimum values of f(x) is (a) pi (b) pi/2 (c) 2pi (d) (3pi)/2

Let f(x)=sin^(-1)2x + cos^(-1)2x + sec^(-1)2x . Then the sum of the maximum and minimum values of f(x) is (a) pi (b) pi/2 (c) 2pi (d) (3pi)/2

{(x){(1-sin^(2)x)/(3cos^(2)x),x (pi)/(2) then f(x) is continuous at x=(pi)/(2), if (a)a=(1)/(3),b=2 (b) a=(1)/(3),=(8)/(3)(c)a=(2)/(3),b=(8)/(3)(d) none of these

If sin^(-1)x+sin^(-1)y=(2 pi)/(3) ,then the value of cos^(-1)x+cos^(-1)y is (A) (2 pi)/(3) (B) (pi)/(3) (C) (pi)/(2) (D) pi

Let f:[-pi/3,(2pi)/3]vec[0,4] be a function defined as f(x)=sqrt(3)sinx-cosx+2. Then f^(-1)(x) is given by (a) sin^(-1)((x-2)/2)-pi/6 (b) sin^(-1)((x-2)/2)+pi/6 (c) (2pi)/3+cos^(-1)((x-2)/2) (d) none of these