For `0 < theta < 2pi` , `sin^(-1)(sintheta)>cos^(-1)(sintheta)` is true when `theta` belongs to (a)`(pi/4,pi)` (b) `(pi,(3pi)/2)` (c)`(pi/4,(3pi)/4)` (d) `((3pi)/4,2pi)`

Given both thetaa n dphi are acute angles and sintheta=1/2,cosvarphi=1/3, then the value of theta+varphi belongs to (a) (pi/3,pi/2] (b) (pi/2,(2pi)/3] (c) ((2pi)/3,(5pi)/6] (d) ((5pi)/6,pi]

If roots of the equation 2x^2-4x+2sintheta-1=0 are of opposite sign, then theta belongs to (pi/6,(5pi)/6) (b) (0,pi/6)uu((5pi)/6,pi) ((13pi)/6,(17pi)/6) (d) (0,pi)

Range of tan^(-1)((2x)/(1+x^2)) is (a) [-pi/4,pi/4] (b) (-pi/2,pi/2) (c) (-pi/2,pi/4) (d) [pi/4,pi/2]

In which of the following sets the inequality sin^6x+cos^6x >5/8 holds good? (a) (-pi/3,pi/8) (b) ((3pi)/8,(5pi)/8) (c) (pi/4,(3pi)/4) (d) ((7pi)/8,(9pi)/8)

A solution of the equation cos^2theta+sintheta+1=0 lies in the interval a. (-pi//4,pi//4) b. (pi//4,3pi//4) c. (3pi//4,5pi//4) d. (5pi//4,7pi//4)

The smallest positive root of the equation tanx-x=0 lies in (0,pi/2) (b) (pi/2,pi) (pi,(3pi)/2) (d) ((3pi)/2,2pi)

In which of the following intervals the inequality, sinx < cos x < tanx < cot x can hold good ? (a) ((7pi)/4,2pi) (b) ((3pi)/4,pi) (c) ((5pi)/4,(3pi)/2) (d) (0,(pi)/4)

f(x)=min(sinx, cosx),x in (-pi,pi) the values of x where f(x) is non differentiable, is the set A . Then A is subset of (A) {(-3pi)/4, (-pi)/4, (3pi)/4} (B) {(-pi)/4, pi/4, (3pi)/3} (C) {(-3pi)/4, (3pi)/4} (D) {(-3pi)/4, (-pi)/4, pi/4, (3pi)/4}

Range of f(x)=sin^(-1)x+tan^(-1)x+sec^(-1)x is (a) (pi/4,(3pi)/4) (b) [pi/4,(3pi)/4] (c) {pi/4,(3pi)/4} (d) none of these

If cos(sinx)=0, then x lies in (a) (pi/4,pi/2)uu(pi/2,\ pi) (b) (-pi/4,\ 0) (c) (pi,(3pi)/2) (d) null set