The least positive solution of `cot(pi/(3sqrt3) sin2x)=sqrt3` lie (a) `(0,pi/6]` (b) `(pi/9,pi/6)` (c) `(pi/12,pi/9)` (d) `(pi/3,pi/2)`

One of the root equation cosx-x+1/2=0 lies in the interval (a) (0,pi/2) (b) (-pi/(2,0)) (c) (pi/2,pi) (d) (pi,(3pi)/2)

int_(5/2)^5(sqrt((25-x^2)^3))/(x^4)dx is equal to (a) pi/6 (b) (2pi)/3 (c) (5pi)/6 (d) pi/3

The range of f(x)=sin^(-1)(sqrt(x^2+x+1))i s (0,pi/2) (b) (0,pi/3) (c) [pi/3,pi/2] (d) [pi/6,pi/3]

If log_10(sin x) + log_10(tany)+ log_10 2=0 and coty= 2sqrt3 cos x, then ordered pair (x, y) satisfying the equations simultaneously is(are) (A) (pi/3 ,pi/3) (B) (pi/3 ,pi/6) (C) (pi/6 ,(2pi)/3) (D) (pi/3 , (7pi)/6)

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)

The variable x satisfying the equation |sinxcosx|+sqrt(2+tan^2 x+cot^2x)=sqrt(3) belongs to the interval (a) [0,pi/3] (b) (pi/3,pi/3) (c) [(3pi)/4,pi] (d) none-existent

The smallest positive x satisfying the equation (log)_(cosx)sinx+(log)_(sinx)cosx=2 is pi/2 (b) pi/3 (c) pi/4 (d) pi/6

The smallest positive value of x (in radians) satisfying the equation (log)_(cosx)((sqrt(3))/2sinx)=2-(log)_(secx)(tanx) is (a) pi/(12) (b) pi/6 (c) pi/4 (d) pi/3

The least and the greatest values of (sin^(-1)x)^3+(cos^(-1)x)^3 are (a) (-pi)/2,pi/2 (b) (-pi^3)/8,(pi^3)/8 (c) (pi^3)/(32),(7pi^3)/8 (d) none of these

If tan(A-B)=1a n dsec(A+B)=2/(sqrt(3)) , then the smallest positive values of A and B, respectively, are (25pi)/(24),(19pi)/(24) (b) (19pi)/(24),(25pi)/(24) (31pi)/(24),(31pi)/(24) (d) (13pi)/(24),(31pi)/(24)