The value of `theta in (0,2pi)` for which `2sin^2theta-5sintheta+2>0` is (a) `(0,pi/6)uu((5pi)/6,2pi)` (b) `(pi/8,(pipi)/6)` (c) `(0,pi/8)uu(pi/6pi/6)` (d) `((41pi)/(48),pi)`

The general values of theta satisfying the equation 2sin^2theta-3sintheta-2=0 is (n in Z)dot npi+(-1)^npi/6 (b) npi+(-1)^npi/2 npi+(-1)^n(5pi)/6 (d) npi+(-1)^n(7pi)/6

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)

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)

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]

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 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)

The expression cos3theta+sin3theta+(2sin2theta-3)(sintheta-costheta) is positive for all theta in (a) (2npi-(3pi)/4,2npi+pi/4),n in Z (b) (2npi-pi/4,2npi+pi/6),n in Z (c) (2npi-pi/3,2npi+pi/3),n in Z (d) (2npi-pi/4,2npi+(3pi)/4),n in Z

The maximum value of the function f(x)=sin(x+pi/6)+cos(x+pi/6) in the interval (0,pi/2) occurs at pi/(12) (b) pi/6 (c) pi/4 (d) pi/3

Let 2sin^2x+3sinx-2>0 andx^2-x-2<0(x is measured in radians). Then x lies in the interval (a) (pi/6,(5pi)/6) (b) (-1,(5pi)/6) (c) (-1,2) (d) (pi/6,2)

The value of the definite integral int_0^(pi/2)(sin5x)/(sinx)dxi s 0 (b) pi/2 (c) pi (d) 2pi