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)`

The equation (cosp-1)x^2+(cos p)x+sin p=0 in the variable x has real roots. The p can take any value in the interval (a) (0,2pi) (b) (-pi,0) (c) (-pi/2,pi/2) (d) (0,pi)

Let f:(-1,1)rarrB be a function defined by f(x)=tan^(-1)[(2x)/(1-x^2)] . Then f is both one-one and onto when B is the interval. (a) [0,pi/2) (b) (0,pi/2) (c) (-pi/2,pi/2) (d) [-pi/2,pi/2]

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 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 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

If | vec a+ vec b|<| vec a- vec b|, then the angle between vec aa n d vec b can lie in the interval a. (pi//2,pi//2) b. (0,pi) c. (pi//2,3pi//2) d. (0,2pi)

The number of solutions of the equation tanx+secx=2cosx lying in the interval [0,2pi] is 0 (b) 1 (c) 2 (d) 3

The function f(x)=tan^(-1)(sinx+cosx) is an increasing function in (-pi/2,pi/4) (b) (0,pi/2) (-pi/2,pi/2) (d) (pi/4,pi/2)

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 sum of all the solution in [0,4pi] of the equation tanx+cotx+1=cos(x+pi/4)i s (a) 3pi (b) pi/2 (c) (7pi)/2 (d) 4pi