1.The inverse of cosine function is defined in the intervals (A) [ `-pi , 0`]
(B) [ `-pi/2,0`] (C) [`0,pi/2`] (D) [ `pi/2 , pi`]

One root of the equation cos x-x+1/2=0 lies in the interval (A) [0,pi/2] (B) [-pi/2,0] (C) [pi/2,0] (D) none

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]

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

The value of c in Lagranges theorem for the function f(x)=logsinx in the interval [pi/6,(5pi)/6] is (a) pi/4 (b) pi/2 (c) (2pi)/3 (d) none of these

int_0^pi cos2xlogsinxdx= (A) pi (B) -pi/2 (C) pi/2 (D) none of these

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

Period of sin^2 theta is(A) pi^2 (B) pi (C) 2pi (D) pi/2

If the point (2costheta, 2sintheta), for theta in (0, 2pi) lies in the region between the lines x+y=1 and x-y=2 containing the origin then theta lies in (A) (0, pi/2)cup((3pi)/2, 2pi) (B) [0,pi] (C) (pi/2, (3pi)/2) (D) [pi/4, pi/2]

Range of function f(x)=cot^(-1)(2x-x^2), is (a) [pi/4,(3pi)/2] (b) [0,pi/4] [0,pi/2] (d) [pi/4,pi]

The maximum value of (1+cosx)sinx in interval 0lexle pi/2 is for (A) x =pi/2 (B) x= pi/6 (C) x=0 (D) x= pi/3