`int_0^pi(xtanx)/(secx+cosx)dxi s` `(pi^2)/4` (b) `(pi^2)/2` (c) `(3pi^2)/2` (d) `(pi^2)/3`

int_(-pi/3)^0[cot^(-1)(2/(2cosx-1))+cot^(-1)(cosx-1/2)]dx i s equal to (a) (pi^2)/6 (b) (pi^2)/3 (c) (pi^2)/8 (d) (3pi^2)/8

G i v e nint_0^(pi/2)(dx)/(1+sinx+cosx)=log2. Then the value of integral int_0^(pi/2)(sinx)/(1+sinx+cosx)dx is equal to (a) 1/2log2 (b) pi/2-log2 (c) pi/4-1/2log2 (d) pi/2+log2

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

(lim)_(xvecpi/2)((1-s in x)(8x^3-pi^3)cos x)/((pi-2x)^4) (pi^2)/6 b. (3pi^2)/(16) c. (pi^2)/(16) d. -(3pi^2)/(16)

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 length of the longest interval in which the function 3sinx-4sin^3x is increasing is pi/3 (b) pi/2 (c) (3pi)/2 (d) pi

If 2|sin2alpha|=|tanbeta+cotbeta|,alpha,beta in (pi/2,pi), then the value of alpha+beta is (a) (3pi)/4 (b) pi (c) (3pi)/2 (d) (5pi)/4

The principal value of sin^(-1)(sin((2pi)/3)) is (a) -(2pi)/3 (b) (2pi)/3 (c) (pi)/3 (d) (5pi)/3 (e) none of these

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]

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)