The range of the function `tan^(-1)((x^2+1)/(x^2+sqrt(3))),x in R` is a.`[pi/6,pi/2)` b. `[pi/6,pi/3)` c. `[pi/6,pi/4]` d. none of these

The range of f(x)=sin^(-1)((x^2+1)/(x^2+2)) is (a)[0,pi/2] (b) (0,pi/6) (c) [pi/6,pi/2] (d) none of these

The range of f(x)=sin^(-1)((x^2+1)/(x^2+2)) is (a) [0,pi/2] (b) (0,pi/6) (c) [pi/6,pi/2] (d) none of these

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

Range of tan^(-1)((2x)/(1+x^2)) is (a) [-pi/4,pi/4] (b) (-pi/2,pi/2) (c) (-pi/2,pi/4) (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]

Range of f(x)=sin^(-1)x+tan^(-1)x+sec^(-1)x is (a) (pi/4,(3pi)/4) (b) [pi/4,(3pi)/4] (c) {pi/4,(3pi)/4} (d) none of these

The range of f(x)=sec^(-1)((log)_3tanx+(log)_(tanx)3) is (a) [pi/3,pi/2]uu[pi/2,(2pi)/3] (b) [0,pi/2] (c) ((2pi)/3,pi) (d) none of these

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_1^(sqrt(3))1/(1+x^2)dx is equal to a. pi/(12) b. pi/4 c. pi/6 d. pi/3

sin^-1 (sin ((7pi)/6))= (A) (7pi)/6 (B) pi/6 (C) -pi/6 (D) none of these