The 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]`

The exhaustive set of values of a for which a-cot^(-1) 3x = 2 tan^(-1) 3x + cos^(-1)xsqrt3+ sin^(-1) x sqrt3 may have solution a) [-pi/4,pi/4] b) (pi/2,(3pi)/2) c) [(2pi)/3,(4pi)/3] d) [-(3pi)/6,(7pi)/6]

The 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 the function f(x) = cot^(-1)log_(0.5) (x^4 -2x^(2) +3) is a) (0,pi) b) (0,3pi//4) c) [3pi//4,pi) d) [pi//2, 3pi//4]

The principal value of tan^-1(-1) is [pi/4,-pi/4,pi-pi/4,pi+pi/4]

Range of the function f(x) = sqrt(cos^(-1)(sqrtlog_(4)x)-pi/2)+sin^(-1)((1+x^2)/(4x)) is a (0,pi/2+sqrt(pi/2)] b) [pi/2,pi/2+sqrt(pi/2)] c) [pi/6,pi/2] d) {pi/6}

Let f(x)=cos^(-1)((x^2)/(1+x^2)) . The range of f is a) [0,pi/2] b) [-pi/2,pi/2] c) [-pi/2,0] d)None of these

If x in (0,1) then the value of tan^(-1)((1-x^2)/(2x))+cos^(-1)((1-x^2)/(1+x^2)) is equal to a) -pi/2 b)0 c) pi/2 d) pi

The value of int_(-pi)^(pi)("sin"^(2)x)/(1+7^(x))dx is a) 7^(x) b) pi c) (pi)/(2) d) 2^(pi)

int_1^sqrt(3) (d x)/(1+x^2) equals a) pi/3 b) (2 pi)/3 c) pi/6 d) pi/(12)