If `f(x)=sqrt(1+cos^2(x^2)),t h e nf^(prime)((sqrt(pi))/2)` is `(sqrt(pi))/6` (b) `-sqrt(pi//6)` `1//sqrt(6)` (d) `pi//sqrt(6)`

If y=cos(sinx^(2)), " then " (dy)/(dx) " at " x=sqrt(pi/2) is

Evaluate int_((pi)/(6))^((pi)/(3))(sqrt(sinx))/(sqrt(sinx)+sqrt(cosx))dx

Range of the function f(x)=sqrt(cos^(- 1)(sqrt(log_4x))-pi/2)+sin^(- 1)((1+x^2)/(4x)) is equal to (A) (0,pi/2+sqrt(pi/2)] (B) [pi/2,pi/2+sqrt(pi/2)] (C) [pi/6,pi/4) (D) {pi/6}

The value of the definite integral int_0^(pi/2)sqrt(tanx)dx is sqrt(2)pi (b) pi/(sqrt(2)) 2sqrt(2)pi (d) pi/(2sqrt(2))

The value of the definite integral int_0^(pi/2)sqrt(tanx)dx is sqrt(2)pi (b) pi/(sqrt(2)) 2sqrt(2)pi (d) pi/(2sqrt(2))

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)

The value of (lim)_(xvecoo)(tan^(-1)x))) is equal to (a)-1 (b) pi/2 (c) -1/(sqrt(2)) (d) 1/(sqrt(2))

If f(x)=2sin^(-1)sqrt(1-x)+sin^(-1)(2sqrt(x(1-x))) , where x in (0,1/2),t h e nf^(prime)(x) is (a) 2/(sqrt(x(1-x))) (b) zero (c) -2/(sqrt(x(1-x))) (d) pi

Simplify (1)/(3 - sqrt(8)) - (1)/(sqrt(8) - sqrt(7)) + (1)/(sqrt(7) - sqrt(6)) - (1)/(sqrt(6) - sqrt(5)) + (1)/(sqrt(5) - 2)