The solution for `x` of the equation `int_(sqrt(2))^x(dt)/(tsqrt(t^2-1))=pi/2` is `pi` (b) `(sqrt(3))/2` (c) `2sqrt(2)` (d) none of these

The sum of the solution of the equation 2sin^(-1)sqrt(x^2+x+1)+cos^(-1)sqrt(x^2+x)=(3pi)/2 is (a)0 (b) -1 (c) 1 (d) 2

Find the real solutions of the eqution tan^(-1)sqrt(x(x+1))+sin^(-1)sqrt(x^(2)+x+1)=(pi)/(2)

Which of the following is not the solution of (log)_3(x^2-2)<(log)_3(3/2|x|-1) is (a) (sqrt(2),2) (b) (-2,-sqrt(2)) (c) (-sqrt(2),2 (d) none of these

The value of ("lim")_(xto2)(sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)i s (a) 1/(8sqrt(3)) (b) 1/(4sqrt(3)) (c) 0 (d) none of these

Find the equation of tangent to y=int_(x^2)^(x^3)(dt)/(sqrt(1+t^2))a tx=1.

The number of solutions of the equation sqrt(x^(2))-sqrt((x-1)^(2))+sqrt((x-2)^(2))=sqrt(5) is

If y=|cosx|+|sinx|,t h e n(dy)/(dx)a tx=(2pi)/3 is (1-sqrt(3))/2 (b) 0 (c) 1/2(sqrt(3)-1) (d) none of these

The number of real solutions of tan^(-1)sqrt(x(x+1))+sin^(-1)sqrt(x^2+x+1)=pi/2 is

Solution of the equation sin(sqrt(1+sin2theta))=sintheta+costhetai s(n in Z) (a) npi-pi/4 (b) npi+pi/(12) (c) npi+pi/6 (d) none of these

If tan^(-1)(a+x)/a+tan^(-1)(a-x)/a=pi/6,t h e nx^2= (a) 2sqrt(3)a (b) sqrt(3)a (c) 2sqrt(3)a^2 (d) none of these