If \(\sin ^{-1} x+\sin ^{-1} y=\frac{2 \pi}{3}\), then the value of \(\cos ^{-1} x+\cos ^{-1} y\) is:

The value of the integral \(\int_0^\pi 2 x \sin ^3 x\ d x\) is:

The general solution of the differential equation \(y d x-\left(x+2 y^2\right) d y=0\) is:

If the objective function for an L.P.P. is \(z=3 x-4 y\) and the corner points for the bounded feasible region are \((0,0),(5,0),(6,5),(6,8),(4,10)\) and \((0,8)\), then the minimum value of \(z\) occurs at :

The value of the integral \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos ^2 x d x\) is:

The relation \(R=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}\) on the set \(A=\{1,2,3\}\) is :

For \(y=x e^x\), which of the following is correct ?

Which one of the followings is not a transgenic animal?

The linear programming problem:
Maximize \(Z = x + y\),
subject to the constraints \(x-y \leq-1,-x+y \leq 0, x, y \geq 0\) has

Read the passage carefully and give the answers to the question :
India was amongst the first countries in the world to initiate action plans and programmes at a national level to attain total reproductive health as a social goal.
These programmes called 'family planning' were initiated in 1951 and were periodically assessed over the past decades. Improved programmes covering wider reproduction-related areas are currently in operation. Creating awareness among the people about various reproduction-related aspects and providing facilities and support for building up a reproductively healthy society are the major tasks under these programmes.
Which of the following is not a Sexually Transmitted Disease?

Which of the following functions satisfies Rolle's theorem?

Antipyretic drugs prevent platelet coagulation, apart from reducing fever. Because of this action, antipyretic aspirin is also used:

If \(\tan ^{-1}(2 x)+\tan ^{-1}(3 x)=\frac{\pi}{4}\), then number of solution(s) of the given equation is :