$\int_0^{\pi / 2} \sin ^8 x \cos ^2 x \, dx$ is equal to

$A$ thin hollow sphere of mass $m$ is completely filled with a liquid of mass $m$. When the sphere rolls with a velocity $v$,the kinetic energy of the system is (neglect friction).

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+4x+1=0$,then $(\alpha+\beta)^{-1}+(\beta+\gamma)^{-1}+(\gamma+\alpha)^{-1}$ is equal to

The vectors $b$ and $c$ are in the direction of north-east and north-west respectively and $|b|=|c|= 4$. The magnitude and direction of the vector $d = c - b$ are:

In which of the following is the sporophyte parasitic on the gametophyte?

$A$ vessel contains $110\,g$ of water. The heat capacity of the vessel is equivalent to $10\,g$ of water. The initial temperature of the water in the vessel is $10\,^{\circ}C$. If $220\,g$ of hot water at $70\,^{\circ}C$ is poured into the vessel,the final temperature,neglecting radiation loss,will be ........ $^{\circ}C$.