For the reaction sequence given below, the correct statement$(s)$ is$(are)$
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$(A) \ P$ is optically active.
$(B) \ S$ gives Bayer's test.
$(C) \ Q$ gives effervescence with aq. $NaHCO _3$.
$(D) \ R$ is an alkyne.

Suppose there is a hole in a copper plate. On heating the plate,the diameter of the hole would:

$A$ uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended,with its length vertical,from a fixed point by a massless spring such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. The extension $x_0$ of the spring when it is in equilibrium is:

If $\omega$ is a complex cube root of unity,then $\sin \left\{\left(\omega^{10}+\omega^{23}\right) \pi-\frac{\pi}{4}\right\}$ is equal to

The terminal velocity of a liquid drop of radius $r$ falling through air is $v$. If two such drops are combined to form a bigger drop, the terminal velocity with which the bigger drop falls through air is (ignore any buoyant force due to air).

The angle between the pair of straight lines formed by joining the points of intersection of $x^2+y^2=4$ and $y=3x+c$ to the origin is a right angle. Then $c^2$ is equal to