The Lassaigne’s extract is boiled with dil. $HNO_3$ before testing for halogens because

If $x=a\left[\cos \theta+\log \left\{\tan \left(\frac{\theta}{2}\right)\right\}\right]$ and $y=a \sin \theta$,then $\frac{dy}{dx}$ is equal to

Which of the following pairs of orbitals possess two nodal planes?

$A$ vertical pole subtends an angle $\tan ^{-1}\left(\frac{1}{2}\right)$ at a point $P$ on the ground. If the angles subtended by the upper half and the lower half of the pole at $P$ are respectively $\alpha$ and $\beta$,then $(\tan \alpha, \tan \beta)$ is equal to

$C_6H_6 + 3O_3$ $\longrightarrow X \stackrel{Zn / H_2O}{}$ ${\longrightarrow} Y$; $X$ and $Y$ are respectively

$A$ parallel plate capacitor of capacity $100 \mu F$ is charged by a battery of $50 \text{ V}$. The battery remains connected,and if the plates of the capacitor are separated so that the distance between them becomes double the original distance,the additional energy supplied by the battery to the capacitor in joules is: