The polar equation $\cos \theta + 7 \sin \theta = \frac{1}{r}$ represents a

If $\alpha, \beta$ and $\gamma$ are the lengths of the altitudes of a $\triangle ABC$ with area $\Delta$,then $\frac{\Delta^2}{R^2}\left(\frac{1}{\alpha^2}+\frac{1}{\beta^2}+\frac{1}{\gamma^2}\right)$ is equal to

$A$ nucleus at rest splits into two nuclear parts having the same density and radii in the ratio $1 : 2$. Their velocities are in the ratio: (in $: 1$)

Identify the product in the following reaction:
$Phenol + CHCl_3 + NaOH \rightarrow \text{Product}$

Which one of the following is a correct pair with respect to the molecular formula of a xenon compound and the hybridization state of xenon in it?

Observe the following statements :
$I$. Bleaching powder is used in the preparation of chloroform.
$II$. Bleaching powder decomposes in the presence of $CoCl_2$ to liberate $O_2$.
$III$. Aqueous $KHF_2$ is used in the preparation of fluorine.
The correct combination is :