If $\sin 6 \theta = 32 \cos^5 \theta \sin \theta - 32 \cos^3 \theta \sin \theta + 3x$,then $x$ is equal to:

The eccentricity of the ellipse $9x^2 + 5y^2 - 30y = 0$ is

The percentage composition of an organic compound $A$ is: carbon $85.71 \%$ and hydrogen $14.29 \%$. Its vapour density is $14$. Consider the following reaction sequence:
$A$ $\xrightarrow{Cl_2 / H_2O} B$ $\xrightarrow[(ii) H_3O^+]{(i) KCN / EtOH} C$
Identify $\underline{C}$.

Two coherent narrow slits emitting light of wavelength $\lambda$ in the same phase are placed parallel to each other at a small separation of $3\lambda$. The light is collected on a screen $S$ which is placed at a distance $D$ from the slits. Find the smallest distance $x$ from the central point $O$ such that point $P$ is a maxima.

$CH_4$ diffuses two times faster than a gas $X$. The number of molecules present in $32 \ g$ of gas $X$ is ($N$ is Avogadro number).

The minimum value of $|z-1|+|z-5|$ is