In the following reaction,$X$ and $Y$ are respectively:
$CH_3COOH + NH_3$ $\longrightarrow X \stackrel{\Delta}{}$ ${\longrightarrow} Y + H_2O$

Assertion $(A)$: Propagation of light through an optical fibre is due to total internal reflection taking place at the core-clad interface.
Reason $(R)$: Refractive index of the material of the core of the optical fibre is greater than that of air.

The minimum value of $2x^2+x-1$ is:

The height at which the weight of a body becomes $\frac{1}{9}^{th}$ of its weight on the surface of the Earth (radius of Earth $R$) is:

If $\operatorname{adj}\begin{bmatrix} 1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1 \end{bmatrix} = \begin{bmatrix} 5 & a & -2 \\ 1 & 1 & 0 \\ -2 & -2 & b \end{bmatrix}$,then $\begin{bmatrix} a & b \end{bmatrix}$ is equal to

If $\frac{1}{2} \leq x \leq 1$,then $\cos ^{-1} x+\cos ^{-1}\left(\frac{x}{2}+\frac{1}{2} \sqrt{3-3 x^2}\right)$ is equal to