In which of the following combinations is buffer action expected?
$A$. $NH_4OH + NH_4Cl$
$B$. $HCl + NaCl$
$C$. $NH_4OH + HCl$ in $2 : 1$ mole ratio
Select the correct answer using the code given below:

If $(a + \sqrt{2} b \cos x)(a - \sqrt{2} b \cos y) = a^2 - b^2$,where $a > b > 0$,then $\frac{dx}{dy}$ at $(\frac{\pi}{4}, \frac{\pi}{4})$ is

$A$ person moves $30\, m$ north and then $20\, m$ towards east and finally $30\sqrt{2}\, m$ in south-west direction. The displacement of the person from the origin will be

For the reaction $N_{2(g)} + O_{2(g)} \rightleftharpoons 2NO_{(g)}$,the equilibrium constant $(K_c)$ at temperature $T$ is $4 \times 10^{-4}$. What is the value of $K_c$ for the reaction $NO_{(g)} \rightleftharpoons 1/2 N_{2(g)} + 1/2 O_{2(g)}$ at the same temperature?

If three unit vectors $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ satisfy $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$,then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is

From a group of $10$ men and $8$ women,the number of ways of forming a committee of $8$ members with not more than $5$ men and not less than $5$ women is