The $pK_{b}$ of dimethylamine and $pK_{a}$ of acetic acid are $3.27$ and $4.77$ respectively at $T(K)$. The correct option for the $pH$ of dimethylammonium acetate solution is :

Statement $A$: $pH$ of a buffer increases with increasing temperature. Statement $B$: The value of $K_W$ of water decreases with decreasing temperature.

Calculate the ionic product of the solution formed by mixing equal volumes of $0.004 \, M \, CaSO_4$ and $0.002 \, M \, H_2SO_4$.

If $20 \, mL$ of $0.25 \, N$ strong acid and $30 \, mL$ of $0.2 \, N$ strong base are mixed,then the resulting solution is

At $25^{\circ}C$,$20.0 \ mL$ of $0.2 \ M$ weak monoprotic acid $HX$ is titrated against $0.2 \ M$ $NaOH$. The $pH$ of the solution $(a)$ at the start of the titration (when $NaOH$ has not been added) and $(b)$ when $10 \ mL$ of $NaOH$ is added respectively,are:
Given: $K_a = 5 \times 10^{-4}, pK_a = 3.3, \alpha << 1$

When $100 \ mL$ of $1 \ M$ $NaOH$ solution is mixed with $10 \ mL$ of $10 \ M$ $H_2SO_4$,the resulting mixture will be