What is the $[OH^-]$ in the final solution prepared by mixing $20.0 \ mL$ of $0.050 \ M \ HCl$ with $30.0 \ mL$ of $0.10 \ M \ Ba(OH)_2$?

Which of the following statement$(s)$ is/are correct?
$ (A) $ The $pH$ of $1 \times 10^{-8} \ M \ HCl$ solution is $8$.
$ (B) $ The conjugate base of $H_2PO_4^{-}$ is $HPO_4^{2-}$.
$ (C) $ $K_w$ increases with increase in temperature.
$ (D) $ When a solution of weak monoprotic acid is titrated against a strong base at half neutralisation point,$pH = pK_a$.
Choose the correct answer from the option given below.

The ionization constant of dimethylamine is $5.4 \times 10^{-4}$. Calculate its degree of ionization in its $0.02 \ M$ solution. What percentage of dimethylamine is ionized if the solution is also $0.1 \ M$ in $NaOH$?

Equal volumes of three acid solutions with $pH$ values of $3, 4,$ and $5$ are mixed. What will be the concentration of $H^+$ ions in the resulting mixture?

The pairs of compounds which cannot exist together in aqueous solution are :
$I. NaH_2PO_4$ and $Na_2CO_3$ $II. Na_2CO_3$ and $NaHCO_3$
$III. NaOH$ and $NaH_2PO_4$ $IV. NaHCO_3$ and $NaOH$

Which of the following undergoes hydrolysis when dissolved in water?