$A$ buffer solution is a mixture of

Find $pH$ of the resultant solution formed by the addition of $500 \ mL$ $0.1 \ M$ $Ba(OH)_2$ and $500 \ mL$ $0.6 \ M$ $NH_4Cl$ in $1 \ L$ pure $H_2O$ at $25 \ ^oC$ (Use $\log \ 2 = 0.3$,$\log \ 3 = 0.5$,$\log \ 5 = 0.7$,$K_b(NH_3) = 10^{-5}$)

$A$ solution is prepared by mixing $0.01 \ mol$ each of $H_2CO_3$,$NaHCO_3$,$Na_2CO_3$,and $NaOH$ in $100 \ mL$ of water. The $pH$ of the resulting solution is. . . . . . .
[Given : $pK_{a1}$ and $pK_{a2}$ of $H_2CO_3$ are $6.37$ and $10.32$,respectively; $\log 2=0.30$ ]

Assertion : In a titration of weak acid and $NaOH$,the $pH$ at half equivalence point is $pK_a$.
Reason : At half equivalence point,it forms an acidic buffer and the buffer capacity is maximum where $[acid] = [salt]$.

Derive the equation for the calculation of $pH$ of an acidic buffer solution.

Which of the following mixtures in water acts as a buffer?