When $200 \ mL$ solution of $HCl$ of $pH=2$ is mixed with $300 \ mL$ solution of $NaOH$ of $pH=12$,the $pH$ of resulting solution is $(\log 2=0.3)$

Dilution processes of different aqueous solutions with water are given in $LIST-I$. The effects of dilution of the solutions on $[H^{+}]$ are given in $LIST-II$. (Note: Degree of dissociation $(\alpha)$ of weak acid and weak base is $ << 1$; degree of hydrolysis of salt $ << 1$; $[H^{+}]$ represents the concentration of $H^{+}$ ions)

$LIST-I$	$LIST-II$
$P$. ($10 \ mL$ of $0.1 \ M$ $NaOH$ + $20 \ mL$ of $0.1 \ M$ acetic acid) diluted to $60 \ mL$	$1$. The value of $[H^{+}]$ does not change on dilution
$Q$. ($20 \ mL$ of $0.1 \ M$ $NaOH$ + $20 \ mL$ of $0.1 \ M$ acetic acid) diluted to $80 \ mL$	$2$. The value of $[H^{+}]$ changes to half of its initial value on dilution
$R$. ($20 \ mL$ of $0.1 \ M$ $HCl$ + $20 \ mL$ of $0.1 \ M$ ammonia solution) diluted to $80 \ mL$	$3$. The value of $[H^{+}]$ changes to $1/\sqrt{2}$ times of its initial value on dilution
$S$. $10 \ mL$ saturated solution of $Ni(OH)_2$ in equilibrium with excess solid $Ni(OH)_2$ is diluted to $20 \ mL$ (solid $Ni(OH)_2$ is still present after dilution)	$4$. The value of $[H^{+}]$ changes to $\sqrt{2}$ times of its initial value on dilution

Match each process given in $LIST-I$ with one or more effect$(s)$ in $LIST-II$. The correct option is:

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

$A$ soft drink was bottled with a partial pressure of $CO_2$ of $3 \ bar$ over the liquid at room temperature. The partial pressure of $CO_2$ over the solution approaches a value of $30 \ bar$ when $44 \ g$ of $CO_2$ is dissolved in $1 \ kg$ of water at room temperature. The approximate $pH$ of the soft drink is............... $\times 10^{-1}$ (First dissociation constant of $H_2CO_3 = 4.0 \times 10^{-7}$; $\log 2 = 0.3$; density of the soft drink $= 1 \ g \ mL^{-1}$)

Conductivity of $0.00241 \, M$ acetic acid is $7.896 \times 10^{-5} \, S \, cm^{-1}$. Calculate its molar conductivity. If $\Lambda_m^o$ for acetic acid is $390.5 \, S \, cm^2 \, mol^{-1}$,what is its dissociation constant?

$20 \ mL$,$0.1 \ M \ HA$ $[(K_b)_{A^-} = 10^{-10}]$ is titrated against $0.2 \ M \ NaOH$. Select the correct statement [Given : $\log 2 = 0.3, \log 3 = 0.48$ ]