Calculate the molar solubility of $AgCl$ at $25\,^oC$ in $3.0\ M\ NH_3$ ($K_{sp}$ of $AgCl = 2.0 \times 10^{-10}$,$K_f$ of $[Ag(NH_3)_2]^+ = 1.25 \times 10^7$) (in $M$)

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.

$A$ weak acid is titrated with a weak base. Consider the following statements regarding the $pH$ of the solution at the equivalence point.
$(i)$ $pH$ depends on the concentration of acid and base
$(ii)$ $pH$ is independent of the concentration of acid and base
$(iii)$ $pH$ depends on the $pK_{a}$ of acid and $pK_{b}$ of base
$(iv)$ $pH$ is independent of the $pK_{a}$ of acid and $pK_{b}$ of base
The correct statements are

What will be the $pH$ of a solution formed by mixing $40 \, cm^3$ of $0.1 \, M \, HCl$ with $10 \, cm^3$ of $0.45 \, M \, NaOH$?

If the dissociation constant of a weak acid is $1.0 \times 10^{-5}$,then the equilibrium constant for its reaction with a strong base will be......