(s) about acidity and basicity of organic compounds (aqueous solution, 298 K).

(A) True. In water, alkyl groups raise basicity by their $+I$ effect, but solvation of the ammonium ion (fewest N-H bonds in the tertiary ion) and steric crowding offset this for the tertiary amine; the observed $\mathrm{p}K_b$ values are about 3.27, 3.38, 4.22 and 4.75 for dimethylamine, methylamine, trimethylamine and ammonia respectively. (For the ethylamines the order is different, $(\mathrm{C_2H_5})_2\mathrm{NH}>(\mathrm{C_2H_5})_3\mathrm{N}>\mathrm{C_2H_5NH_2}>\mathrm{NH_3}$.)
(B) False. The $p$-nitro group stabilises the phenoxide by resonance (the negative charge reaches the nitro group), whereas the meta group acts only inductively. Hence $p$-nitrophenol ($\mathrm{p}K_a\approx7.15$) is more acidic than $m$-nitrophenol ($\approx8.4$).
(C) False. The $+M$ effect of $\mathrm{OCH_3}$ at para destabilises the carboxylate, so the acid is weaker ($\mathrm{p}K_a\approx4.5$ against $4.2$ for benzoic acid).
(D) True. The ortho effect (steric twisting of $\mathrm{COOH}$ out of the ring plane plus the strong $-I$ of a close nitro group) makes the ortho isomer ($\mathrm{p}K_a\approx2.2$) stronger than the para isomer ($\approx3.4$).
Correct options: (A) and (D).