Which of the following statements are correct?

AThe $S_{N} 1$ solvolysis rate of $(CH X_{3}) X_{3} C - Cl$ increases as the ionising power of the solvent increases.
B $Cl X^{-}$ is a stronger nucleophile toward $CH X_{3} I$ in DMSO than in methanol.
CIn methanol the nucleophilicity order is $F X^{-} > I X^{-}$ .
DDMSO solvates anions strongly through hydrogen bonding.

Answer: A, B

Ionisation develops charge, so more ionising solvents speed

S_{N} 1

(A true). In methanol

Cl X^{-}

is hydrogen bonded, but in DMSO it is nearly bare, so it is more nucleophilic there (B true). In protic methanol

I X^{-} > F X^{-}

(C false). DMSO has no hydrogen-bond-donating hydrogen (D false).