a) is only correct in polar protic solvents. The hydrogen bonding extent is higher in F- than Cl- and Br-, so the greater solvation causes it to be more hindered and thus F is the weakest nucleophile among the three.

F- is still the most basic due to having the highest charge density of the three, and the charge being spread out the least due to having the smallest electron cloud of the three.

F- has the the higher tendency to take a proton/H+ ion since the negative charge is stabilised the least.

c) is correct, and the nucleophilicity correlates with basicity here.

CH3- is the least electronegative here and thus the electrons are less tightly held. So it is the most nucleophilic.

It is also the most basic as the stability of the negative charge is lowest since the it has the lowest electronegativity compared to the rest in the same period.

d) is correct. H2O has a higher pKa than H2S , so it is more basic.

The stability of the negative charge upon deprotonation is higher for H2S since S has a bigger electron cloud and polarisability, so the negative charge can be dispersed to a greater extent.

S is more polarisable than O , having a larger electron cloud and the lower electronegativity means the electron donation is more feasible than O as the electrons are less tightly held.

So H2S is a better nucleophile.

We need to find incorrect and answer is b) but I don't know how

b) is not correct as OOH- is less basic than OH-.

Since H2O2 has 2 oxygen atoms, the electronegativity is greater than in H2O where there is only 1 O atom. So there is a greater electron withdrawing inductive effec. And thus the tendency to lose a proton is greater. It is more acidic.

Hence, the conjugate base OOH- is less basic than OH- since the negative charge is more stabilised it it can be dispersed over 2 O instead of only 1 O in OH-

By the way, the basicity here refers to Bronsted basicity and not Lewis Basicity.

Okay got it.
Thanks