Nucleophilic nature of ions Consider the following species:
  
  $$
\underset{(\text{A})}{\ce{\overset{⊖}{O}H}}
\quad
\underset{(\text{B})}{\ce{CH3-\overset{⊖}{O}}}
\quad
\underset{(\text{C})}{\ce{\overset{⊖}{C}H3}}
\quad
\underset{(\text{D})}{\ce{\overset{⊖}{N}H2}}
\quad
$$ 
  
  Arrange these species in their decreasing order of nucleophilicity.
  
  (a) C > D > A > B
  (b) B > A > C > D
  (c) A > B > C > D
  (d) C > A > B > D  


My teacher taught in polar protic solvent nucleophilicity is inversely proportional to basic character. I assumed solvent to be $\ce{H2O}$ as solvent was not mentioned in the question.
As acidity order is

$$\ce{H2O} &gt; \ce{CH3OH} &gt; \ce{NH3} &gt; \ce{CH4},$$

so basicity order should be

$$\ce{CH3-} &gt; \ce{NH2-} &gt; \ce{CH3O-} &gt; \ce{OH-},$$

therefore using above proportionality I arrived at the nucleophilicity order

$$\ce{OH-} &gt; \ce{CH3O-} &gt; \ce{NH2-} &gt; \ce{CH3-},$$

but you can see the option is not even given. Why is it so?
What you probably missed was that the order you mention is for the SAME GROUP elements. For example, down the group basicity of halide ions is-

F->Cl->Br->I-

But the the nucleophilicity order in polar protic solvents is-

I->Br->Cl->F-

This reverse in order is due to higher charge density of smaller halide ions and thus better interaction with polar protic solvents.

But along a period the charge density is similar and thus the interaction between solvent and nucleophile is almost similar. Thus, along a period the order follows basicity order.