Recall the characteristics of an $S_N1$ reaction

The $S_N1$ mechanism occurs in two steps:

$R-LG \rightarrow R^+ + LG^-$ $R^+ + Nu \rightarrow R-Nu$

The rate-determining step is the formation of the carbocation $R^+$. Therefore, factors that stabilize the carbocation or help ionization favor the reaction.

Check statement (a): The reaction is favoured by weak nucleophiles.

In an $S_N1$ reaction, the nucleophile attacks after the slow step. Since the rate depends mainly on carbocation formation, even weak nucleophiles can participate.

So, (a) is correct.

Check statement (b): $R^+$ would be easily formed if the substituents are bulky.

Bulky substituents usually mean more alkyl groups around the carbon, which can stabilize the carbocation by $+I$ effect and hyperconjugation.

Thus, tertiary carbocations form more easily than secondary, and secondary more easily than primary:

$3^\circ > 2^\circ > 1^\circ$

So, (b) is correct.

Check statement (c): The reaction is accompanied by racemization.

In $S_N1$, a planar carbocation intermediate is formed. Since it is planar, the nucleophile can attack from either side, producing both retention and inversion.

Hence, the product is racemized (often partial racemization in practice).

So, (c) is correct.

Check statement (d): The reaction is favoured by non-polar solvents.

$S_N1$ reactions are favored by polar protic solvents because they stabilize both the carbocation and the leaving group.

Non-polar solvents do not favor ionization.

So, (d) is incorrect.

Identify the correct option

Correct statements are:

$(a), (b), (c)$

Therefore, the correct option is B.