Answer : B
The Given Grammar is Context Sensitive Grammar. And It means that the Expansion/Reduction of Any Non-terminal will depend on the Context. Like here, In $G$ and $G'$, We can say that $A$ will expand into $A$ only if $A$ is immediately followed by $b$ and then we can use the Production rule $Ab \rightarrow A$ which will replace respective $Ab$ by $A$.
$G :$
$S \rightarrow bSb |AcA$
$Ab \rightarrow A, Ab \rightarrow b$
$bA \rightarrow b$
$S$ will go to $b^nSb^n$, and then to generate a String, $S$ will expand into $AcA$, So, We can say that All the strings Generated by $S$ are of the form $b^nAcAb^n$
Now, Take Some value of $n$ and Observe the behaviour of $b^nAcAb^n$
Say, $n = 4$, So, We have $S \rightarrow bbbb\,AcA\,bbbb$
Now, To generate a String, We need to vanish the non-terminal $A$. Observe that the former $A$(First $A$) can only be Vanished by the Production rule $bA \rightarrow b$, Which means, Now we have $S \rightarrow bbbb\, cA\,bbbb$
Now, To vanish the remaining $A$(Second $A$ ), we can use either of the Two productions $Ab \rightarrow b $ or $Ab \rightarrow A $ ...
If you use $Ab \rightarrow b$ then $A$ will immediately vanish and we will have $b^4cb^4$. But if you use, $Ab \rightarrow A$, One $b$ will vanish and Now, To remove the $A$, we will repeat the same....i.e. Either Use $Ab \rightarrow b $ or $Ab \rightarrow A $.
Which will give us $L(G) = \left \{ b^n c b^m | n \geq m, m \geq 1\right \}$ ..Which is Context Free and Non-regular.
$G' :$
$S \rightarrow bSb |AcA$
$Ab \rightarrow A, Ab \rightarrow b$
$bA \rightarrow b$, $bA \rightarrow A$
$S$ will go to $b^nSb^n$, and then to generate a String, $S$ will expand into $AcA$, So, We can say that All the strings Generated by $S$ are of the form $b^nAcAb^n$
Now, Take Some value of $n$ and Observe the behavior of $b^nAcAb^n$
Say, $n = 4$, So, We have $S \rightarrow bbbb\,AcA\,bbbb$
Now, To generate a String, We need to vanish the non-terminal $A$. Observe that the former $A$(First $A$) can be Vanished by the Production rules $bA \rightarrow b$ or $bA \rightarrow A$. If you use $bA \rightarrow b$ then $A$ will immediately vanish and we will have $b^4cAb^4$. But if you use, $bA \rightarrow A$, One $b$ will vanish and Now, To remove the $A$, we will repeat the same....i.e. Either Use $bA \rightarrow b $ or $bA \rightarrow A $.
Now, To vanish the remaining $A$(Second $A$ ), we can use either of the Two productions $Ab \rightarrow b $ or $Ab \rightarrow A $ ...
If you use $Ab \rightarrow b$ then $A$ will immediately vanish and we will have $b^4cb^4$. But if you use, $Ab \rightarrow A$, One $b$ will vanish and Now, To remove the $A$, we will repeat the same....i.e. Either Use $Ab \rightarrow b $ or $Ab \rightarrow A $.
Which will give us $L(G') = \left \{ b^n c b^m | n, m \geq 1\right \}$ ..Which is Regular.