Answer

Correct Option: (ii) $A \rightarrow \epsilon$

Explanation

Context-Sensitive Grammar (CSG, Type-1): Production $\alpha \rightarrow \beta$ where $\alpha,\beta \in (V\cup T)^*$ and $|\alpha| \le |\beta|$ (non-contracting), except possibly $S \rightarrow \epsilon$ with $S$ not appearing on RHS.

Check each:

• (i) $AB \rightarrow BA$ : $|\alpha|=2$, $|\beta|=2$ → $2 \le 2$ allowed (context-sensitive, length-preserving).
• (ii) $A \rightarrow \epsilon$ : $|\alpha|=1$, $|\beta|=0$ → $1 \le 0$ false, contracting, not allowed in CSG (unless $A=S$ and $S$ is start with special $\epsilon$ rule).
• (iii) $A \rightarrow a$ : $1 \le 1$ allowed.
• (iv) $aB \rightarrow ab$ : $2 \le 2$ allowed (context $a$).

Hence only $A \rightarrow \epsilon$ violates the monotonicity condition.

Final Answer

Not allowed: $A \rightarrow \epsilon$ → Option (ii).