Step 1: Understanding the Concept:
The question asks for the meaning of 'Mubara'at', a specific form of dissolution of marriage under Muslim personal law. Muslim law recognizes various modes of divorce, some initiated by the husband, some by the wife, and some by mutual agreement.
Step 2: Detailed Explanation:
Let's analyze the different forms of divorce mentioned or implied in the options:
\begin{itemize}
\item Divorce at the instance of Wife (Khula): This is a form of divorce where the wife initiates the separation by giving consideration to the husband (often by forgoing her dower or 'mahr'). It is a divorce purchased by the wife.
\item Cruelty: This is a ground for seeking judicial divorce under the Dissolution of Muslim Marriages Act, 1939, not a form of divorce in itself.
\item Dissolution of marriage with mutual consent (Mubara'at): 'Mubara'at' literally means mutual release. It is a form of divorce where both husband and wife are mutually averse to continuing the marriage and agree to dissolve it. The proposal for separation can come from either side. It is a dissolution of marriage by mutual consent.
\item Ila: This is a form of constructive divorce where the husband takes an oath to abstain from sexual relations with his wife for a period of four months or more. If he adheres to the oath, the marriage is dissolved upon the expiry of the period.
\end{itemize}
The term 'Mubara'at' correctly corresponds to a divorce by mutual consent.
Step 3: Final Answer:
Mubara'at under Muslim law refers to the Dissolution of marriage with mutual consent.