Concept:
High Courts in India often have jurisdiction over more than one State or Union Territory. The Kerala High Court is located in Kochi and has a unique geographical and historical identity.
Step 1: Analyzing Territorial Jurisdiction (Statement 1).
Under Article 231, Parliament can establish a common High Court for two or more States or for two or more States and a Union Territory. The Kerala High Court has territorial jurisdiction over the State of Kerala and the Union Territory of Lakshadweep.
$\text{Jurisdiction} = \text{Kerala} + \text{Lakshadweep}$
Statement 1 is correct.
Step 2: Analyzing Establishment and Leadership (Statement 2).
The High Court of Kerala was established on November 1, 1956, following the States Reorganisation Act, which merged the Travancore-Cochin High Court with parts of the Madras High Court.
As of the current period, Justice Nitin Jamdar serves as the Chief Justice (having been sworn ippointed recently).
$\text{Established Date} = 01-11-1956$
Statement 2 is correct.
Step 3: Conclusion.
Since both the jurisdictional fact and the historical/current data are accurate, both statements are true.
Final Answer: Option C