Step 1: Identify the law.
The dispute is about the jurisdiction of an arbitral tribunal under the Arbitration and Conciliation Act, 1996. The key section is Section 16, which carries the doctrine of Kompetenz-Kompetenz.
Step 2: Check Statement I.
Statement I says the tribunal may rule on its own jurisdiction. Section 16(1) clearly allows this, including questions about the existence or validity of the arbitration agreement. So Statement I is true.
Step 3: Understand why this power exists.
The idea of Kompetenz-Kompetenz lets the tribunal decide its own authority first, instead of running to court at every step. This keeps arbitration quick and self-contained.
Step 4: Check Statement II.
Statement II says a plea that the tribunal lacks jurisdiction must be raised not later than the submission of the statement of defence, unless the tribunal allows it later. Section 16(2) says exactly this. So Statement II is true.
Step 5: Why the time limit matters.
Forcing the objection early stops a party from sitting silent, taking part fully, and then springing a jurisdiction challenge at the end. The tribunal can still permit a late plea if there is good reason.
Step 6: Conclude.
Both statements correctly state Section 16, so both are true.
\[ \boxed{\text{Both Statements I and II are true}} \]