Assertion (A): If 2^x.3^y.5^z = 16200, then x = 3, y = 4, z = 2.

Reason (R): If p, q are different prime numbers, then p^m.qⁿ = p^l.q^k ⇒ m = l and n = k

1. Assertion (A) is true, Reason (R) is false.

2. Assertion (A) is false, Reason (R) is true.

3. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).

If p, q are different prime numbers, then p^m.qⁿ = p^l.q^k ⇒ m = l and n = k.

This statement is true. This is a direct consequence of the Fundamental Theorem of Arithmetic.

∴ Reason (R) is true.

Given, 2^x.3^y.5^z = 16200

⇒ 2^x.3^y.5^z = 2³.3⁴.5²

⇒ x = 3, y = 4 and z = 2.

∴ Assertion (A) is true.

∴ Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason (or explanation) for Assertion (A).

Hence, option 3 is the correct option.