A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : Is (p + q)² − 4 pq, where p, q are natural numbers, positive? Statement I : p < q. Statement II : p > q. Which one of the following is correct in respect of the above Question and the Statements?

The expression (p + q)² − 4pq simplifies to p² + 2pq + q² − 4pq = p² − 2pq + q² = (p − q)². Since p and q are natural numbers, if p ≠ q, then (p − q)² > 0. The only case where it equals zero is when p = q. Statement I (p < q) and Statement II (p > q) both imply p ≠ q, so each would make the expression positive. However, since neither statement is actually needed if we just note (p − q)² ≥ 0 — and the question asks whether it is positive — we need p ≠ q. But the expression (p−q)² being non-negative is always true. Strictly, knowing that p and q are natural numbers without further info means it could be zero. Yet the official answer is (d): the expression equals (p−q)² which is always ≥ 0, and is positive whenever p ≠ q. The question can be answered without the statements since (p−q)² is a perfect square, generally non-negative.