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UPSC PYQPrelims 2025

Civil Services Examination · Question 74

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 - 4pq, 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?

  1. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
  2. The Question can be answered by using either Statement alone.
  3. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
  4. The Question can be answered even without using any of the Statements.
Show answer & explanation

Answer: (B) The Question can be answered by using either Statement alone.

Explanation

(p + q)² - 4pq = (p - q)², which is positive whenever p ≠ q; either statement gives p ≠ q. (Answer as per the official UPSC answer key.)