दो धनपूर्ण संख्याओं p और q के बारे में, जो इस प्रकार हैं कि p अभाज्य और q भाज्य संख्या है, निम्नलिखित कथनों पर विचार कीजिए :
- 1.p × q विषम संख्या हो सकती है।
- 2.q / p अभाज्य संख्या हो सकती है।
- 3.p + q अभाज्य संख्या हो सकती है।
उपर्युक्त कथनों में से कौन-से सही हैं?
Read this question in English
Consider the following statements in respect of two natural numbers p and q such that p is a prime number and q is a composite number:
1. p × q can be an odd number.
2. q/p can be a prime number.
3. p + q can be a prime number.
Which of the above statements are correct?
(a) 1 and 2 only · (b) 2 and 3 only · (c) 1 and 3 only · (d) 1, 2 and 3
उत्तर और व्याख्या · explanation in English
Answer: (d) 1, 2 और 3
Each statement says ‘can be’, so one example is enough for each: 3 × 9 = 27 is odd, 6 ÷ 2 = 3 is prime, and 2 + 9 = 11 is prime. All three are correct.
- p = 3, q = 9: p × q = 27 is odd, so statement 1 is correct.
- p = 2, q = 6: q/p = 3 is prime, so statement 2 is correct.
- p = 2, q = 9: p + q = 11 is prime, so statement 3 is correct.
- All three statements are correct.
- ✓ 1. An odd prime times an odd composite is odd, e.g. 3 × 9 = 27.
- ✓ 2. e.g. 6 ÷ 2 = 3 (also 15 ÷ 5 = 3).
- ✓ 3. e.g. 2 + 9 = 11 (also 3 + 4 = 7).
Remember · ‘Can be’ statements need just one valid example; ‘must be’ statements need just one counter-example to fail.
Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·