यदि P का अर्थ ‘से बृहत्तर (>)’ है; Q का अर्थ ‘से लघुतर (<)’ है; R का अर्थ ‘से बृहत्तर नहीं (≯)’ है; S का अर्थ ‘से लघुतर नहीं (≮)’ है और T का अर्थ ‘बराबर (=)’ है, तो निम्नलिखित कथनों पर विचार कीजिए :
- 1.यदि 2x(S)3y और 3x(T)4z, तो 9y(P)8z.
- 2.यदि x(Q)2y और y(R)z, तो x(R)z.
उपर्युक्त कथनों में से कौन-सा/कौन-से सही है/हैं?
Read this question in English
If P means ‘greater than (>)’; Q means ‘less than (<)’; R means ‘not greater than (≯)’; S means ‘not less than (≮)’ and T means ‘equal to (=)’, then consider the following statements:
1. If 2x(S)3y and 3x(T)4z, then 9y(P)8z.
2. If x(Q)2y and y(R)z, then x(R)z.
Which of the statements given above is/are correct?
(a) 1 only · (b) 2 only · (c) Both 1 and 2 · (d) Neither 1 nor 2
उत्तर और व्याख्या · explanation in English
Answer: (d) न तो 1 और न ही 2
Statement 1 gives 2x ≥ 3y and 3x = 4z, which lead to 9y ≤ 8z, so ‘9y > 8z’ fails. Statement 2 gives x < 2y and y ≤ z, which still allow x > z (for example x = 1.5, y = z = 1). Neither is correct.
- Decode: P is >, Q is <, R is ≤ (not greater than), S is ≥ (not less than), T is =.
- Statement 1: 2x ≥ 3y gives 9y ≤ 6x; 3x = 4z gives 8z = 6x. So 9y ≤ 8z, which rules out 9y > 8z. Incorrect.
- Statement 2: x < 2y and y ≤ z. Take x = 1.5, y = 1, z = 1: both conditions hold, but x ≤ z fails. Incorrect.
- So neither statement is correct.
- ✗ 1. From 2x ≥ 3y and 3x = 4z, 9y ≤ 6x = 8z, so 9y can never be greater than 8z.
- ✗ 2. x < 2y and y ≤ z only give x < 2z; x = 1.5, y = z = 1 satisfies both conditions but has x greater than z.
Remember · Decode the symbols, bring both sides to a common term (here 6x), and use one counter-example to kill an ‘always’ claim.
Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·