x, y और z तीन चर हैं, जो 2, 3, 4 या 5 के इस प्रकार मान प्राप्त करते हैं कि उनका मान सदा भिन्न रहे। यदि {(x × y) + z} व्यंजक के लिए M और N क्रमशः बृहत्तम संभाव्य मान तथा लघुतम संभाव्य मान को निरूपित करते हैं, तो M − N है
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Three variables x, y and z take values 2, 3, 4 or 5 such that their values are always distinct. If M and N denote the largest possible value and the smallest possible value, respectively, for the expression {(x × y) + z}; then M − N is
(a) 11 · (b) 12 · (c) 13 · (d) 14
उत्तर और व्याख्या · explanation in English
Answer: (c) 13
The product dominates the sum, so put the two largest values in the product for M and the two smallest for N. M = 5 × 4 + 3 = 23 and N = 2 × 3 + 4 = 10, so M − N = 13.
- Largest: x × y = 5 × 4 = 20, z = 3 (largest value left): M = 23. (5 × 3 + 4 = 19 is smaller.)
- Smallest: x × y = 2 × 3 = 6, z = 4 (smallest value left): N = 10. (2 × 4 + 3 = 11 is larger.)
- M − N = 23 − 10 = 13.
Remember · To maximise or minimise xy + z, decide the product first; the added term matters less.
Question and answer: UPSC's provisional GS Paper II (2026, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·