2016 · Q73
If m and n are distinct natural numbers, then which of the following is/are integer / integers?1. m/n+n/m2. mn(m/n+n/m)(m²+n²)⁻¹3. mn/(m²+n²)Select the correct answer using the code given below.
Elementary MathematicsNumber System
- A1 and 2
- B2 only
- C2 and 3
- D3 only
Explanation
Expression 2 simplifies: mn(m/n+n/m)/(m²+n²) = mn·((m²+n²)/mn)/(m²+n²) = 1, always an integer. But m/n+n/m (e.g. m=1,n=2 gives 2.5) and mn/(m²+n²) (2/5) need not be integers. Hence 2 only, option B.