2024 · Q58
If P² varies as R and Q² varies as R, (P ≠ Q), then which of the following are correct?
- 1P² + Q² varies as R.
- 2PQ varies as R.
- 3P² - Q² varies as R.
Select the correct answer using the code given below:
Elementary MathematicsRatio and Proportion
- A1 and 2 only
- B2 and 3 only
- C1 and 3 only
- D1, 2 and 3
Explanation
Write P² = kR and Q² = k′R with k ≠ k′. Then P² + Q² = (k + k′)R, PQ = √(kk′)·R, and P² − Q² = (k − k′)R are all constant multiples of R. All three statements hold: option (d).