If P^{2} varies as R and Q^{2} varies as R, (P \neq Q), then which of the following are correct?<br>1. P^{2}+Q^{2} varies as R.<br>2. PQ varies as R.<br>3. P^{2}-Q^{2} varies as R.<br>Select the correct answer using the code given below:

  1. A. 1 and 2 only
  2. B. 2 and 3 only
  3. C. 1 and 3 only
  4. D. 1, 2 and 3 ✓

Correct Answer: D. 1, 2 and 3

Explanation

We are given that P^2 = k_1 R and Q^2 = k_2 R for some proportionality constants k_1 and k_2. Adding them gives P^2 + Q^2 = (k_1 + k_2)R, which clearly varies directly with R. Multiplying them gives P^2 Q^2 = k_1 k_2 R^2, which simplifies to PQ = R \sqrt{k_1 k_2}, showing PQ also varies directly with R. Finally, subtracting them yields P^2 - Q^2 = (k_1 - k_2)R, which again varies directly with R. Thus, all three statements are mathematically correct.

Related questions on Arithmetic

Practice more CDS Elementary Mathematics questions