Consider the following statements :<br>1. If x is directly proportional to z and y is directly proportional to z, then (x^{2}-y^{2}) is directly proportional to z^{2}.<br>2. If x is inversely proportional to z and y is inversely proportional to z, then (xy) is inversely proportional to z^{2}.<br>Which of the above statements is/are correct?
- A. 1 only
- B. 2 only
- C. Both 1 and 2 ✓
- D. Neither 1 nor 2
Correct Answer: C. Both 1 and 2
Explanation
Statement 1: x = k_1z and y = k_2z, so x^2-y^2 = (k_1^2-k_2^2)z^2, which is directly proportional to z^2. Statement 2: x = k_1/z and y = k_2/z, so xy = (k_1k_2)/z^2, which is inversely proportional to z^2. Both statements are correct.
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