75. A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : Two circles with radii p, q (p > q) in cm touch externally, where p, q are natural numbers and each greater than 1. What is the value of (p - q) ? Statement-I : The sum of their areas is 130\pi \text{ cm}^2. Statement-II : The distance between the centres of the two circles is 14 cm.
- A. The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
- B. The Question can be answered by using either Statement alone
- C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone ✓
- D. The Question cannot be answered even by using both the Statements together
Correct Answer: C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
Explanation
Statement I gives p^2+q^2=130, which allows multiple integer solutions like (11,3) or (9,7). Statement II gives p+q=14, which also has multiple solutions. Together, solving p^2+q^2=130 and p+q=14 yields a unique solution of p=11, q=3, making p-q=8.
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