77. A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : Is (p^2 + q^2) always composite number, where p and q are different prime numbers ? Statement-I : (p - q) is an odd integer Statement-II : (p + q) is an odd integer

  1. A. The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
  2. B. The Question can be answered by using either Statement alone ✓
  3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
  4. D. The Question cannot be answered even by using both the Statements together

Correct Answer: B. The Question can be answered by using either Statement alone

Explanation

Both statements imply that one of the primes is even (must be 2) and the other is odd. Testing p=2, q=3 gives 4+9=13, which is prime. Thus, the answer is definitively 'No'. Either statement alone provides this definitive answer.

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