78. A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : Is (0.5)^n + (0.5)^{-n} always greater than 2, where n is an integer ? Statement-I : n is an even integer Statement-II : n is negative

  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 can be answered even without using both the Statements

Correct Answer: A. The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone

Explanation

The expression simplifies to 2^{-n} + 2^n. By AM-GM, x + 1/x > 2 unless x=1 (i.e., n=0). Statement II states n is negative, ensuring n \neq 0, so the value is definitively > 2. Statement I allows n=0, where the sum is exactly 2, so it's insufficient.

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