Since T is divisible by 12. Let's assume T to be 12. Then, \(T^2\) =144.
Then the minimum value for which \(T^2\) is not an integer when divided by 2^a is when a=5.
Hence D is the answer.

Explanation

If t is divisible by 12, then \(t^2\) must be divisible by 144 or \(2 \times 2 \times 2 \times 2 \times 3 \times 3\). Therefore, \(t^2\) can be divided evenly by 2 at least four times, so a must be at least 5 before \(\frac{t^2}{2^a}\) might not be an integer.
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