$$10^2+1=100+1=101$$
$$12^2+1=144+1=145$$
$$24^2+1=576+1=577$$
$$26^2-1=676-1=675$$
All the pairs except 26 - 675 are in the form of n - (n+1)$$^2$$
$$\therefore\ $$26 - 675 is the odd one among the given number pairs.
Hence, the correct answer is Option D
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