$\begin{array}{1 1}(A)\;10\\(B)\;12\\(C)\;14\\(D)\;16\end{array} $

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- $(x-a)^n=nC_0x^n a^0-nC_1x^{n-1} a^1+nC_2 x^na^2.......nC_n x^0 a^n$

$(25)^{15}=(26-1)^{15}$

$\Rightarrow 15C_0 (26)^{15}(-1)^0+15C_2 (26)^{14}(-1)^1+15C_{15}.(26) (-1)^{15}$

Hence the last term $2b=13\times 2$ which is divisible by 13.Hence no remainder.

$\Rightarrow $ The last term is $(-1)^{15}=-1$

Hence the remainder of (-1) by 13 is $-1=13\times (-1)+12$

Hence the answer is 12.

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