$\begin{array}{1 1} 50 \\ 51 \\ 101 \\ 202 \end{array}$

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- The expansion of $(x+y)^n$ has $n+1$ terms

$(x+y)^{100}$ and $(x-y)^{100}$ have 101 terms each

In the expansion of $(x+y)^{100}+(x-y)^{100}$,

$2^{nd},4^{th},6^{th}.$..............terms get cancelled (total 50 terms) and

$1^{st},3^{rd}$.......... terms (total 51 terms) are added twice.

$\therefore$ no. of terms left over in the expansion = 51

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