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Each question in this section has four choices (a), (b), (c) and (d) out of which only one is correct. Mark your choices as follows:
(a) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
(b) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
(c) STATEMENT-1 is True, STATEMENT-2 is False
(d) STATEMENT-1 is False, STATEMENT-2 is True
Statement-1: For non-negative integers \( m, n, r \) and
- \( k \)
\( -\sum_{m=0}^{k}(n-m) \frac{(r+m) !}{m !}=\frac{(r+k+1) !}{k !}\left[\frac{n}{r+1}-\frac{k}{r+2}\right] \)
Statement-2: \( \sum_{m=0}^{k}\left(\begin{array}{c}r+m \\ m\end{array}\right)=\left(\begin{array}{c}r+k+1 \\ k\end{array}\right) \)
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