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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
For \( m, n \in \mathbf{N}, n \leq m \), let
\( -(m, n)=\frac{\left(1-x^{m}\right)\left(1-x^{m-1}\right) \cdots\left(1-x^{m-n+1}\right)}{(1-x)\left(1-x^{2}\right) \cdots\left(1-x^{n}\right)} \)
Statement-1: \( (m, n+1)=(m-1 n+1) \)
\[
+x^{m-n-1}(m-1, n)
\]
Statement-2: \( (m, n) \) is a polynomial of degree
\( -m+n-2 \)
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