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: If \( a_{i}, b_{i} \in \mathbf{N} \), for \( i=1,2,3 \) and
\( -\quad \Delta(x)=\left|\begin{array}{lll}(1+x)^{a_{1} b_{1}} & (1+x)^{a_{1} b_{2}} & (1+x)^{a_{1} b_{3}} \\ (1+x)^{a_{2} b_{1}} & (1+x)^{a_{2} b_{2}} & (1+x)^{a_{2} b_{3}} \\ (1+x)^{a_{3} b_{1}} & (1+x)^{a_{3} b_{2}} & (1+x)^{a_{3} b_{3}}\end{array}\right| \),
then coefficient of \( x \) in expansion of \( \Delta(x) \) is 0 .
Statement-2: If \( P(x)=(1+x)^{n}, n \in \mathbf{N} \) then coefficient of \( x \) in the expansion of \( P(x) \) is \( P^{\prime}(0) \).
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