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7.Binomial Theorem
normal
In the expansion of
$(2x + 1).(2x + 5) . (2x + 9) . (2x + 13)...(2x + 49),$ find the coefficient of $x^{12}$ is :-
A
$\frac{325}{2}$
B
$325 \cdot (2^{12})$
C
$325 \cdot (2^{11})$
D
None of these
Solution
These are $13$ factors so $2^{13}\left(\mathrm{x}+\frac{1}{2}\right)\left(\mathrm{x}+\frac{5}{2}\right)$
$\left(x+\frac{9}{2}\right) \cdots\left(x+\frac{49}{2}\right)$
$ \text { so coefficient of } x^{12} =2^{13}\left(\frac{1}{2}+\frac{5}{2}+\frac{9}{2}+\cdots+\frac{49}{2}\right) $
$=325.2^{12} $
Standard 11
Mathematics