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7.Binomial Theorem
easy
${(1 + x)^{2n}}$ ના વિસ્તરણમાં મધ્યમપદ મેળવો.
A
$\frac{{1.3.5....(5n - 1)}}{{n!}}{x^n}$
B
$\frac{{2.4.6....2n}}{{n!}}{x^{2n + 1}}$
C
$\frac{{1.3.5....(2n - 1)}}{{n!}}{x^n}$
D
$\frac{{1.3.5....(2n - 1)}}{{n!}}{2^n}{x^n}$
Solution
(d) Middle term of ${(1 + x)^{2n}}$ is ${T_{n + 1}} = {\,^{2n}}{C_n}{x^n}$
$ = \frac{{(2n)!}}{{n!\,\,n!}}{x^n} = \frac{{1.3.5….(2n – 1)}}{{n!}}{2^n}{x^n}$.
Standard 11
Mathematics
