A) \[A=B\]
B) \[A=2B\]
C) \[2A=B\]
D) None of these
Correct Answer: B
Solution :
\[\frac{\text{Coefficient}\,\text{of}\,{{x}^{n}}\,\text{in}\,\text{expansion}\,\,\text{of}{{(1+x)}^{2n}}}{\text{Coefficient}\,\text{of}\,{{x}^{n}}\,\text{in}\,\text{expansion}\,\,\text{of}\,{{(1+x)}^{2n-1}}}\] \[=\frac{^{2n}{{C}_{n}}}{^{(2n-1)}{{C}_{n}}}=\frac{(2n)!}{n!\,n!}\times \frac{(n-1)!\,n!}{(2n-1)!}\] \[=\frac{(2n)(2n-1)!(n-1)!}{n(n-1)!\,\,(2n-1)!}=\frac{2n}{n}=2:1\] Þ \[\frac{A}{B}=\frac{2}{1}\] Þ \[A=2B\].
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