A) \[\frac{n}{n+2}<x<\frac{n+2}{n}\]
B) \[\frac{n+1}{n}<x<\frac{n}{n+1}\]
C) \[\frac{n}{n+4}<x<\frac{n+4}{4}\]
D) None of these
Correct Answer: A
Solution :
If n is even, the greatest coefficient is \[^{n}{{C}_{n/2}}\] Therefore the greatest term \[={{\,}^{n}}{{C}_{n/2}}{{x}^{n/2}}\] \[\therefore \,{{\,}^{n}}{{C}_{n/2}}{{x}^{n/2}}>{{\,}^{n}}{{C}_{(n/2)-1}}{{x}^{(n-2)/2}}\] and \[^{n}{{C}_{n/2}}{{x}^{n/2}}>{{\,}^{n}}{{C}_{(n/2)+1}}{{x}^{(n/2)+1}}\] Þ \[\frac{n-\frac{n}{2}+1}{\frac{n}{2}}x>1\]and \[\frac{\frac{n}{2}}{\frac{n}{2}+1}x<1\] Þ \[x>\frac{\frac{n}{2}}{\frac{n}{2}+1}\] and \[x<\frac{\frac{n}{2}+1}{\frac{n}{2}}\] Þ \[x>\frac{n}{n+2}\]and \[x<\frac{n+2}{n}\]
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