Question

If \(\mathrm{n}\) is even positive integer, then the condition that the greatest term in the expansion of \((1+\mathrm{x})^{\mathrm{n}}\) may also have the greatest coefficient is
(A) \(\frac{n}{n+2}<x<\frac{n+2}{n}\)
(B) \(\frac{n}{n+1}<x<\frac{n+1}{n}\)
(C) \(\frac{n+1}{n+2}<x<\frac{n+2}{n+1}\)
(D) \(\frac{n+2}{n+3}<x<\frac{n+3}{n+2}\)

Answer 1

Ans : (A)
Hint \(: \frac{n}{2}<\frac{x(n+1)}{x+1}<\frac{n}{2}+1 \Rightarrow \frac{n}{n+2}<x<\frac{n+2}{n}\)