Question

r and n are positive integers $r > 1, n > 2$ and coefficient of $(r+2)^{th}$ term and $3r^{th}$ term in the expansion of $(1 + x)^{2n }$ are equal, then n equals

• A. $3r$
• B. $3r + 1$
• C. $2r$
• D. $2r + 1$

Answer 1

Answer: (C)

$2r$

Answer 2

$t_{r+2} = {^{2n}C_{r+1}} \,x^{r+1}; t_{3r} = {^{2n}C_{3r-1} } x^{3r-1}$ Given ${^{2n}C_{r+1} } = {^{2n}C_{3r-1}} ;$ $\Rightarrow \, {^{2n }C_{2n -\left(r+1\right)}} = {^{2n }C_{3r-1}}$ $\Rightarrow 2n-r-1=3r-1 \Rightarrow 2n = 4r \Rightarrow n= 2r$