Question

If the expansion of $(1+x{)}^{20}$, then coefficients of rth and (r+4)th terms are equal, then r is equal to

• A. 7
• B. 8
• C. 9
• D. 10

Answer 1

The correct option is C

9

Coefficients of the rth and (r+4)th terms in the given expansion are ${}^{20}{C}_{r-1}$ and ${}^{20}{C}_{r+3}$

Here,

${}^{20}{C}_{r-1}{=}^{20}{C}_{r+3}$

$\Rightarrow r-1+r+3=20$

$[\because I{f}^n{C}_x{=}^n{C}_y\Rightarrow x=yorx+y=n]$

$\Rightarrow r=2or2r=18$

$\Rightarrow r=9$