Question

If the coefficients of the r th term and the $ (r+1)th $ term in the expansion of $ {{(1+x)}^{20}} $ are in the ratio $ 1:2, $ then r is equal to:

• A. 6
• B. 7
• C. 8
• D. 9
• E. 5

Answer 1

Answer: (B)

$ {{T}_{r}}={{T}_{(r-1)+1}}{{=}^{20}}{{C}_{r-1}}.{{x}^{r-1}} $ $ \therefore $ Coefficient of the r th term $ {{=}^{20}}{{C}_{r-1}} $ and coefficient of the $ (r+1) $ th term $ {{=}^{20}}{{C}_{r}} $ $ \therefore $ $ \frac{^{20}{{C}_{r-1}}}{^{20}{{C}_{r}}}=\frac{1}{2} $ $ \Rightarrow $ $ \frac{r}{21-r}=\frac{1}{2} $ $ \Rightarrow $ $ r=7 $