Question

The two successive terms in the expansion of $(1+x{)}^{24}$ whose coeff are in ratio $1:4$ are

• A. $3^{rd}$ and $4^{th}$
• B. $4^{th}$ and $5^{th}$
• C. $4^{th}$ and $6^{th}$
• D. $6^{th}$ and $7^{th}$

Answer 1

The correct option is B $4^{th}$ and $5^{th}$

Solution:

We know that in the coefficient of $r^{th}$ term in expansion of $(1+x{)}^n={}^n{C}_{r-1}$

Let two successive terms of expansion $(1+x{)}^{24}$ are $T_r$ and $T_{r+1}.$

And

$\frac{T_r}{T_{r+1}}=\frac{1}{4}$

or, $\frac{r+1}{24-r}=\frac{1}{4}$

or, $4r+4=24-r$

or, $5r=20$

or, $r=4$

Hence, two successive terms are $4^{th}$ and $5^{th}.$

Hence, B is the correct option.