Question

If 21st and 22nd terms in the expansion of $(1+x{)}^{44}$ are equal, then $x$ is equal to.

• A. $\frac{21}{22}$
• B. $\frac{23}{24}$
• C. $\frac{8}{7}$
• D. $\frac{7}{8}$

Answer 1

The correct option is D $\frac{7}{8}$

$(r+1)$th term in the expansion of $(1+x{)}^{44}$ is given by ${}^{44}{C}_r{x}^{44-r}$.

Therefore,

$21$st term is given by ${}^{44}{C}_{20}{x}^{24}$.

And $22$nd term is given by ${}^{44}{C}_{21}{x}^{23}$.

Now it is given that both are same

${\Rightarrow }^{44}{C}_{20}{x}^{20}{=}^{44}{C}_{21}{x}^{21}$

$\Rightarrow x=\frac{{}^{44}{C}_{20}}{{}^{44}{C}_{21}}=\frac{\frac{44!}{24!20!}}{\frac{44!}{23!21!}}=\frac{7}{8}$