If in expansion of {(1 + x)^{21}} , coefficients of {x^r} and {x^{r + 1}} be equal, then r is equal

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7.Binomial Theorem

easy

If in the expansion of ${(1 + x)^{21}}$, the coefficients of ${x^r}$ and ${x^{r + 1}}$ be equal, then $r$ is equal to

A

$9$

B

$10$

C

$11$

D

$12$

Solution

(b) ${T_{r + 1}} = {\,^{21}}{C_r}{(1)^{21 – r}}{(x)^r} = {\,^{21}}{C_r}$

$\therefore $Coefficient of ${x^r} = {\,^{21}}{C_r}$ and coefficient of ${x^{r + 1}} = {\,^{21}}{C_{r + 1}}$

So, we must have $^{21}{C_r} = {\,^{21}}{C_{r + 1}} \Rightarrow r = 10$.

Standard 11

Mathematics

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