(D) Given,the binomial expansion is $(1+x)^{15}$.The coefficient of $x^{r}$ is $^{15}C_{r}$ and the coefficient of $x^{r+3}$ is $^{15}C_{r+3}$.Accordi

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(D) Given,the binomial expansion is $(1+x)^{15}$.The coefficient of $x^{r}$ is $^{15}C_{r}$ and the coefficient of $x^{r+3}$ is $^{15}C_{r+3}$.According to the problem,the coefficients are equal:$^{15}C_{r} = ^{15}C_{r+3}$Using the property of binomial coefficients,if $^{n}C_{x} = ^{n}C_{y}$,then either $x = y$ or $x + y = n$.Here,$r \neq r+3$,so we must have $r + (r+3) = 15$.$2r + 3 = 15$$2r = 12$$r = 6$

Class 11 Mathematics Binomial Theorem General term, Coefficient of any power of x, Independent term, Middle term and Greatest term and Greatest coefficient

Medium

In the binomial expansion of $(1+x)^{15}$,the coefficients of $x^{r}$ and $x^{r+3}$ are equal. Then,$r$ is

KCET 2010 All KCET

A
$8$
B
$7$
C
$4$
D
$6$

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Binomial Theorem

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General term, Coefficient of any power of x, Independent term, Middle term and Greatest term and Greatest coefficient

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In the binomial expansion of $(1+x)^{15}$,the coefficients of $x^{r}$ and $x^{r+3}$ are equal. Then,$r$ is

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