(D) The general term in the expansion of $(x+a)^n$ is given by $T_{r+1} = {^nC_r} x^{n-r} a^r$.The coefficient of the term $x^{n-r}a^r$ is ${^nC_r}$.T

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(D) The general term in the expansion of $(x+a)^n$ is given by $T_{r+1} = {^nC_r} x^{n-r} a^r$.The coefficient of the term $x^{n-r}a^r$ is ${^nC_r}$.The coefficient of the term $x^ra^{n-r}$ is ${^nC_{n-r}}$.We know that ${^nC_r} = {^nC_{n-r}}$.Therefore,the ratio of the coefficients is $\frac{{^nC_r}}{{^nC_{n-r}}} = \frac{{^nC_r}}{{^nC_r}} = 1:1$.

Class 11 Mathematics Binomial Theorem Properties of binomial coefficients

Easy

The ratio of the coefficients of the terms $x^{n-r}a^r$ and $x^ra^{n-r}$ in the binomial expansion of $(x+a)^n$ is:

A
$x:a$
B
$n:r$
C
$x:n$
D
$1:1$

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Chapter

Binomial Theorem

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Properties of binomial coefficients

The value of $\sum\limits_{r = 0}^{n - 1} {\frac{{^n{C_r}}}{{^n{C_r} + {\,^n}{C_{r + 1}}}}} $ equals

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The value of $\frac{1}{1! 50!} + \frac{1}{3! 48!} + \frac{1}{5! 46!} + \dots + \frac{1}{49! 2!} + \frac{1}{51! 1!}$ is $.............$.

DifficultJEE MAIN 2023

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The mean of the values $0, 1, 2, \dots, n$ having corresponding weights $^nC_0, ^nC_1, ^nC_2, \dots, ^nC_n$ respectively is

Difficult

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The sum of the last $30$ coefficients in the expansion of $(1+x)^{59}$,when expanded in ascending powers of $x$,is:

MediumWBJEE 2010

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If $n$ is an integer greater than $1$,then $a - ^nC_1(a - 1) + ^nC_2(a - 2) + \dots + (-1)^n(a - n) = $

MediumIIT 1972

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The ratio of the coefficients of the terms $x^{n-r}a^r$ and $x^ra^{n-r}$ in the binomial expansion of $(x+a)^n$ is:

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