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Standard XII

Mathematics

Greatest Binomial Coefficients

In the binomi...

Question

In the binomial expansion of $(1 + a)^{m + n}$ , if the coefficients of $a^{m}$ and $a^{n}$ are $A$ and $B$ respectively, then

m A = n B

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n A = m B

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A

and

B

cannot be related.

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A = B

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Solution

The correct option is D $A = B$
Given expansion is ${(1 + a)}^{m + n}$ ,
The coefficient of $a^{m}$ is $(\begin{matrix} m + n m \end{matrix})$ ,
The coefficient of $a^{n}$ is $(\begin{matrix} m + n n \end{matrix})$ ,
$∴ A = B$

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State true or false.

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In the binomial expansion of (1+a)m+n, if the coefficients of am and an are A and B respectively, then

The correct option is D A=BGiven expansion is (1+a)m+n,The coefficient of am is (m+nm),The coefficient of an is (m+nn),∴A=B

In the binomial expansion of $(1 + a)^{m + n}$ , if the coefficients of $a^{m}$ and $a^{n}$ are $A$ and $B$ respectively, then

The correct option is D $A = B$
Given expansion is ${(1 + a)}^{m + n}$ ,
The coefficient of $a^{m}$ is $(\begin{matrix} m + n m \end{matrix})$ ,
The coefficient of $a^{n}$ is $(\begin{matrix} m + n n \end{matrix})$ ,
$∴ A = B$