If p and q be positive- then the coefficients of x p and x q in the expansion of 1- x p - q will be-A- EqualB- Reciprocal to each otherC- UnequalD- None of the above

The correct option is A EqualCoefficient of x^p is ^p+qC_p and coefficient of x^q is ^p+qC_q. nbsp; So both the coefficients are equal. [∵ ^nC_r= ^nC_n r] ...

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Standard XII

Mathematics

Binomial Coefficients

If p and q be...

Question

If $p$ and $q$ be positive, then the coefficients of $x^{p}$ and $x^{q}$ in the expansion of $(1 + x)^{p + q}$ will be:

Equal

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Unequal

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Reciprocal to each other

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None of the above

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Solution

The correct option is A Equal
Coefficient of $x^{p}$ is $^{p + q} C_{p}$ and coefficient of $x^{q}$ is $^{p + q} C_{q}$ .
So both the coefficients are equal.
$[∵^{n} C_{r} =^{n} C_{n - r}]$

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If p and q be positive, then the coefficients of xp and xq in the expansion of (1+x)p+q will be:

The correct option is A EqualCoefficient of xp is p+qCp and coefficient of xq is p+qCq. So both the coefficients are equal. [∵ nCr= nCn−r]

If $p$ and $q$ be positive, then the coefficients of $x^{p}$ and $x^{q}$ in the expansion of $(1 + x)^{p + q}$ will be:

The correct option is A Equal
Coefficient of $x^{p}$ is $^{p + q} C_{p}$ and coefficient of $x^{q}$ is $^{p + q} C_{q}$ .
So both the coefficients are equal.
$[∵^{n} C_{r} =^{n} C_{n - r}]$