(A) The general term in the expansion of $(1 + x)^n$ is given by $T_{r+1} = ^nC_r x^r$.For the expansion of $(1 + x)^{p+q}$,the coefficient of $x^p$ i

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(A) The general term in the expansion of $(1 + x)^n$ is given by $T_{r+1} = ^nC_r x^r$.For the expansion of $(1 + x)^{p+q}$,the coefficient of $x^p$ is $^{p+q}C_p$.Similarly,the coefficient of $x^q$ is $^{p+q}C_q$.Using the property of binomial coefficients,$^nC_r = ^nC_{n-r}$,we have:$^{p+q}C_p = ^{p+q}C_{(p+q)-p} = ^{p+q}C_q$.Therefore,the coefficients of $x^p$ and $x^q$ are equal.

Class 11 Mathematics Binomial Theorem Properties of binomial coefficients

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

AIEEE 2002 All AIEEE

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Equal
B
Equal in magnitude but opposite in sign
C
Reciprocal to each other
D
None of these

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

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