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:

• A. Equal
• B. Unequal
• C. Reciprocal to each other
• D. None of the above

Answer 1

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.
$[\because {}^n{C}_r={}^n{C}_{n-r}]$