JEE MATHEMATICS MCQ: BINOMIAL THEOREM

Option A ($a_p=a_q$) is correct because $a_r$ represents the coefficient of $x^r$ in the expansion of $(1+x)^{p+q}$, and $a_p = { }^{p+q}C_p$ and $a_q = { }^{p+q}C_q$. Since ${ }^{n}C_r = { }^{n}C_{n-r}$, and ${ }^{p+q}C_p = { }^{p+q}C_{(p+q)-p} = { }^{p+q}C_q$, therefore $a_p = a_q$.