If $a$ and $b$ denote respectively the coefficients of
Question:

If $a$ and $b$ denote respectively the coefficients of $x^{m}$ and $x^{n}$ in the expansion of $(1+x)^{m+n}$, then write the relation between $a$ and $b$.

Solution:

Coefficient of $x^{m}$ in the given expansion $={ }^{m+n} C_{m}=a$

Coefficient of $x^{n}$ in the given expansion $={ }^{m+n} C_{n}=b$

$\therefore a=b \quad\left[\because{ }^{m+n} C_{m}={ }^{m+n} C_{n}\right]$