The coefficients of $x^p$ and $x^q$ in the expansion of $(1+x)^{p+q}$ are

The coefficients of $x^p$ and $x^q$ in the expansion of $(1+x)^{p+q}$ are
  1. equal
  2. equal with opposite signs
  3. reciprocals of each other
  4. none of these

Solution

We have $t_{p+1}={ }^{p+q} C_p x^p$ and $t_{q+1}={ }^{p+q} C_q x^q \quad{ }^{p+q} C_p={ }^{p+q} C_q$

Asked in: JEE Main 2002

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