If $\mathrm{x}$ is positive, the first negative term in the expansion of $(1+x)^{27 / 5}$ is

If $\mathrm{x}$ is positive, the first negative term in the expansion of $(1+x)^{27 / 5}$ is
  1. 6th term
  2. 7th term
  3. 5th term
  4. 8th term

Solution

$T_{r+1}=\frac{n(n-1)(n-2) \ldots \ldots \ldots(n-r+1)}{r !}(x)^r$ For first negative term, $n-r+1 < 0$ or $r>\frac{32}{5}$ $\therefore \mathrm{r}=7$. Therefore, first negative term is $\mathrm{T}_8$.

Asked in: JEE Main 2003

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