Q43 / 120 · JEE Main 2007 · Mathematics

In the binomial expansion of $(a-b)^n, n \geq 5$, the sum of $5^{\text {th }}$ and $6^{\text {th }}$ terms is zero, then $\frac{a}{b}$ equals

  • A
    $\frac{5}{n-4}$
  • B
    $\frac{6}{n-5}$
  • C
    $\frac{n-5}{6}$
  • Correct answer
    D
    $\frac{n-4}{5}$

Solution

${ }^n C_4 a^{n-4}(-b)^4+{ }^n C_5 a^{n-5}(-b)^5=0$ $\Rightarrow\left(\frac{a}{b}\right)=\frac{n-5+1}{5}$.

Hence, the correct answer is option: 'D'.

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