Q88 / 160 · WBJEE 2011 · Mathematics

If \({ }^n C_4,{ }^n C_5\) and \({ }^n C_6\) are in A.P., then \(n\) is

  • Correct answer
    A
    7 or 14
  • B
    7
  • C
    14
  • D
    14 or 21

Solution

Hints: \({ }^n \mathrm{C}_4,{ }^n \mathrm{C}_5,{ }^n \mathrm{C}_6\) are in \(\mathrm{AP}\) \(\begin{aligned} & \text { 2. }{ }^n \mathrm{C}_5={ }^n \mathrm{C}_4+{ }^n \mathrm{C}_6 \\ & \frac{2}{5(n-5)}=\frac{1}{(n-4)}+\frac{1}{30} \\ & \end{aligned}\) by solving \(n=14\) or 7

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

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