WBJEE · Maths · Binomial Theorem
If \({ }^n C_4,{ }^n C_5\) and \({ }^n C_6\) are in A.P., then \(n\) is
- A 7 or 14
- B 7
- C 14
- D 14 or 21
Answer & Solution
Correct Answer
(A) 7 or 14
Step-by-step Solution
Detailed explanation
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
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