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Question: Answered & Verified by Expert
If \({ }^n C_4,{ }^n C_5\) and \({ }^n C_6\) are in A.P., then \(n\) is
MathematicsBinomial TheoremWBJEEWBJEE 2011
Options:
  • A 7 or 14
  • B 7
  • C 14
  • D 14 or 21
Solution:
1381 Upvotes Verified Answer
The correct answer is: 7 or 14
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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