JEE Mains · Maths · STD 11 - 7. binomial theoram
If for some positive integer \(n,\) the coefficients of three consecutive terms in the binomial expansion of \((1+x)^{n+5}\) are in the ratio \(5: 10: 14,\) then the largest coefficient in this expansion is
- A \(792\)
- B \(252\)
- C \(462\)
- D \(330\)
Answer & Solution
Correct Answer
(C) \(462\)
Step-by-step Solution
Detailed explanation
Let \(n+5=N\) \(N _{ C _{ r -1}}: N _{ C _{ r }}: N _{ C _{ r +1}}=5: 10: 14\) \(\Rightarrow \frac{ N _{ C _{r}}}{ N _{ C _{ r -1}}}=\frac{ N +1- r }{ r }=2\) \(\frac{N_{C_{r+1}}}{N_{C_{r}}}=\frac{N-r}{r+1}=\frac{7}{5}\) \(\Rightarrow \quad r=4, N=11\)…
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