JEE Mains · Maths · STD 11 - 7. binomial theoram
For some \(n \neq 10\), let the coefficients of the 5 th, 6 th and 7 th terms in the binomial expansion of \((1+\mathrm{x})^{\mathrm{n}+4}\) be in A.P. Then the largest coefficient in the expansion of \((1+\mathrm{x})^{\mathrm{n}+4}\) is:
- A \(20\)
- B \(10\)
- C \(35\)
- D \(70\)
Answer & Solution
Correct Answer
(C) \(35\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & (1+x)^{n+4} \\ & { }^{n+4} C_4,{ }^{n+4} C_5,{ }^{n+4} C_6, \rightarrow \text { A.P. } \\ & \Rightarrow 2 \times { }^{n+4} C_5={ }^{n+4} C_4+{ }^{n+4} C_6 \\ & \Rightarrow 4 \times{ }^{n+4} C_5=\left({ }^{n+4} C_4+{ }^{n+4} C_5\right)+\left({ }^{n+4} C_5+{…
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