JEE Mains · Maths · STD 11 - 7. binomial theoram
The mean of the coefficients of \(x, x^2, \ldots \ldots x ^7\) in the binomial expansion of \((2+x)^9\) is \(...........\).
- A \(2735\)
- B \(2736\)
- C \(2734\)
- D \(2785\)
Answer & Solution
Correct Answer
(B) \(2736\)
Step-by-step Solution
Detailed explanation
Coefficient of \(x ={ }^9 C _1 2^8\) Of \(x ^2={ }^9 C _2 2^7\) Of \(x ^7={ }^9 C _7 \cdot 2^2\) Mean \(=\frac{{ }^9 C _1 \cdot 2^8+{ }^9 C _2 \cdot 2^7 \ldots . .+{ }^9 C _7 \cdot 2^2}{7}\) \(=\frac{(1+2)^9-{ }^9 C _0 \cdot 2^9-{ }^9 C _8 \cdot 2^1-{ }^9 C _9}{7}\)…
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