JEE Mains · Maths · STD 11 - 8. sequence and series
For an integer \(\mathrm{n} \geq 2\), if the arithmetic mean of all coefficients in the binomial expansion of \((x+y)^{2 n-3}\) is 16 , then the distance of the point \(P\left(2 n-1, n^2-4 n\right)\) from the line \(x+y=8\) is:
- A \(\sqrt{2}\)
- B \(2 \sqrt{2}\)
- C \(5 \sqrt{2}\)
- D \(3 \sqrt{2}\)
Answer & Solution
Correct Answer
(D) \(3 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
No. of terms in \((x+y)^{(2 n-3)} \Rightarrow\left[\begin{array}{c}(2 n-3+1) \\ (2 n-2)\end{array}\right].\) \(\therefore\) sum of all coefficients \(=2^{2 n-3}\) (Put \(\mathrm{x}=\mathrm{y}=1\) ) \(\therefore\) Arithmetic mean of all coefficients…
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