COMEDK · Maths · 7. Binomial Theorem
Given, the positive integers \(r>1, n>2\) and the coefficients of \((3 r)\) th and \((r+2)\) th terms in the expansion of \((1+x)^{2 n}\) are equal, then \(n=\)
- A \(2 r\)
- B \(2 r-1\)
- C \(2 r+1\)
- D \(3 r\)
Answer & Solution
Correct Answer
(A) \(2 r\)
Step-by-step Solution
Detailed explanation
\(\left(\begin{array}{c}2 n \\ 3 r-1\end{array}\right)=\left(\begin{array}{c}2 n \\ r+1\end{array}\right)\) \(\left\{\begin{array}{c} { }^{n} C_{x}={ }^{n} C_{y} \Rightarrow x+y=n \\ \text { or } n-x=y \end{array}\right\}\) \(\Rightarrow \quad 2 n=3 r-1+r+1 \Rightarrow n=2 r\)
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