JEE Mains · Maths · STD 11 - 7. binomial theoram
Let \([ x ]\) denote greatest integer less than or equal to \(x .\) If for \(n \in N ,\left(1-x+x^{3}\right)^{n}=\sum_{j=0}^{3 n} a_{j} x^{j}\), then \(\sum_{j=0}^{\left[\frac{3 n}{2}\right]} a_{2 j}+4 \sum_{j=0}^{\left[\frac{3 n-1}{2}\right]} a_{2 j+1}\) is equal to
- A \(2\)
- B \(2^{ n -1}\)
- C \(1\)
- D \(n\)
Answer & Solution
Correct Answer
(C) \(1\)
Step-by-step Solution
Detailed explanation
\(\left(1-x+x^{3}\right)^{n}=\sum_{j=0}^{3 n} a_{j} x^{j}\) \(\left(1-x+x^{3}\right)^{n}=a_{0}+a_{1} x+a_{2} x^{2} \ldots \ldots .+a_{3 n} x^{3 n}\) \(\sum_{j=0}^{\left[\frac{3 n}{2}\right]} a_{2 j}=\operatorname{Sum}\) of \(a_{0}+a_{2}+a_{4} \ldots \ldots . .\)…
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