JEE Mains · Maths · STD 11 - 7. binomial theoram
If the sum of the coefficients of all even powers of \(x\) in the product \(\left(1+x+x^{2}+\ldots+x^{2 n}\right)\left(1-x+x^{2}-x^{3}+\ldots+x^{2 n}\right)\) is \(61,\) then \(\mathrm{n}\) is equal to
- A \(30\)
- B \(26\)
- C \(22\)
- D \(20\)
Answer & Solution
Correct Answer
(A) \(30\)
Step-by-step Solution
Detailed explanation
Let \(\left(1+x+x^{2}+\ldots+x^{2 n}\right)\left(1-x+x^{2}-x^{3}+\ldots+x^{2 n}\right)\) \(=a_{0}+a_{1} x_{+} a_{2} x^{2}+a_{3} x^{3}+a_{4} x^{4}+\ldots+a_{4 n} x^{4 n}\) \(\mathrm{So}\) \(a_{0}+a_{1}+a_{2}+\ldots+a_{4 n}=2 n+1\) \(a_{0}-a_{1}+a_{2}-a_{3} \ldots+a_{4 n}=2 n+1\)…
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