AP EAMCET · Maths · Binomial Theorem
If the sum of the coefficients of even powers of \(x\) in the expansion of \(\left(1-x+x^2\right)^{2 n}\) is 3281 , then \(\mathrm{n}=\)
- A 4
- B 5
- C 6
- D 3
Answer & Solution
Correct Answer
(A) 4
Step-by-step Solution
Detailed explanation
Let \(\left(1-x+x^2\right)^{2 n}=a_0+a_1 x+a_2 x^2+\ldots+a_{2 n} x^{4 n}\) put \(x=1\), we get \[ 1^{2 \mathrm{n}}=1=\mathrm{a}_0+\mathrm{a}_1+\mathrm{a}_2+\ldots+\mathrm{a}_{2 \mathrm{n}}.....(i) \] Put \(x=-1\), we get \[ 3^{2 n}=a_0-a_1+a_2-\ldots+a_{2 n}.....(ii) \] Adding…
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