AP EAMCET · Maths · Binomial Theorem
If \(\left(1-x+x^2\right)^{10}=a_0+a_1 x+a_2 x^2+\ldots+a_{20} x^{20}\), then \(2 a_2+3 a_3+4 a_4+\ldots+20 a_{20}=\)
- A 0
- B 10
- C 20
- D -20
Answer & Solution
Correct Answer
(C) 20
Step-by-step Solution
Detailed explanation
\(\left(1-x+x^2\right)^{10}=a_0+a_1 x+a_2 x^2+\ldots \ldots+a_{20} x^{20}\) On differentiating \(\begin{aligned} & 10\left(1-x+x^2\right)^9 \cdot(-1+2 x)=a_1+2 a_2 x+3 a_3 x^2 \\ & +\ldots \ldots+20 a_{20} x^{19} \end{aligned}\) At \(x=1\)…
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