AP EAMCET · Maths · Binomial Theorem
Coefficient of \(x^{10}\) in the expansion of \((2+3 x) e^{-x}\) is
- A \(\frac{-26}{(10) !}\)
- B \(\frac{-28}{(10) !}\)
- C \(\frac{-30}{(10) !}\)
- D \(\frac{-32}{(10) !}\)
Answer & Solution
Correct Answer
(B) \(\frac{-28}{(10) !}\)
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} (2+3 x) e^{-x} & \\ & =(2+3 x)\left(1-\frac{x}{1 !}+\frac{x^2}{2 !}-\frac{x^3}{3 !}+\ldots\right) \end{aligned} \] \(\therefore\) Coefficient of \(x^{10}\) in the above series…
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