AP EAMCET · Maths · Binomial Theorem
The coefficient of \(x^5\) in the expansion of \(\left(x^2+2 x+3\right)^5\), is
- A 1052
- B 540
- C 480
- D 1020
Answer & Solution
Correct Answer
(A) 1052
Step-by-step Solution
Detailed explanation
Given, \(\left(3+2 x+x^2\right)^5\) \(=\Sigma \frac{n !}{(p !)(q !)(r !)}(3)^p(2 x)^q\left(x^2\right)^r\)...(i) Where, \(\quad p+q+r=n=5\) For \(x^5\), we have, \(q+2 r=5\) \(\begin{aligned} & \therefore \quad r=0, q=5, p=0 \\ & r=1, q=3, p=1 \\ & r=2, q=1, p=2 \end{aligned}\)…
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