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AP EAMCET · Maths · Binomial Theorem

The coefficient of \(x^{10}\) in the expansion of \(\left(x+\frac{2}{x}-5\right)^{12}\) is

  1. A \(1674\)
  2. B \(2132\)
  3. C \(1892\)
  4. D \(862\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(1674\)

Step-by-step Solution

Detailed explanation

Let the general term be \(\frac{12!}{p!q!r!} (x)^p \left(\frac{2}{x}\right)^q (-5)^r\). This simplifies to \(\frac{12!}{p!q!r!} 2^q (-5)^r x^{p-q}\). We need \(p-q=10\) and \(p+q+r=12\). From \(p-q=10 \Rightarrow p=q+10\). Substitute into…