AP EAMCET · Maths · Binomial Theorem
If the \(m\) th term is the middle term in expansion of \(\left(x^2-\frac{1}{2 x}\right)^{20}\). Find coefficient of \(T_{m+3}\).
- A \({ }^{20} \mathrm{C}_{13} 2^{-13}\)
- B \(-{ }^{20} \mathrm{C}_{13} 2^{13}\)
- C \(-{ }^{20} \mathrm{C}_{13} 2^{-13}\)
- D \({ }^{20} \mathrm{C}_{13} 2^{13}\)
Answer & Solution
Correct Answer
(A) \({ }^{20} \mathrm{C}_{13} 2^{-13}\)
Step-by-step Solution
Detailed explanation
Expansion of \(\left(x^2-\frac{1}{2 x}\right)^{20}\) contains ' 21 ' terms. So middle term is, \(\frac{20}{2}+1=11\) term \(\Rightarrow \quad m=11\) Now,…
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