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Question
Find the middle term in the expansion of:
(iii) \[\left( x^2 - \frac{2}{x} \right)^{10}\]
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Solution
(iii) Here,
n = 10 (Even number)
Therefore, the middle term is the \[\left( \frac{n}{2} + 1 \right)th\] i.e. 6th term
\[Now, \]
\[ T_6 = T_{5 + 1} \]
\[ = ^{10}{}{C}_5 ( x^2 )^{10 - 5} \left( \frac{- 2}{x} \right)^5 \]
\[ = - \frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2} \times 32 x^5 \]
\[ = - 8064 x^5 \]
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