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Question
Determine whether the expansion of `(x^2 - 2/x)^18` will contain a term containing x10?
Solution
Let Tr+1 contain x10.
Then Tr+1 = `""^18"C"_r (x^2)^(18 - r) (-2^r)/x`
= `""^18"C"_r x^(36 - 2r) (-1)^r * 2^r x^(-r)`
= `(-1)^r 2^r ""^18"C"_r x^(36 - 3r)`
Thus, 36 – 3r = 10
i.e., r = `36/3`
Since r is a fraction, the given expansion cannot have a term containing x10.
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