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Question
Find the coefficient of x11 in the expansion of `(x^3 - 2/x^2)^12`
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Solution
Let the general term, i.e., (r + 1)th contain x11.
We have `"T"_(r + 1) = ""^12"C"_r (x^3)^(12 - r) (- 2/x^2)^r`
= `""^12"C"_r x^(36 - 3r - 2r) (- 1)^r 2r`
= `""^12"C"_r (-1)^r 2r x^(36 - 5r)`
Now for this to contain x11
We observe that 36 – 5r = 11
i.e., r = 5
Thus, the coefficient of x11 is
`""^12"C"_5 (-1)^5 2^5 = - (12 xx 11 xx 10 xx 9 xx 8)/(5 xx 4 xx 3 xx 2) xx 32`
= – 25344
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