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Question
If rth term in the expansion of \[\left( 2 x^2 - \frac{1}{x} \right)^{12}\] is without x, then r is equal to
Options
8
7
9
10
Solution
9
\[\text{ rth term in the given expansion is } ^{12}{}{C}_{r - 1} (2 x^2 )^{12 - r + 1} \left( \frac{- 1}{x} \right)^{r - 1} \]
`= ( - 1 )^{r - 1} "^12C_{r - 1} 2^{13 - r} x^{26 - 2r - r + 1} `
\[\text{ For this term to be independent of x, we must have: } \]
\[27 - 3r = 0\]
\[ \Rightarrow r = 9\]
\[\text{ Hence, the 9th term in the expansion is independent of x } .\]
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