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Question
In the expansion of \[\left( x - \frac{1}{3 x^2} \right)^9\] , the term independent of x is
Options
T3
T4
T5
none of these
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Solution
T4
\[\text{ Suppose } T_{r + 1} \text{ is the term in the given expression that is independent of x } . \]
\[\text{ Thus, we have: } \]
\[ T_{r + 1} =^{9}{}{C}_r x^{9 - r} \left( \frac{- 1}{3 x^2} \right)^r \]
`= ( - 1 )^r " ^ 9C _r \frac{1}{3^r} x^{9 - r - 2r} `
\[\text{ For this term to be independent of x, we must have } \]
\[9 - 3r = 0\]
\[ \Rightarrow r = 3\]
\[\text{ Hence, the required term is the 4th term i . e .} T_4 \]
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