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Question
If in the expansion of \[\left( x^4 - \frac{1}{x^3} \right)^{15}\] , \[x^{- 17}\] occurs in rth term, then
Options
r = 10
r = 11
r = 12
r = 13
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Solution
r = 12
Here,
\[T_r =^{15}{}{C}_{r - 1} ( x^4 )^{15 - r + 1} \left( \frac{- 1}{x^3} \right)^{r - 1} \]
\[ = ( - 1 )^r \times^{15}{}{C}_{r - 1} x^{64 - 4r - 3r + 3} \]
\[\text{ For this term to contain } x^{- 17} , \text{ we must have:} \]
\[67 - 7r = - 17\]
\[ \Rightarrow r = 12\]
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