Given that the term of the expansion $(x^{1 / 3} + x^{- 1 / 2})^{15}$ which does not contain $x$ is $5$ m , where m $\in$ N , m $=$

1100

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1010

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1001

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None of these

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Solution

The correct option is C 1001
Given,

$(x^{\frac{1}{3}} + x^{- \frac{1}{2}})^{15}$

$T_{r + 1} =^{15} C_{r} (x^{\frac{1}{3}})^{15 - r} (x^{- \frac{1}{2}})^{r}$

Power of $x = \frac{15 - r}{3} - \frac{r}{2} = 0$ for $x^{0}$

$2 (15 - r) - 3 r = 0$

$30 - 2 r - 3 r = 0$

$30 - 5 r = 0$

$r = 6$

$T_{r + 1} =^{15} C_{6} = 5005$

$5 m = 5005 \Rightarrow m = 1001$

Suggest Corrections

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