Given that term of expansion (x^{1/3} - x^{-1/2})^{15} which does not contain x is 5, m where m ∈

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7.Binomial Theorem

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

A

$1100$

B

$1010$

C

$1001$

D

none

Solution

$T_{r + 1} = ^{15}C_r (x^{1/3})^{15 – r} (-x ^{-1/2}) ^r$

$\Rightarrow \frac{{15\, – \,r}}{3} – \frac{r}{2} = 0$

$\Rightarrow r = 6$

Hence $T_7$ is independent of $x$ and $T_7 = ^{15}C_6 = 5005 = 5m$

$\Rightarrow m = 1001$

Standard 11

Mathematics

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