The coefficient of x4 in (2x−x23)10 is

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The coefficient of x^4 in ({x}{2} - {3}{x^2})^{10} is

Question

The coefficient of $x^{4}$ in $(\frac{x}{2} - \frac{3}{x ^{2}})^{10}$ is

\frac{405}{256}

\frac{504}{259}

\frac{450}{263}

\frac{405}{128}

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Daniel Discussed

The coefficient of

x^{4}

(\frac{x}{2} - \frac{3}{x ^{2}})^{10}

15 mins ago

Discuss this question LIVE

15 mins ago

T_{r + 1} =^{n} C_{r} a^{n - r} b^{r}

Applying to the above question we get

T_{r + 1} = (- 1)^{r}^{10} C_{r} x^{10 - r} 2^{r - 10} 3^{r} x^{- 2 r}

= (- 1)^{r}^{10} C_{r} x^{10 - 3 r} 2^{r - 10} 3^{r}

...(i)
For the coefficient of

x^{4}

10 - 3 r = 4

6 = 3 r

r = 2

Substituting in (i) we get

T_{3} =^{10} C_{2} x^{4} 2^{- 8} 3^{2}

= \frac{10.9. 3 ^{2}}{2 ! 2 ^{8}}

= \frac{405}{256}

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Question Text	The coefficient of $x^{4}$ in $(\frac{x}{2} - \frac{3}{x ^{2}})^{10}$ is
Answer Type	Text solution:1
Upvotes	150