5th term from the end in the expansion of x22 - 2x2 12 is

The correct option is D 7920x^ 4 5 ^ th term in the expansion of ( x ^ 2 2 2 x ^ 2 #160;) #160;^ 12 is T _ r+1 = ^nC_r x ^ r . ...

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Standard XII

Mathematics

Middle Terms

5th term from...

Question

$5^{t h}$ term from the end in the expansion of ${(\frac{x^{2}}{2} - \frac{2}{x^{2}})}^{12}$ is

- 7920 x^{- 4}

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7920 x^{4}

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7920 x^{- 4}

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- 7920 x^{4}

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Solution

The correct option is D $7920 x^{- 4}$
$5^{t h}$ term in the expansion of ${(\frac{x^{2}}{2} - \frac{2}{x^{2}})}^{12}$ is
$T_{r + 1} =^{n} C_{r} x^{r} . y^{n - r}$
$T_{5} =^{12} C_{4} [{(\frac{x^{2}}{2})}^{4} {(\frac{- 2}{x^{2}})}^{8}]$
$= \frac{12!}{4! 8!} . \frac{x^{8}}{2^{4}} . \frac{2^{8}}{x^{16}}$
$= {7920 x}^{- 4}$

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5th term from the end in the expansion of (x22−2x2)12 is

The correct option is D 7920x−45th term in the expansion of(x22−2x2)12 isTr+1=nCrxr.yn−rT5=12C4[(x22)4(−2x2)8]=12!4!8!.x824.28x16=7920x−4

$5^{t h}$ term from the end in the expansion of ${(\frac{x^{2}}{2} - \frac{2}{x^{2}})}^{12}$ is