# If the 6th term in the expansion of $(\frac{1}{x^{8/3}} +x^{2}log_{10}x)^{8}$is 5600 then the value of x is Option 1) 20 Option 2) 10 Option 3) 100 Option 4) None of these

As we learnt in

General Term in the expansion of (x+a)^n -

$T_{r+1}= ^{n}c_{r}\cdot x^{n-r}\cdot a^{r}$

- wherein

Where $r\geqslant 0 \, and \, r\leqslant n$

$r= 0,1,2,----n$

$\\T_{6}=^{8}C_{5}\left ( \frac{1}{x^{\frac{8}{3}}} \right )\left ( x^{2}\log_{10}x \right )^{5}=5600\\*\\\frac{8!}{5!3!}x^{2}\left ( \log_{10}x \right )^{5}=5600\\*\\ Thus\: \: x^{2}\left ( \log_{10}x \right )^{5}=100$

and x=10

Option 1)

20

Incorrect

Option 2)

10

Correct

Option 3)

100

Incorrect

Option 4)

None of these

Incorrect

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