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

 

Answers (1)

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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