Question

If it is known that the third term of the binomial expansion ${(x+x^{{\log }_{10}x})}^{3}is{10}^6$ then $x$ is equal to

• A. $10$
• B. ${10}^{\frac{-5}{2}}$
• C. $100$
• D. $5$

Answer 1

The correct option is C $100$

We have,

${(x+x^{{\log }_{10}x})}^3={10}^6$

Now,

Third term is

${}^3{C}_0{x}^{3-0}{\left(x^{{\log }_{10}x}\right)}^0={10}^6$

$\Rightarrow 1x^3\times 1=1000000({\therefore }^n{C}_0=1)$

$\Rightarrow x^3={10}^6$

$\Rightarrow x=100$

Hence, this is the answer.