What will come in place of both the question marks in the following question : $$\frac{{{{\left( ? \right)}^{\frac{2}{3}}}}}{{42}} = \frac{5}{{{{\left( ? \right)}^{\frac{1}{3}}}}}$$

A. 10

B. $${\text{10}}\sqrt 2 $$

C. $$\sqrt {20} $$

D. 20

E. 210

Answer: Option E

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let }}\frac{{{{\left( x \right)}^{\frac{2}{3}}}}}{{42}} = \frac{5}{{{{\left( x \right)}^{\frac{1}{3}}}}} \cr & {\text{Then,}} \cr & {x^{\frac{2}{3}}}.{x^{\frac{1}{3}}} = 42 \times 5 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 210 \cr & \Rightarrow {x^{\left( {\frac{2}{3} + \frac{1}{3}} \right)}} = 210 \cr & \Rightarrow x = 210 \cr} $$