Question

If $x^{b}y=\frac{2x^5}{y}\sqrt{\frac{y^4}{4}}$ then find the value of ${\left(\frac{1}{2}\right)}^b.\frac{1}{\sqrt{3}}$

• A. $2$
• B. $\frac{2}{\sqrt{3}}$
• C. $\frac{1}{32\sqrt{3}}$
• D. 1

Answer 1

The correct option is C $\frac{1}{32\sqrt{3}}$

We have,

$\Rightarrow$$x^{b}y=\frac{2x^5}{y}\sqrt{\frac{y^4}{4}}$

$\Rightarrow$$x^{b}y=\frac{2x^5}{y}\times \frac{y^2}{2}$

$\Rightarrow$$x^{b}y=x^{5}y$

On comparing coth sides,

$\Rightarrow$$b=5$

Therefore,

$\Rightarrow {\left(\frac{1}{2}\right)}^b.\frac{1}{\sqrt{3}}$

$\Rightarrow {\left(\frac{1}{2}\right)}^5.\frac{1}{\sqrt{3}}$

$\Rightarrow \left(\frac{1}{32}\right).\frac{1}{\sqrt{3}}$

$\Rightarrow \frac{1}{32\sqrt{3}}$

Hence, this is the answer.