Question

If $x=\frac{\sqrt{7}}{5}\mathrm{and}\frac{5}{x}=p\sqrt{7}$ then the value of p is
(a) $\frac{7}{25}$

(b) $\frac{25}{7}$

(c) $\frac{7}{15}$

(d) $\frac{15}{7}$

Answer 1

$$\begin{gathered} \frac{5}{x}=p\sqrt{7} \\ \Rightarrow \frac{5}{{\displaystyle \frac{\sqrt{7}}{5}}}=p\sqrt{7}\left(\because x=\frac{\sqrt{7}}{5}\right) \\ \Rightarrow \frac{5\times 5}{{\displaystyle \sqrt{7}}}=p\sqrt{7} \\ \Rightarrow \frac{25}{{\displaystyle \sqrt{7}}}=p\sqrt{7} \\ \Rightarrow \frac{25}{{\displaystyle \sqrt{7}\times \sqrt{7}}}=p \\ \Rightarrow \frac{25}{{\displaystyle 7}}=p \\ \therefore \mathrm{The}\mathrm{value}\mathrm{of}p\mathrm{is}\frac{25}{7}. \end{gathered}$$

Hence, the correct option is (b).