Answer the following by appropriately matching the lists based on the information given in the paragraph.
A musical instrument is made using four different metal strings, $1,\mathrm{ }2,\mathrm{ }3$ and $4$ with mass per unit length $\mathrm{\mu },2\mathrm{\mu },3\mathrm{\mu }$ and $4\mathrm{\mu }$ respectively. The instrument is played by vibrating the strings by varying the free length in between the range ${\mathrm{L}}_0$ and $2{\mathrm{L}}_0.$ It is found that in string- $1\left(\mathrm{\mu }\right)$ at free length ${\mathrm{L}}_0$ and tension ${\mathrm{T}}_0$ the fundamental mode frequency is ${\mathrm{f}}_0.$
List-I gives the above four strings while list-II lists the magnitude of some quantity.
 

	List I		List II
$\left(\mathrm{a}\right)$	String $-1\left(\mathrm{\mu }\right)$	$\left(\mathrm{p}\right)$	$1$
$\left(\mathrm{b}\right)$	String $-2\left(2\mathrm{\mu }\right)$	$\left(\mathrm{q}\right)$	$\frac{1}{2}$
$\left(\mathrm{c}\right)$	String $-3\left(3\mathrm{\mu }\right)$	$\left(\mathrm{r}\right)$	$\frac{1}{\sqrt{2}}$
$\left(\mathrm{d}\right)$	String $-4\left(4\mathrm{\mu }\right)$	$\left(\mathrm{s}\right)$	$\frac{1}{\sqrt{3}}$
		$\left(\mathrm{t}\right)$	$\frac{3}{16}$
		$\left(\mathrm{u}\right)$	$\frac{1}{16}$

If the tension in each string is ${\mathrm{T}}_0,$ the correct match for the highest fundamental frequency in ${\mathrm{f}}_0$ units will be,

• Correct answer
  A

  $\mathrm{a}-\mathrm{p},\mathrm{ }\mathrm{b}-\mathrm{r},\mathrm{ }\mathrm{c}-\mathrm{s},\mathrm{ }\mathrm{d}-\mathrm{q}$
• B

  $\mathrm{a}-\mathrm{p},\mathrm{ }\mathrm{b}-\mathrm{q},\mathrm{ }\mathrm{c}-\mathrm{t},\mathrm{ }\mathrm{d}-\mathrm{s}$
• C

  $\mathrm{a}-\mathrm{q},\mathrm{ }\mathrm{b}-\mathrm{s},\mathrm{ }\mathrm{c}-\mathrm{r},\mathrm{ }\mathrm{d}-\mathrm{p}$
• D

  $\mathrm{a}-\mathrm{q},\mathrm{ }\mathrm{b}-\mathrm{p},\mathrm{ }\mathrm{c}-\mathrm{r},\mathrm{ }\mathrm{d}-\mathrm{t}$

Hence, the correct answer is option: 'A'.