Two algorithms, P and Q$,$ have time complexities p$($n$)$ and q$($n$),$ respectively, where p$($n$)$

is O$($q$($n$))$ and q$($n$)$ is not O$($p$($n$)).$ Three computers C$1,$ C$2,$ C$3$ are used to execute these

programs. Computer C$2$ is $1\mathrm{.}2$ times faster that computer C$1$ and computer C$3$ is $10$ times

faster than computer C$2.$ Which of the following statements is true?

$($A$)$ When executed on the same computer P is always faster than Q$.$

$($B$)$ When P is executed on C$1$ and Q is executed on C$2,$ Q is faster than P for large inputs.

$($C$)$ When P is executed on C$3$ and Q is executed on C$1,$ P is always faster than Q$.$

$($D$)$ When P is executed on C$1$ and Q is executed on C$3,$ Q is always faster than P $.$

$($E$)$ When P and Q are executed on C$2,$ P is faster than Q for large inputs.