Match the rate expressions in LIST-I for the decomposition of (X)...

$\left(I\right)$ rate $= \dfrac{k\left[X\right]}{{X}_{S} + \left[X\right]}$

Case-1: \left[X\right] > > {X}_{s}; \left[X\right] + {X}_{s} \approx \left[X\right]$</p><p>rate$= \dfrac{k\left[X\right]}{\left[X\right]} = k$(Zero order w.r.t.$X$)</p><p>$I \to P, S$</p><table border="1" cellpadding="1" cellspacing="1" style="width: 500px;"> <tbody> <tr> <td><img src="https://cdn-question-pool.Quantrex.app/pyq/jee_advanced/dfd719b5-fdeb-4cb1-9ce2-423daaafee1f-image.png" style="width: 220px; height: 142px;" /></td> </tr> </tbody></table><table border="1" cellpadding="1" cellspacing="1" style="width: 500px;"> <tbody> <tr> <td><img src="https://cdn-question-pool.Quantrex.app/pyq/jee_advanced/e9e7ebc4-703c-4316-a90b-e794bf7f2290-image.png" style="width: 180px; height: 137px;" /></td> </tr> </tbody></table><p> </p><p>Case-2:$\left[X\right] ≪ {X}_{s}; \left[X\right] + {X}_{s} \approx {X}_{s}$</p><p>$∴$rate$= \dfrac{k\left[X\right]}{{X}_{S}} = {k}^{'}\left[X\right]$(${1}^{st}$order w.r.t.$X$)</p><p>$∴ I \to Q, T$</p><p>Case-3: \left[X\right] \approx {X}_{S}$

rate $= \dfrac{k\left[X\right]}{{X}_{s} + \left[X\right]}$

In this case curve-$R$ given in List-II will match.

$∴ I \to P, Q, R, S, T$ (The graph of half-life should start from origin)

\left(II\right)$rate$= \dfrac{k\left[X\right]}{{X}_{S} + \left[X\right]}

$∵ \left[X\right] ≪ {X}_{S}$

$∴ {X}_{s} + \left[X\right] \approx {X}_{s}$

$∴$ rate $= \dfrac{k\left[X\right]}{{X}_{S}} = {k}^{'}\left[X\right]$ (${1}^{st}$ order w.r.t. $X$)

$∴ II \to Q, T$

$\left(III\right)$ rate $= \dfrac{k\left[X\right]}{{X}_{s} + \left[X\right]}$

$∵ \left[X\right] > > {X}_{s}$

$∴ {X}_{s} + \left[X\right] \approx \left[X\right]$

$∴$ rate $= \dfrac{k\left[X\right]}{\left[X\right]} = k$ (Zero order w.r.t. $X$)

$∴ III \to P, S$

\left(IV\right)$rate$= \dfrac{k{\left[X\right]}^{2}}{{X}_{s} + \left[X\right]}

$∵ \left[X\right] > > {X}_{S}$

$∴ {X}_{S} + \left[X\right] \approx \left[X\right]$

$∴$ rate = \dfrac{k{\left[X\right]}^{2}}{\left[X\right]} = k \left[X\right] (${1}^{st}$ order w.r.t. $X$)

$∴ IV \to Q, T$