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For an exothermic reversible reaction, which one of the following correctly describes the dependence of the equilibrium constant $(K)$ with temperature $(T)$ and pressure $(P)$?

- $K$ is independent of $T$ and $P$
- $K$ increases with an increase in $T$ and $P$
- $K$ increases with $T$ and decreases with $P$
- $K$ decreases with an increase in $T$ and is independent of $P$