The correct option is A Rate of reaction I remain unchanged if concentration of OH− increases
First reaction is SN1 i.e. first order in which rate does not depend on concentration of nucleophile.
Second reaction is E2 reaction in which rate depends on concentration of substrate and base both because it is a second order reaction; first order with respect to each of substrate and base.
So, by doubling the conentration of OH−, rate of reaction I does not change.
Hence, (a) is the correct option.