For the reaction $2A \rightarrow B$, the rate law is given as $\text{Rate} = k[A]^2$. If the concentration of A is doubled, the new rate will be $\text{Rate}' = k(2[A])^2 = 4k[A]^2 = 4 \times \text{Rate}$. Thus, the rate of reaction will increase by four times, making statement (d) correct. The rate constant ($k$) is a proportionality constant that depends on temperature and the presence of a catalyst, but it is independent of the initial concentrations of the reactants. Therefore, the rate constant will remain unchanged. Also, from the rate equation, the rate of reaction is directly proportional to the rate constant. This makes statement (b) correct. Therefore, the correct statements are (b) and (d).