It is given that a reaction is first order in \\\\(A\\\\) and second order in \\\\(B\\\\).i) The differential rate equation is as follows: Rate \\\\(\\displaystyle = k[A][B]^2\\\\)(ii) On increasing the concentration of \\\\(B\\\\) three times, rate becomes \\\\(9\\\\) times.\\\\(\\displaystyle (d[B])^2 = 3^2 = 9\\\\)(iii) When the concentrations of both \\\\(A\\\\) and \\\\(B\\\\) are doubled, rate becomes \\\\(8\\\\) times.\\\\(\\displaystyle d[A] (d[B])^2 = 2 \ imes 2^2 = 8\\\\)