For the reaction $A + B\rightarrow$products, it is observed that : <br> (1) On doubling the initial concentration of A only, the rate of reaction is also doubled and <br> (2) On doubling the initial concentration of both A and B, there is a change by a factor of 8 in the rate of the reaction. <br> The rate of this reaction is given by :

Question

( A ) $rate = k[A] [B] $
( B ) $rate= k[A]^{2} [B] $
( C ) $rate = k[A][B]^{2}$
( D ) $rate = k[A]{^2}[B]{^2}$