(b)
For second order reaction
$r = k\lbrack A\rbrack^{2\ \ \ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ldots(1)$
When concentration of A(reactant)is doubled
$r' = k\lbrack 2A\rbrack^{2\ \ \ \ \ \ \ \ }$
$r^{'} = 4k\lbrack A\rbrack^{2\ \ \ \ \ \ \ \ }\ \ \ldots(2)$
Comparing Eqs.(1)and(2)
r’ =4r