Let the order of reaction are a and b with respect to A and B respectively.
r = k[A]^a[B]^b ....(1)
According to the question,
2r = k[A]^a[2B]^b....(2)
and
4r = k[2A]^a[B]^b ....(3)
3/1, we have 2^2 = 2^a or, a = 2
2/1, we have 2^1 = 2^b or, b = 1.
So, rate law : r = k[A]^2[B]^1
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