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(D) Let the order of reaction with respect to $A$ and $B$ be $m$ and $n$ respectively.Then,$rate = k[A]^{m}[B]^{n}$From the table:$2 = k[0.2]^{m}[0.2]

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$r=k[A]^{2}[B]$

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(D) Let the order of reaction with respect to $A$ and $B$ be $m$ and $n$ respectively.Then,$rate = k[A]^{m}[B]^{n}$From the table:$2 = k[0.2]^{m}[0.2]^{n}$ $(i)$$4 = k[0.2]^{m}[0.4]^{n}$ $(ii)$$36 = k[0.6]^{m}[0.4]^{n}$ $(iii)$On comparing Eqs. $(i)$ and $(ii)$:$\frac{4}{2} = \frac{k[0.2]^{m}[0.4]^{n}}{k[0.2]^{m}[0.2]^{n}}$$2 = (\frac{0.4}{0.2})^{n} = 2^{n}$$n = 1$On comparing Eqs. $(ii)$ and $(iii)$:$\frac{36}{4} = \frac{k[0.6]^{m}[0.4]^{n}}{k[0.2]^{m}[0.4]^{n}}$$9 = (\frac{0.6}{0.2})^{m} = 3^{m}$$3^{2} = 3^{m}$$m = 2$Therefore,the rate law is $r = k[A]^{2}[B]$.

Expt. no.	$[A]$	$[B]$	Rate $(\text{mol} \ \text{dm}^{-3} \ \text{s}^{-1})$
$1$	$0.2$	$0.2$	$2$
$2$	$0.2$	$0.4$	$4$
$3$	$0.6$	$0.4$	$36$

For a reaction,$A + B \rightarrow$ products,the rate of the reaction at various concentrations is given below. The rate law for the above reaction is:
Expt. no. $[A]$ $[B]$ Rate $(\text{mol} \ \text{dm}^{-3} \ \text{s}^{-1})$
$1$ $0.2$ $0.2$ $2$
$2$ $0.2$ $0.4$ $4$
$3$ $0.6$ $0.4$ $36$

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For a reaction,$A + B \rightarrow$ products,the rate of the reaction at various concentrations is given below. The rate law for the above reaction is:Expt. no.$[A]$$[B]$Rate $(\text{mol} \ \text{dm}^{-3} \ \text{s}^{-1})$$1$$0.2$$0.2$$2$$2$$0.2$$0.4$$4$$3$$0.6$$0.4$$36$