For the reaction between $A$ and $B$ , the initial rate of reaction $(r_0)$ was measured for different initial concentration of $A$ and $B$ as given below Order of the reaction with respect to $A$ and $B$ respectively, is $\sqrt 2  = 1.4 ,\,\sqrt 3  \times 10^{-4}$ 

$A/mol\,L^{-1}$ $0.2$ $0.2$ $0.4$
$B/mol\,L^{-1}$ $0.3$ $0.1$ $0.05$
$r_0/mol^{-1}s^{-1}$ $5.0\times 10^{-5}$ $5.0\times 10^{-5}$ $1.4\times 10^{-4}$

  • A

    $\frac{1}{2},\,0$

  • B

    $\frac{3}{2},\,\frac{1}{3}$

  • C

    $\frac{3}{2},\,0$

  • D

    $0,\,\frac{5}{2}$

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  • [AIIMS 2015]

The rate law of the reaction $A + 2B \to $Product is given by $\frac{{d[dB]}}{{dt}} = k[{B^2}]$. If $ A$  is taken in excess, the order of the reaction will be