For the reaction $\mathrm{A}+\mathrm{B}\to \mathrm{C}$ , Hence rate law is

S no	[A]	[B]	Rate
1	1.0 M	1.0 M	0.25 M min-1
2	2.0 M	1.0 M	0.50 M min-1
3	1.0 M	2.0 M	0.25 M min-1

$\frac{dx}{dt}=k{\left[A\right]}^a{\left[B\right]}^b$

0.25=k[1.0]^a[1.0]^b …………..(i)

0.50= k[2.0]^a[1.0]^b…………..(ii)

0.25= k[1.0]^a[2.0]^b…………..(iii)

Divide values of (ii) by that of (i) and (iii) by that of (i)

2=2^a→a=1

1=2^b

2⁰=2^b→b=0

Thus, $\frac{dx}{dt}$=k[A]