Inversion of cane sugar is an example of pseudo first-order reaction as water is present in large excess. Hence, $\left[ H _{2} O \right]$ remains constant and does not appear in the rate law expression.
$C _{12} H _{22} O _{11}+ H _{2} O \rightarrow C _{6} H _{12} O _{6}$ (glucose ) $+ C _{6} H _{12} O _{6}$ (fructose )
Another example is the hydrolysis of methyl acetate.
The following are the examples of first-order reaction.
(B) Decomposition of $H _{2} O _{2}$
(C) Conversion of cyclopropane to propene
(D) Decomposition of $N _{2} O _{5}$