What is the order of a reaction which has a rate expression $\text{rate} = K[A]^{3/2}[B]^{-1}$?

If the half-life period of a reaction is inversely proportional to the initial concentration,the order of the reaction is:

For the following reaction: $NO_{2(g)} + CO_{(g)} \to NO_{(g)} + CO_{2(g)}$,the rate law is: $\text{Rate} = k [NO_2]^2$. If $0.1 \ mol$ of gaseous carbon monoxide is added at constant temperature to the reaction mixture,which of the following statements is true?

Calculate the overall order of a reaction which has the rate expression:
$(a)$ $\text{Rate} = k[A]^{1/2}[B]^{3/2}$
$(b)$ $\text{Rate} = k[A]^{3/2}[B]^{-1}$

The rate of reaction,$A + B \rightarrow \text{product}$,is $7.2 \times 10^{-2} \ mol \ dm^{-3} \ s^{-1}$ at $[A] = 0.4 \ mol \ dm^{-3}$ and $[B] = 0.1 \ mol \ dm^{-3}$. The reaction is first order in $A$ and second order in $B$. Calculate the rate constant.

The rate of the reaction,$CH_3COOC_2H_5 + NaOH \longrightarrow CH_3COONa + C_2H_5OH$ is given by the equation,$\text{rate} = k[CH_3COOC_2H_5][NaOH]$. If concentration is expressed in $mol \ L^{-1}$,the unit of $k$ is