For the reaction $2A + B \rightarrow A_2B$,if the concentration of reactant $A$ is doubled and the concentration of reactant $B$ is halved,the rate of the reaction will:

Determine True and False from the given statements:
$(a)$ The rate of reaction is directly proportional to the concentration of reactant.
$(b)$ The rate of reaction is inversely proportional to the concentration of reactant.
$(c)$ The rate of reaction does not depend on the concentration of reactant.

For the reaction $2 NO_{(g)} + Cl_{2_{(g)}} \rightarrow 2NOCl_{(g)}$,when the concentration of $Cl_2$ is doubled,the rate of the reaction becomes twice the original rate. When the concentration of $NO$ is doubled,the rate becomes four times the original rate. What is the overall order of the reaction?

The rate constant value for a reaction is $1.75 \times 10^2 \ L^2 \ mol^{-2} \ sec^{-1}$. The half-life period $t_{1/2} \propto$ . . . . . . .

For a reaction,$K = 4.5 \times 10^{-4} \ L \ mol^{-1} \ s^{-1}$. What is the order of the reaction?

The rate constants for the following reactions are:
Reaction $1$: $A \xrightarrow{\text{catalyst } 1} P_1, k_1 = 1 \ s^{-1}$
Reaction $2$: $A \xrightarrow{\text{catalyst } 2} P_2, k_2 = 0.1 \ L \ mol^{-1} \ s^{-1}$
Reaction $3$: $A \xrightarrow{\text{catalyst } 3} P_3, k_3 = 0.01 \ L^2 \ mol^{-2} \ s^{-1}$
What is the correct relation between the rates of the reactions at $[A] = 1 \ M$?