Which of the following rate laws has an overall order of $0.5$ for a reaction involving substances $x$,$y$,and $z$?

For the reaction $A + B \to \text{Product}$,the rate of reaction becomes four times when the concentration of $A$ is doubled. If the rate of reaction does not change when the concentration of $B$ is doubled,the rate law for the reaction will be.....

At a certain temperature,the half-life periods for the catalytic decomposition of $NH_3$ were found to be as follows:

Pressure $(mm \ Hg)$	$50, 100, 200$
Half-life period $(hrs)$	$3.52, 1.76, 0.88$

What will be the pressure when the half-life period is $2.5 \ hrs$?

For the reaction $XA + YB \rightarrow mp + nq$,the rate is given by $\text{Rate} = K[A]^c[B]^d$. What is the overall order of the reaction?

The given plots represent the variation of the concentration of a reactant $R$ with time for two different reactions $(i)$ and $(ii).$ The respective orders of the reactions are

For the reaction,$H_{2(g)} + Br_{2(g)} \longrightarrow 2 HBr_{(g)}$,$r = k[H_2][Br_2]^{\frac{1}{2}}$. What is the molecularity and order of reaction respectively?