In the reaction $2A + B \to A_2B$,if the concentration of $A$ is doubled and the concentration of $B$ is halved,then 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.

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

The results given in the below table were obtained during kinetic studies of the following reaction:
$2 A + B \longrightarrow C + D$

Experiment	$[A] / mol \ L^{-1}$	$[B] / mol \ L^{-1}$	Initial rate / $mol \ L^{-1} \ min^{-1}$
$I$	$0.1$	$0.1$	$6.00 \times 10^{-3}$
$II$	$0.1$	$0.2$	$2.40 \times 10^{-2}$
$III$	$0.2$	$0.1$	$1.20 \times 10^{-2}$
$IV$	$X$	$0.2$	$7.20 \times 10^{-2}$
$V$	$0.3$	$Y$	$2.88 \times 10^{-1}$

$X$ and $Y$ in the given table are respectively :

The rate of reaction between $A$ and $B$ increases by a factor of $100$ when the concentration of $A$ is increased $10$ folds. The order of reaction with respect to $A$ is

The conversion of molecules $X$ to $Y$ follows second order kinetics. If the concentration of $X$ is increased to three times,how will it affect the rate of formation of $Y$?