The rate law for the reaction $A + 2B \rightarrow C + 2D$ is given by:

The following graph shows the relationship between $(a-x)^{-1}$ and time $t$ for a second-order reaction. If $\theta = \tan^{-1}(1/2)$ and $OA = 2 \ L \ mol^{-1}$,then the rate at the start of the reaction will be (in $mol \ L^{-1} \ min^{-1}$):

The following data are for the decomposition of ammonium nitrate in aqueous solution. The order of the reaction is:

$N_2$ volume in $cc$ $(V_t)$	$6.25$	$9.50$	$11.42$	$13.65$	$35.05$ $(V_{\infty})$
Time $(t)$ in minutes	$10$	$15$	$20$	$25$	$\infty$

Consider the following reaction: $A \longrightarrow \text{Products}$. This reaction is completed in $100 \ min$. The rate constant of this reaction at $t_1 = 10 \ min$ is $10^{-2} \ min^{-1}$. What is the rate constant (in $min^{-1}$) at $t_2 = 20 \ min$?

For the reaction $2 \ NOBr_{(g)} \rightarrow 2 \ NO_{(g)} + Br_{2_{(g)}}$,the rate law is $r = k[NOBr]^{2}$. If the rate constant is $1.62 \ M^{-1} \ s^{-1}$ and the concentration of $NOBr$ is $2.00 \times 10^{-3} \ M$,what is the rate of reaction?

For the reaction $A + B \rightarrow$ products,it is observed that
$(i)$ on doubling the initial concentration of $A$ only,the rate of reaction is also doubled and
$(ii)$ on doubling the initial concentration of both $A$ and $B$,there is a change by a factor of $8$ in the rate of the reaction.
The rate of this reaction is given by