For a first-order reaction,the half-life period is $6 \ min$. Find the rate constant of the reaction. (in $min^{-1}$)

For a first order reaction $A_5 \rightarrow 5 B_2$,the concentration vs time plot is as shown. The half-life of the reaction is

$t_{87.5}$ is the time required for the reaction to undergo $87.5 \%$ completion and $t_{50}$ is the time required for the reaction to undergo $50 \%$ completion. The relation between $t_{87.5}$ and $t_{50}$ for a first order reaction is $t_{87.5} = x \times t_{50}$. The value of $x$ is $......$. (Nearest integer)

Which of the following curves represents a first-order reaction?

$A$ first order reaction is $60 \%$ complete in $20 \ min$. How long will the reaction take to be $84 \%$ complete (in $min$)?

The following data is obtained during the first order thermal decomposition of $2A_{(g)} \longrightarrow B_{(g)} + C_{(s)}$ at constant volume and temperature. The rate constant in $min^{-1}$ is:

$S$.No.	Time	Total pressure in Pascal
$1$.	At the end of $10 \ min$	$300$
$2$.	After completion	$200$