What is the half-life time of a first-order reaction if the initial concentration of the reactant is $0.01 \ mol \ L^{-1}$ and the rate of reaction is $0.00352 \ mol \ L^{-1} \ minute^{-1}$?

In a first order reaction,the concentration of the reactant is reduced from $0.6 \ mol \ L^{-1}$ to $0.2 \ mol \ L^{-1}$ in $5 \ min$. What is the rate constant of the reaction (in $min^{-1}$)? $(\log 3 = 0.4771)$

The time taken for $10 \%$ completion of a first order reaction is $20$ minutes. The time required for the completion of $19 \%$ of the same reaction in minutes is

For a first order reaction,a plot of $\log(a-x)$ against time is a straight line with negative slope equal to

Identify True $(T)$ and False $(F)$ statements for the following expressions regarding a first-order reaction $R \rightarrow P$:
Statement $I$: $\text{Rate} = -\frac{d[R]}{dt} = k[R]$
Statement $II$: $\text{Rate} = -\frac{d[R]}{dt} = -k[R]$

$A ( g ) \rightarrow 2 B ( g ) + C ( g )$ is a first order reaction. The initial pressure of the system was found to be $800 \ mm \ Hg$ which increased to $1600 \ mm \ Hg$ after $10 \ min$. The total pressure of the system after $30 \ min$ will be . . . . . . $mm \ Hg$. (Nearest integer)