$A_{(g)} \rightarrow 2B_{(g)}$. Initially,$2 \ mol$ of $A$ are taken in a $5 \ L$ vessel. After $20 \ min$,$[A]_t = \frac{[B]_t}{2}$. Find the half-life time of $A$ in the first-order reaction in $\min$.

For the first order reaction $A \rightarrow B$,the half-life is $30 \ min$. The time taken for $75 \%$ completion of the reaction is $..... \ min$. (Nearest integer)
Given: $\log 2 = 0.3010, \log 3 = 0.4771, \log 5 = 0.6989$

The half-life period of a $1^{st}$ order reaction is $60 \ minutes$. What percentage will be left over after $240 \ minutes$ (in $\%$)?

The rate equation for a first-order reaction is given by $[R] = [R]_0 e^{-kt}$. $A$ straight line with a positive slope is obtained by plotting: ($[R]_0 =$ initial concentration of reactant,$[R] =$ concentration of reactant at time $t$)

When the value of rate constant $(k)$ is $2.0 \text{ min}^{-1}$, then what will be the half-life of the reaction $(t_{1/2})$ in seconds?

The inactivation rate of a viral preparation is proportional to the amount of virus. In the first minute after preparation,$10 \%$ of the virus is inactivated. The rate constant for viral inactivation is $..... \times 10^{-3} \ min^{-1}$. (Nearest integer)
[Use : $\ln 10 = 2.303; \log_{10} 3 = 0.477; \text{property of logarithm} : \log x^y = y \log x$]