The degree of dissociation of a first-order reaction is

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: $\log 2 = 0.3010, \log 3 = 0.4771, \log 5 = 0.6989$

Consider the following two first order reactions occurring at $298 \ K$ with same initial concentration of $A$: $(1)$ $A \rightarrow B$; rate constant, $k=0.693 \ min^{-1}$ $(2)$ $A \rightarrow C$; half-life, $t_{1/2}=0.693 \ min$. Choose the correct option.

The rate constant of the reaction $2H_2O_{2(aq)} \to 2H_2O_{(l)} + O_{2(g)}$ is $3 \times 10^{-3} \ min^{-1}$. At what concentration of $H_2O_2$,the rate of reaction will be $2 \times 10^{-4} \ M \ s^{-1}$? ............ $M$

In a first order reaction,the concentration of reactant decreases from $800 \ mol/dm^3$ to $50 \ mol/dm^3$ in $2 \times 10^2 \ s$. The rate constant of the reaction in $s^{-1}$ is:

Which equation represents the $1/4^{th}$ life for a first-order reaction?