For the first order reaction $A \rightarrow B$,the rate constant is $0.25 \ s^{-1}$. If the concentration of $A$ is reduced to half,the value of the rate constant will be: (in $s^{-1}$)

For the given first order reaction $A \rightarrow B$,the half-life of the reaction is $0.3010 \ min$. The ratio of the initial concentration of reactant to the concentration of reactant at time $2.0 \ min$ will be equal to $........$ (Nearest integer).

For a reaction,$r = k[A]$. If $50 \%$ of $A$ is decomposed in $120 \ \text{minutes}$,the time taken for $90 \%$ decomposition of $A$ is $............ \ \text{minutes}$.

Catalytic decomposition of hydrogen peroxide is a ........ order reaction.

Sucrose hydrolyses in acidic medium into glucose and fructose by first order rate law with $t_{1/2} = 3 \text{ hours}$. The percentage of sucrose remaining after $6 \text{ hours}$ is . . . . . . . (Nearest integer) (Given: $\log 2 = 0.3010$ and $\log 3 = 0.4771$)

The rate constant for the oxidation of hydrogen peroxide by $KMnO_4$ is $6.93 \times 10^{-5} \ s^{-1}$. How much time will it take for the volume of a standard $KMnO_4$ solution to decrease from $20 \ mL$ to $8 \ mL$?