Which of the following is the slope of the graph of rate versus concentration of the reactant for a first-order reaction?

For a first order reaction,the velocity constant is $K = 10^{-3} \ s^{-1}$. The two-third life for it would be ........... $s$.

For the first-order reaction $N_2O_5 \text{ (in } CCl_4) \rightarrow 2NO_2 + \frac{1}{2}O_{2(g)}$,the rate constant is $6.2 \times 10^{-4} \, s^{-1}$. What will be the rate of reaction when $[N_2O_5] = 1.25 \, mol \, L^{-1}$?

The reaction,$X \to$ product follows first order kinetics. In $40 \, min$ the concentration of $X$ changes from $0.1 \, M$ to $0.025 \, M$. Then the rate of reaction when concentration of $X$ is $0.01 \, M$ is:

For a first order reaction,the half-life period is

For a first order reaction,the rate constant is given as $\log_{10} K = 12 - \frac{6 \times 10^3}{T}$. What will be the value of temperature if its half-life period is $6.93 \times 10^{-3} \, \text{min}$ (in $, K$)?