For a first order reaction,the intercept of the graph between $\log \left(\frac{[A]_0}{[A]_t}\right)$ ($Y$-axis) and time ($X$-axis) is equal to

If a $75\%$ first-order reaction is completed in $32 \text{ minutes}$,how many minutes will it take for the same reaction to be $50\%$ completed?

The following results were obtained during kinetic studies of the reaction $2A + B \to$ products:

Experiment	$[A]$ $(mol \ L^{-1})$	$[B]$ $(mol \ L^{-1})$	Initial rate $(mol \ L^{-1} \ min^{-1})$
$I$	$0.10$	$0.20$	$6.93 \times 10^{-3}$
$II$	$0.10$	$0.25$	$6.93 \times 10^{-3}$
$III$	$0.20$	$0.30$	$1.386 \times 10^{-2}$

The time (in minutes) required to consume half of $A$ is:

In the following graphs,which graph$(s)$ belong to a first-order reaction?

An organic compound undergoes first order decomposition. The time taken for its decomposition to $\frac{1}{8}$ and $\frac{1}{10}$ of its initial concentration are $t_{1/8}$ and $t_{1/10}$ respectively. What is the value of $\frac{t_{1/8}}{t_{1/10}}$? $[\log 2 = 0.30]$

If the concentration unit decreases by a factor of $n$,what will be the value of the rate constant for a first-order reaction?