For the reaction $A \rightarrow \text{products}$,the graph of $t_{1/2}$ versus $[A]_0$ is given below. The concentration of $A$ at $10 \ \text{minutes}$ is $.......... \times 10^{-3} \ \text{mol L}^{-1}$ $(nearest \ integer)$. The reaction was started with $2.5 \ \text{mol L}^{-1}$ of $A$.

$5$ milli-moles of a solid $A$ was dissolved in $5$ moles of $H_2O$. On adding to the solvent,$A$ starts polymerising into another insoluble solid following zero order kinetics. On adding $6$ milli-moles of another solid solute $C$ (after $20$ minutes) the polymerisation completely stops. The insoluble solid polymer is removed and the resulting solution was cooled to a temperature less than $-0.186\,^{\circ}C$ (melting point of solution) to cause solidification of some liquid water. Calculate the value of $'X'$ if rate constant for polymerisation reaction is represented as $10^{-X}\,moles/minute$. $[K_f(H_2O) = 1.86\, K\, Kg\,mol^{-1}]$

For the thermal decomposition of reaction $AB_{(g)}$,the following graph is provided. The half-life of the reaction is $x \ min$. Find $x$. (Nearest integer)

For a given reaction,the half-life $t_{1/2}$ varies with different initial concentrations $a$. If $t_{1/2} \propto a$ is constant,then the order of the reaction will be .......

For a zero-order reaction,the ratio of $t_{1/2}$ to $t_{3/4}$ is ....

If the initial concentration is reduced to its $1/4^{th}$ in a zero order reaction,the time taken for half of the reaction to complete