For a reversible reaction $R \rightleftharpoons P$, at constant temperature, both the forward and the backward reactions are first order elementary reactions with rate constants $k_{{f}}$ and $k_{{b}}$, respectively. At time zero, the concentration of $R$ is $[R]_0$ and the concentration of $P$ is zero. At any given time, $[R]$ and $[P]$ are the concentrations of $R$ and $P$, respectively. If $k_{{b}} = 4k_{{f}}$, the correct graphical representation of the reaction is

Match the rate expressions in LIST-I for the decomposition of $X$ with the corresponding profiles provided in LIST-II. $X_{\mathrm{s}}$ and $\mathrm{k}$ are constants having appropriate units.

List-I	List-II
(I) rate $=\frac{\mathrm{k}[\mathrm{X}]}{\mathrm{X}_{\mathrm{s}}+[\mathrm{X}]}$ under all possible initial concentrations of $\mathrm{X}$	(P)
(II) rate $=\frac{k[X]}{X_{s}+[X]}$ where initial concentrations of $X$ are much less than $X_{s}$	(Q)
(III) rate $=\frac{k[X]}{X_{s}+[X]}$ where initial concentrations of $\mathrm{X}$ are much higher than $X_{s}$	(R)
(IV) rate $=\frac{k[X]^{2}}{X_{s}+[X]}$ where initial concentration of $X$ is much higher than $\mathrm{X}_{\mathrm{s}}$	(S)
	(T)

The % yield of ammonia as a function of time in the reaction

N₂(g) + 3H₂(g) $\rightleftharpoons$ 2NH₃(g), $\Delta$H < 0 at (P, T₁) is given below:

If this reactions is conducted at (P, T₂), with T₂ > T₁, the % yield of ammonia as a function of time is represented by

The experimental value of d is found to be smaller than the estimate obtained using Graham's law. This is due to

In the reaction, P + Q $\to$ R + S, the time taken for 75% reaction of P is twice the time taken for 50% reaction of P. The concentration of Q varies with reaction time as shown in the figure. The overall order of the reaction is

Bombardment of aluminium by $\alpha$-particle leads to its artificial disintegration in two ways : (i) and (ii) as shown. Products X, Y and Z, respectively, are

Plots showing the variation of the rate constant ($k$) with temperature ($T$) are given below. The point that follows Arrhenius equation is

For a first-order reaction A $\to$ P, the temperature (T) dependent rate constant (k) was found to follow the equation $\log k = - (2000){1 \over T} + 6.0$. The pre-exponential factor A and activation energy $E_a$, respectively, are

Under the same reaction conditions, initial concentration of 1.386 mol dm$^{-3}$ of a substance becomes half in 40 seconds and 20 seconds through first order and zero order kinetics, respectively. Ratio $\left( {{{{k_1}} \over {{k_0}}}} \right)$ of the rate constants for first order ($k_1$) and zero order ($k_0$) of the reactions is:

Which of the following option is correct?

What should be the age of fossil for meaningful determination of its age?

A nuclear explosion has taken place leading to increase in concentration of ${ }^{14} \mathrm{C}$ in nearby areas. ${ }^{14} \mathrm{C}$ concentration is $\mathrm{C}_1$ in nearby areas and $C_2$ in areas far away. If the age of the fossil is determined to be $T_1$ and $T_2$ at the places respectively then,

$ \text { Match Column I with Column II : } $