For a first-order reaction $\mathbf{R} \rightarrow \mathbf{P}$ at a given temperature, $k$ is the rate constant. For this reaction, at the given temperature, the concentrations of $\mathbf{R}$ and $\mathbf{P}$ at a time $t$ are $[\mathbf{R}]$ and $[\mathbf{P}]$, respectively. The correct graphical representation(s) for this reaction is(are) :

For the following reaction,
$$2X + Y\buildrel k \over \longrightarrow P$$ the rate of reaction is $${{d[P]} \over {dt}} = k[X]$$. Two moles of X are mixed with one mole of Y to make 1.0 L of solution. At 50 s, 0.5 mole of Y is left in the reaction mixture. The correct statement(s) about the reaction is(are)

(Use : ln 2 = 0.693)

Which of the following plots is(are) correct for the given reaction?

([P]₀ is the initial concentration of P)

In the decay sequence.


x₁, x₂, x₃ and x₄ are particles/radiation emitted by the respective isotopes. The correct option(s) is(are)