A reaction takes 30 \ minutes to complete 50% of the reaction and tak…

The correct answer is Option (4) → Zero

Let [R]₀ = a. For a zero order reaction the amount reacted grows linearly with time, kt = [R]₀ − [R]:

    \( \displaystyle t_{50\%} = \frac{a/2}{k} = \frac{a}{2k},\qquad t_{75\%} = \frac{3a/4}{k} = \frac{3a}{4k} \)

    \( \displaystyle \frac{t_{75\%}}{t_{50\%}} = \frac{3a/4k}{a/2k} = 1.5 \)

Given: t_75%/t_50% = 45/30 = 1.5, which fits a zero order reaction. (For a first order reaction the half-life is constant, so 75% would take two half-lives, 60 minutes.)

NCERT (2026-27 edition):
Half-Life of a Reaction – “… For a zero order reaction, rate constant is given by equation 3.7.
\( k = \frac{[R]_0 - [R]}{t} \)
At t = t_1/2, [R] = ½[R]₀
The rate constant at t_1/2 becomes
\( k = \frac{[R]_0 - \frac{1}{2}[R]_0}{t_{1/2}} \)
\( t_{1/2} = \frac{[R]_0}{2k} \)
It is clear that t_1/2 for a zero order reaction is directly proportional to the initial concentration of the reactants and inversely proportional to the rate constant.”