JEE Main · 2025 · 22 Jan 2025 · Shift 1 · Chemical Kinetics

Radioactive decay is a nuclear process governed solely by the decay constant $\lambda$, a fixed property of the nuclide.

After three half-lives, the remaining fraction is $(1/2{)}^3=1/8$ — true.
$\lambda$ does not depend on temperature, pressure or chemical state — true, and this directly rules out the claim that $\lambda$ rises with temperature.
The relation $t_{1/2}=\frac{\ln 2}{\lambda }$ is the standard first-order half-life expression — true.

Unlike a chemical reaction rate, nuclear decay has no activation-energy dependence, so the decay constant does not increase with temperature. That is the statement which is not true.