For a radioactive material, half-life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is

Number of nuclei remaining
N=600-450=150

According to the law of radioactive decay,

$\frac{N}{N_0}={\left(\frac{1}{2}\right)}^{\frac{t}{T_{1/2}}}\text{ ; where }{N}_0\text{ is the number of nuclei initially. }$

$\therefore \frac{150}{600}={\left(\frac{1}{2}\right)}^{\frac{t}{T_{1/2}}};\text{ where }{T}_{1/2}=\text{ half life. }$

$$\begin{gathered} \text{ or }{\left(\frac{1}{2}\right)}^2={\left(\frac{1}{2}\right)}^{\frac{t}{T_{1/2}}}\Rightarrow t=2T_{1/2}=2\times 10\text{ minutes } \\ =20 minutes \end{gathered}$$