JEE Main 2019 — Chemistry Physical Chemistry

2019mcqhard

A bacterial infection in an internal wound grows as ${N}^{'}(t)={N}_{0}exp⁡(t)$ , where the time $t$ is in hours. A dose of antibiotic, taken orally, needs 1 hour to reach the wound. Once it reaches there, the bacterial population goes down as $\frac{dN}{dt}=-5{N}^{2}$ . What will be the plot of $\frac{{N}_{0}}{N}$ vs $t$ after $1$ hour?

Official previous-year question

Held on 10 Apr 2019 · Verified 6 Jul 2026.

Options

Did you get this right?

Solution

From 0 to 1 hour, ${N}^{'}={N}_{0}{e}^{t}$

From 1 hour onwards $\frac{dN}{dt}=-5{N}^{2}$

So at $t=1$ hour, ${N}^{'}=e{N}_{0}$

$\frac{dN}{dt}=-5{N}^{2}$

${\int }_{e{N}_{0}}^{N}{N}^{-2}dN=-5{\int }_{1}^{t}dt$

$\frac{1}{N}-\frac{1}{e{N}_{0}}=5(t-1)$

$\frac{{N}_{0}}{N}-\frac{1}{e}=5{N}_{0}(t-1)$

$\frac{{N}_{0}}{N}=5{N}_{0}(t-1)+\frac{1}{e}$

$\frac{{N}_{0}}{N}=5{N}_{0}t+(\frac{1}{e}-5{N}_{0})$

Which is following $y=mx+C$

Your note

JEE Main Physical Chemistry in other years

Physical Chemistry 2026 Physical Chemistry 2025 Physical Chemistry 2024 Physical Chemistry 2023 Physical Chemistry 2022 Physical Chemistry 2021 Physical Chemistry 2020 Physical Chemistry 2018 Physical Chemistry 2017 Physical Chemistry 2016 Physical Chemistry 2015 Physical Chemistry 2014

Keep practicing Physical Chemistry

Work through every JEE Main Physical Chemistry PYQ, year by year.

Browse all Chemistry topics

JEE Main 2019 — Chemistry Physical Chemistry

2019mcqhard

Official previous-year question

Held on 10 Apr 2019 · Verified 6 Jul 2026.

Options

Did you get this right?

Solution

From 0 to 1 hour, ${N}^{'}={N}_{0}{e}^{t}$

From 1 hour onwards $\frac{dN}{dt}=-5{N}^{2}$

So at $t=1$ hour, ${N}^{'}=e{N}_{0}$

$\frac{dN}{dt}=-5{N}^{2}$

${\int }_{e{N}_{0}}^{N}{N}^{-2}dN=-5{\int }_{1}^{t}dt$

$\frac{1}{N}-\frac{1}{e{N}_{0}}=5(t-1)$

$\frac{{N}_{0}}{N}-\frac{1}{e}=5{N}_{0}(t-1)$

$\frac{{N}_{0}}{N}=5{N}_{0}(t-1)+\frac{1}{e}$

$\frac{{N}_{0}}{N}=5{N}_{0}t+(\frac{1}{e}-5{N}_{0})$

Which is following $y=mx+C$

Your note

JEE Main Physical Chemistry in other years

Keep practicing Physical Chemistry

Work through every JEE Main Physical Chemistry PYQ, year by year.

Browse all Chemistry topics

JEE Main 2019 — Chemistry Physical Chemistry

Options

Did you get this right?

Solution

Your note

JEE Main Physical Chemistry in other years

More JEE Main Physical Chemistry questions

Other Chemistry topics for JEE Main

Organic Chemistry

Inorganic Chemistry

Keep practicing Physical Chemistry

JEE Main 2019 — Chemistry Physical Chemistry

Options

Did you get this right?

Solution

Your note

JEE Main Physical Chemistry in other years

More JEE Main Physical Chemistry questions

Other Chemistry topics for JEE Main

Organic Chemistry

Inorganic Chemistry

Keep practicing Physical Chemistry