JEE Main · Maths · Differential Equations
Proportional Rate Problems
JEE Main asked Proportional Rate Problems 2 times in 2 of the 108 shifts Lumi analysed, in 2021 and 2022. It belongs to Variable Separable Form, in Differential Equations (Maths). The longest wait between two years asking it was 1 year.
Updated 2026-10-24
- Times asked
- 2
- in 2 shifts
- Years
- 2 of 8
- First asked
- 2021
- last in 2022
- Pattern
- Occasional
- across the analysed shifts
Questions on this idea a shift, by year
2017–2026. Asked in 2021 and 2022. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.
Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 1 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.
Shift by shift
Each square is one analysed shift, in date order. Open a filled one for that paper.
How JEE Main framed it
Numerical value is the usual form. Skill tested: calculation.
- Solve initial value differential equation
- Exponential growth rate proportional to quantity
Difficulty
1 of the 2 questions had a numerical answer.
Every question
All 2 questions
From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.
- 30 Jun 2022, Shift 1 · Q26A hostel has 100 students. On a certain day (consider it day zero) it was found that two students are infected with some virus. Assume…MediumNumerical value
- 26 Feb 2021, Shift 1 · Q65The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is 1000 at initial…MediumSingle correct
Shifts: 26 Feb 2021, Shift 1, 30 Jun 2022, Shift 1.
Same topic
Other ideas in Variable Separable Form
Variable Separable Form has 17 ideas JEE Main has asked; 8 of them came up in more than one question. The 12 most asked are below.
- Initial Value Problem15× · 2026
- Reducible to Separable4× · 2024
- Direct Integration3× · 2026
- Geometric Applications3× · 2022
- Physical Modeling Applications2× · 2024
- Separability Check2× · 2024
- Exponential Sum/Difference Separation2× · 2022
- Partial Fractions in Separated Integralsonce · 2024
- Reducible to Separable (Parallel Lines Case)once · 2024
- Substitution of Product (u = xy)once · 2023
- Substitution of Ratio (u = y/x)once · 2023
- Exponential and Logarithmic Substitutionsonce · 2022