JEE Main · Maths · Differential Equations
Variable Separable Form: JEE Main previous year questions
42 questions in the 108 JEE Main shifts Lumi analysed, in 7 of 8 years. Pattern: Asked most years. 12 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 42
- in 39 of 108 shifts
- Years asked
- 7/8
- last asked 2026
- Weighted estimate
- 0.3
- model; history: 0.4 a shift on average, typically 0.2–0.5
Key findings
- 01
Asked in 7 of 8 years with analysed shifts and in 39 of 108 shifts: 42 questions, #79 of 196 topics. The years that asked it were 1.5 apart on average.
- 02
44% of its questions since 2020 tested an idea no earlier year had asked; 17 repeated an idea from the year before.
- 03
The most repeated idea is Initial Value Problem, asked 15 times in 15 shifts (2017, 2020, 2021, 2022, 2023, 2024, 2026), most often as “solve initial value differential equation”.
- 04
JEE Main has asked 17 of the 60 ideas in this topic; 40 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (81%); 19% need a numerical answer, 12% are easy and 31% hard. It went down from 0.5 to 0.2 questions a shift since 2024.
- 06
The skill tested most is multi-step (79%), then calculation (17%).
Questions a shift, year by year
Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.
Raw count: 2017: 1 in 1 shift · 2020: 6 in 12 shifts · 2021: 10 in 24 shifts · 2022: 10 in 24 shifts · 2023: 3 in 12 shifts · 2024: 10 in 18 shifts · 2025: 0 in 8 shifts · 2026: 2 in 9 shifts.
- Up to 2023
- 0.5
- a shift, of 25
- Since 2024
- 0.2
- -0.2
- Usual gap
- 1.5 yrs
- between years asking it
- Shifts with it
- 39/108
- 36% of analysed shifts
How it is asked
Difficulty, format and skill
Across all 42 questions on Variable Separable Form since 2017.
Difficulty
QUESTIONS- Easy5 · 12%
- Medium24 · 57%
- Hard13 · 31%
Format
SHARE- Single correct · 34 Q81%
- Numerical value · 8 Q19%
Skill tested
SHARE- Multi-step · 33 Q79%
- Calculation · 7 Q17%
- Application · 1 Q2%
- Conceptual · 1 Q2%
Repeats
New idea, or one asked before?
Each column is a year. Blue questions tested an idea no earlier year had asked; navy ones went back to an idea from an earlier year. 2017 is the first year, so everything in it counts as new. Heights are question counts, and Lumi analysed 1 to 24 shifts a year, so compare the split inside a column rather than heights across years.
- Idea asked for the first time
- Idea asked in an earlier year
Coverage of the topic
JEE Main has asked 17 of the 60 ideas in this topic. 40 have never been asked yet.
- Asked directly17 · 28%
- Touched inside another question3 · 5%
- Never asked40 · 67%
Ideas come from Lumi’s JEE syllabus map. A never-asked idea is not a safe skip: across all of JEE Main, 22% of questions since 2024 tested an idea no earlier year had asked.
Drill down
Chapter, idea, question
Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.
15 ideas inside
Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.
Ideas
Every idea inside this topic
17 different ideas were tested; 8 came more than once.
solve initial value differential equation
Single correct · 15 shifts · 3 numericalsolve initial value differential equation
Single correct · 4 shifts · 1 numericalsolve initial value differential equation
Single correct · 3 shiftscurve from tangent slope condition
Single correct · 2 shiftsnewton's cooling law differential equation
Single correct · 2 shiftssolve initial value differential equation
Numerical value · 2 shifts · 1 numericalsolve initial value differential equation
Single correct · 2 shiftssolve initial value differential equation
Numerical value · 2 shifts · 1 numericalsolve initial value differential equation
Single correct · 1 shiftsolve initial value differential equation
Numerical value · 1 shift · 1 numericalsolve initial value differential equation
Single correct · 1 shiftdifferential equation from tangent intercept ratio
Numerical value · 1 shift · 1 numericalsolve initial value differential equation
Single correct · 1 shiftarea of triangle from tangents to solution curve
Single correct · 1 shiftdifferential equation from determinant condition
Single correct · 1 shiftsolve initial value differential equation
Single correct · 1 shiftsolve initial value differential equation
Single correct · 1 shift
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Initial Value Problemsolve initial value differential equation | 15 | 15 | Single correctMulti-step | 3 | |
| Reducible to Separablesolve initial value differential equation | 4 | 4 | Single correctMulti-step | 1 | |
| Direct Integrationsolve initial value differential equation | 3 | 3 | Single correctMulti-step | – | |
| Geometric Applicationscurve from tangent slope condition | 3 | 2 | Single correctMulti-step | – | |
| Physical Modeling Applicationsnewton's cooling law differential equation | 2 | 2 | Single correctApplication | – | |
| Separability Checksolve initial value differential equation | 2 | 2 | Numerical valueCalculation | 1 | |
| Exponential Sum/Difference Separationsolve initial value differential equation | 2 | 2 | Single correctCalculation | – | |
| Proportional Rate Problemssolve initial value differential equation | 2 | 2 | Numerical valueCalculation | 1 | |
| Partial Fractions in Separated Integralssolve initial value differential equation | 1 | 1 | Single correctMulti-step | – | |
| Reducible to Separable (Parallel Lines Case)solve initial value differential equation | 1 | 1 | Numerical valueMulti-step | 1 | |
| Substitution of Product (u = xy)solve initial value differential equation | 1 | 1 | Single correctMulti-step | – | |
| Substitution of Ratio (u = y/x)differential equation from tangent intercept ratio | 1 | 1 | Numerical valueMulti-step | 1 | |
| Exponential and Logarithmic Substitutionssolve initial value differential equation | 1 | 1 | Single correctMulti-step | – | |
| Implicit Solution Curve Analysisarea of triangle from tangents to solution curve | 1 | 1 | Single correctMulti-step | – | |
| Determinant Form Differential Equationsdifferential equation from determinant condition | 1 | 1 | Single correctMulti-step | – | |
| Exact Differential Groupingsolve initial value differential equation | 1 | 1 | Single correctMulti-step | – | |
| Inverse Trigonometric Form Simplificationsolve initial value differential equation | 1 | 1 | Single correctCalculation | – |
Times and shifts count every analysed shift. Across JEE Main, 78% of questions since 2024 went back to an idea an earlier year had asked; the rest were new. All repeated ideas
Every question
Variable Separable Form questions, year by year
The newest 40 show their opening words as they appeared in the official paper; older ones name the idea they tested. Open one for its options and the official answer.
JEE Main 20262 questions in 2 shifts
- 2 Apr, Shift 1Q17If the curve passes through the point and satisfies the differential equation , , then …
Idea: Direct Integration
EasySingle correct - 4 Apr, Shift 1Q20Let be the solution of the differential equation , . Then is equal to
Idea: Initial Value Problem
MediumSingle correct
JEE Main 202410 questions in 9 shifts
- 4 Apr, Shift 1Q14If the solution of the differential equation satisfies , then…
Idea: Partial Fractions in Separated Integrals
New ideaHardSingle correct - 4 Apr, Shift 2Q27Let be the solution of the differential equation , . Let the maximum and minimum values of the function…
Idea: Reducible to Separable
HardNumerical value - 6 Apr, Shift 2Q26If the solution of the given differential equation passes through the point…
Idea: Separability Check
EasyNumerical value - 8 Apr, Shift 1Q13Let be the solution of the differential equation , . Then…
Idea: Initial Value Problem
Asked the year beforeMediumSingle correct - 9 Apr, Shift 1Q11The solution curve, of the differential equation , passing through the point is a conic, whose…
Idea: Initial Value Problem
Asked the year beforeMediumSingle correct - 1 Feb, Shift 1Q11Let be the solution of the differential equation , . Then,…
Idea: Reducible to Separable
HardSingle correct - 27 Jan, Shift 1Q13Let and be solutions of the differential equations and respectively,…
Idea: Initial Value Problem
Asked the year beforeMediumSingle correct - 27 Jan, Shift 1Q27If the solution of the differential equation , , is ,…
Idea: Reducible to Separable (Parallel Lines Case)
New ideaHardNumerical value - 29 Jan, Shift 1Q26If the solution curve of the differential equation , passes through the point and…
Idea: Initial Value Problem
Asked the year beforeMediumNumerical value - 31 Jan, Shift 2Q13The temperature of a body at time is F and it decreases continuously as per the differential equation…
Idea: Physical Modeling Applications
EasySingle correct
JEE Main 20233 questions in 3 shifts
- 10 Apr, Shift 2Q27Let the tangent at any point P on a curve passing through the points and , intersect positive…
Idea: Substitution of Ratio (u = y/x)
New ideaHardNumerical value - 11 Apr, Shift 1Q20Let be a solution curve of the differential equation. . If the line intersects the…
Idea: Substitution of Product (u = xy)
New ideaMediumSingle correct - 13 Apr, Shift 1Q14Let and be the solution curves of the differential equation with initial conditions …
Idea: Initial Value Problem
Asked the year beforeEasySingle correct
JEE Main 202210 questions in 8 shifts
- 25 Jul, Shift 2Q11Let a smooth curve be such that the slope of the tangent at any point on it is directly proportional to…
Idea: Geometric Applications
New ideaMediumSingle correct - 30 Jul, Shift 2Q74Let the area enclosed by the solution curve of the differential equation , b > 0, y(5) = 0…
Idea: Implicit Solution Curve Analysis
New ideaHardSingle correct - 24 Jun, Shift 2Q8A particle is moving in the -plane along a curve passing through the point . The tangent to the curve at the point …
Idea: Geometric Applications
New ideaMediumSingle correct - 24 Jun, Shift 2Q19The slope of normal at any point , , on the curve is given by . If the…
Idea: Geometric Applications
New ideaHardSingle correct - 26 Jun, Shift 1Q30Let . Let , , be the…
Idea: Initial Value Problem
Asked the year beforeHardNumerical value - 27 Jun, Shift 1Q11If , , , then is equal to :
Idea: Exponential Sum/Difference Separation
Asked the year beforeMediumSingle correct - 28 Jun, Shift 2Q10Let be the solution of the differential equation such that . Then,…
Idea: Exponential and Logarithmic Substitutions
New ideaHardSingle correct - 29 Jun, Shift 2Q9If is the solution of the differential equation and…
Idea: Initial Value Problem
Asked the year beforeMediumSingle correct - 30 Jun, Shift 1Q12Let , a, b, , represents a circle with center . Then,…
Idea: Direct Integration
Asked the year beforeHardSingle correct - 30 Jun, Shift 1Q26A hostel has 100 students. On a certain day (consider it day zero) it was found that two students are infected with some virus. Assume…
Idea: Proportional Rate Problems
Asked the year beforeMediumNumerical value
JEE Main 202110 questions in 10 shifts
- 3 Aug, Shift 1Q71If is the solution of the differential equation,…
Idea: Exact Differential Grouping
New ideaHardSingle correct - 4 Aug, Shift 1Q71If is the solution of the differential equation, such that , then…
Idea: Inverse Trigonometric Form Simplification
New ideaMediumSingle correct - 31 Aug, Shift 1Q71If , , then is equal to :
Idea: Exponential Sum/Difference Separation
New ideaMediumSingle correct - 31 Aug, Shift 2Q70If , , then for , the value of …
Idea: Direct Integration
New ideaHardSingle correct - 24 Feb, Shift 1Q72The population at time 't' of a certain species follows the differential equation . If…
Idea: Physical Modeling Applications
New ideaMediumSingle correct - 24 Feb, Shift 2Q69Let be a twice differentiable function defined on R such that , and for all R. If…
Idea: Determinant Form Differential Equations
New ideaMediumSingle correct - 26 Feb, Shift 1Q65The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is 1000 at initial…
Idea: Proportional Rate Problems
New ideaMediumSingle correct - 25 Jul, Shift 1Q62Let be the solution of the differential equation , , then, the minimum value…
Idea: Reducible to Separable
Asked the year beforeHardSingle correct - 25 Jul, Shift 2Q86Let a curve pass through the point and have slope for all positive real value of .…
Idea: Initial Value Problem
Asked the year beforeMediumNumerical value - 17 Mar, Shift 1Q72Which of the following is true for that satisfies the differential equation ; :
Idea: Initial Value Problem
Asked the year beforeMediumSingle correct
JEE Main 20206 questions in 6 shifts
- 8 Jan, Shift 1Q62Let be a solution of the differential equation, , . If…
Idea: Initial Value Problem
Asked the year beforeMediumSingle correct - 2 Sep, Shift 1Q63Let be the solution of the differential equation, . If …
Idea: Initial Value Problem
Asked the year beforeMediumSingle correct - 3 Sep, Shift 1Q62The solution curve of the differential equation, , which passes through the point (0, 1), is :
Idea: Initial Value Problem
Asked the year beforeMediumSingle correct - 3 Sep, Shift 2Q62If ; and , then is equal to :
Idea: Separability Check
New ideaMediumSingle correct - 4 Sep, Shift 2Q63The solution of the differential equation is : (where C is a constant of integration.)
Idea: Reducible to Separable
New ideaMediumSingle correct - 5 Sep, Shift 1 · Q63Initial Value ProblemAsked the year beforeEasy
JEE Main 20171 question in 1 shift
Questions from the official JEE Main Paper 1 shifts published by NTA (CBSE for 2017). Questions NTA dropped are left out. Topic and idea tags, counts and notes are Lumi’s.