JEE Main · Maths · Application of Derivatives
Maxima and Minima: JEE Main previous year questions
80 questions in the 108 JEE Main shifts Lumi analysed, in 8 of 8 years. Pattern: Asked most years. 26 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 80
- in 67 of 108 shifts
- Years asked
- 8/8
- last asked 2026
- Weighted estimate
- 0.6
- model; history: 0.7 a shift on average, typically 0.4–0.9
Key findings
- 01
Asked in 8 of 8 years with analysed shifts and in 67 of 108 shifts: 80 questions, #18 of 196 topics. It came in every year with analysed shifts.
- 02
44% of its questions since 2020 tested an idea no earlier year had asked; 26 repeated an idea from the year before.
- 03
The most repeated idea is Optimization Problems, asked 13 times in 13 shifts (2017, 2021, 2022, 2023, 2024), most often as “minimum area of triangle cut by line”.
- 04
JEE Main has asked 31 of the 65 ideas in this topic; 29 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (73%); 26% need a numerical answer, 3% are easy and 23% hard.
- 06
The skill tested most is multi-step (80%), then calculation (10%).
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: 8 in 12 shifts · 2021: 20 in 24 shifts · 2022: 21 in 24 shifts · 2023: 4 in 12 shifts · 2024: 15 in 18 shifts · 2025: 7 in 8 shifts · 2026: 4 in 9 shifts.
- Up to 2023
- 0.7
- a shift, of 25
- Since 2024
- 0.7
- 0.0
- Usual gap
- 1.3 yrs
- between years asking it
- Shifts with it
- 67/108
- 62% of analysed shifts
Recent framings
- integer values for trigonometric equation solvability
- numerical: max of trig expression on interval
- determine polynomial from extrema and limit
Revise first
- Closed Interval Extrema · asked 2021, 2022, 2023, 2024, 2025, 2026
- Optimization Problems · asked 2017, 2021, 2022, 2023, 2024
- Finding Parameters from Given Extrema · asked 2021, 2024, 2025
How it is asked
Difficulty, format and skill
Across all 80 questions on Maxima and Minima since 2017.
Difficulty
QUESTIONS- Easy2 · 3%
- Medium60 · 75%
- Hard18 · 23%
Format
SHARE- Single correct · 58 Q73%
- Numerical value · 21 Q26%
- Other · 1 Q1%
Skill tested
SHARE- Multi-step · 64 Q80%
- Calculation · 8 Q10%
- Application · 6 Q8%
- Conceptual · 1 Q1%
- Recall · 1 Q1%
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 31 of the 65 ideas in this topic. 29 have never been asked yet.
- Asked directly31 · 48%
- Touched inside another question5 · 8%
- Never asked29 · 45%
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.
29 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
31 different ideas were tested; 14 came more than once.
minimum area of triangle cut by line
Single correct · 13 shifts · 3 numericalmax of trig expression on interval
Single correct · 8 shifts · 1 numericalcount real roots of polynomial equation
Numerical value · 6 shifts · 3 numericaldetermine polynomial from extrema and limit
Numerical value · 5 shifts · 3 numericalminimum of sum of intercepts of line
Single correct · 5 shifts · 1 numericalfind parameter from locations of local extrema
Single correct · 4 shiftslocal minimum location constrained by rational inequality
Single correct · 4 shifts · 1 numericalcount critical points of modulus function
Numerical value · 3 shifts · 2 numericalshortest distance between parabola and circle
Single correct · 3 shiftsmaximum area of inscribed figure
Single correct · 3 shifts · 1 numericalminimum value of function from derivative condition
Numerical value · 3 shifts · 2 numericalinteger values for trigonometric equation solvability
Single correct · 2 shiftslocal maximum of variable-base exponential function
Single correct · 2 shiftsnature of critical point of integral function
Single correct · 2 shiftsdetermine polynomial from extrema and limit
Single correct · 1 shiftcount local extrema of nested modulus function
Single correct · 1 shiftcount of local maxima
Single correct · 1 shiftcount of critical points
Single correct · 1 shiftextrema of integral-defined function
Numerical value · 1 shift · 1 numericalmax and min of rational quadratic ratio
Single correct · 1 shiftcompare powers using extremum of x^(1/x)
Single correct · 1 shiftmin and max of sum of square root functions
Single correct · 1 shiftgreatest term of a sequence
Numerical value · 1 shift · 1 numericalparameter range for extremum at piecewise junction
Single correct · 1 shiftextrema of function with modulus and greatest integer
Numerical value · 1 shift · 1 numericalextreme values of modulus function on interval
Single correct · 1 shiftcount local extrema of modulus function
Numerical value · 1 shift · 1 numericalcount true statements on extrema and inflection of a function
Other · 1 shiftidentify extremal figure inscribed in circle
Single correct · 1 shiftmaximum area of rectangle inscribed under curve
Single correct · 1 shiftfarthest point on conic from given point
Single correct · 1 shift
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Optimization Problemsminimum area of triangle cut by line | 13 | 13 | Single correctMulti-step | 3 | |
| Closed Interval Extremamax of trig expression on interval | 8 | 8 | Single correctMulti-step | 1 | |
| Analyzing Polynomial Roots via Extremacount real roots of polynomial equation | 6 | 6 | Numerical valueMulti-step | 3 | |
| Determining Coefficients from Extremadetermine polynomial from extrema and limit | 5 | 5 | Numerical valueMulti-step | 3 | |
| Optimization via AM-GM Inequalityminimum of sum of intercepts of line | 5 | 5 | Single correctApplication | 1 | |
| Finding Parameters from Given Extremafind parameter from locations of local extrema | 4 | 4 | Single correctMulti-step | – | |
| First Derivative Testlocal minimum location constrained by rational inequality | 4 | 4 | Single correctMulti-step | 1 | |
| Critical vs Stationary Pointscount critical points of modulus function | 3 | 3 | Numerical valueMulti-step | 2 | |
| Shortest Distance Between Curvesshortest distance between parabola and circle | 3 | 3 | Single correctMulti-step | – | |
| Max/Min of Inscribed Geometric Figuresmaximum area of inscribed figure | 3 | 3 | Single correctMulti-step | 1 | |
| Second Derivative Testminimum value of function from derivative condition | 3 | 3 | Numerical valueMulti-step | 2 | |
| Extrema of Trigonometric Compositionsinteger values for trigonometric equation solvability | 2 | 2 | Single correctMulti-step | – | |
| Extrema of Variable-Base Exponentialslocal maximum of variable-base exponential function | 2 | 2 | Single correctCalculation | – | |
| Extrema of Integral Functionsnature of critical point of integral function | 2 | 2 | Single correctMulti-step | – | |
| Determining Unknown Coefficients from Extremadetermine polynomial from extrema and limit | 1 | 1 | Single correctMulti-step | – | |
| Extrema at Non-Differentiable Pointscount local extrema of nested modulus function | 1 | 1 | Single correctMulti-step | – | |
| Counting Extrema in Periodic Functionscount of local maxima | 1 | 1 | Single correctMulti-step | – | |
| Cusp Extrema in Fractional Power Functionscount of critical points | 1 | 1 | Single correctCalculation | – | |
| Extrema of Integral Functions (Leibniz Rule)extrema of integral-defined function | 1 | 1 | Numerical valueMulti-step | 1 | |
| Extrema of Quadratic over Quadraticmax and min of rational quadratic ratio | 1 | 1 | Single correctMulti-step | – | |
| Extrema of x^x and x^(1/x)compare powers using extremum of x^(1/x) | 1 | 1 | Single correctMulti-step | – | |
| Optimization via Cauchy-Schwarz Inequalitymin and max of sum of square root functions | 1 | 1 | Single correctMulti-step | – | |
| Extrema of Discrete Sequences via Calculusgreatest term of a sequence | 1 | 1 | Numerical valueMulti-step | 1 | |
| Extrema at Piecewise Junctionsparameter range for extremum at piecewise junction | 1 | 1 | Single correctMulti-step | – | |
| Extrema Involving Greatest Integer Functionextrema of function with modulus and greatest integer | 1 | 1 | Numerical valueMulti-step | 1 | |
| Extrema of Absolute Value Functionsextreme values of modulus function on interval | 1 | 1 | Single correctCalculation | – | |
| Extrema of Modulus Functionscount local extrema of modulus function | 1 | 1 | Numerical valueMulti-step | 1 | |
| Points of Inflectioncount true statements on extrema and inflection of a function | 1 | 1 | OtherMulti-step | – | |
| Standard Geometric Optimization Resultsidentify extremal figure inscribed in circle | 1 | 1 | Single correctRecall | – | |
| Inscribed 2D Geometry Optimizationmaximum area of rectangle inscribed under curve | 1 | 1 | Single correctMulti-step | – | |
| Shortest Distance from Point to Curvefarthest point on conic from given point | 1 | 1 | Single correctMulti-step | – |
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
Maxima and Minima 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 20264 questions in 4 shifts
- 2 Apr, Shift 1Q18The number of critical points of the function in the…
Idea: Critical vs Stationary Points
HardSingle correct - 2 Apr, Shift 2Q18Let be a polynomial of degree 5, and have extrema at and . If ,…
Idea: Determining Unknown Coefficients from Extrema
New ideaMediumSingle correct - 4 Apr, Shift 2Q12is equal to:
Idea: Closed Interval Extrema
Asked the year beforeMediumSingle correct - 5 Apr, Shift 1Q12The sum of all the integral values of such that the equation , , has at least one…
Idea: Extrema of Trigonometric Compositions
MediumSingle correct
JEE Main 20257 questions in 5 shifts
- 2 Apr, Shift 1Q8If the function , where , attains its local maximum and local minimum values at p and q, respectively, such…
Idea: Finding Parameters from Given Extrema
Asked the year beforeMediumSingle correct - 3 Apr, Shift 2Q16Let be a function defined by . If is the number of points of local…
Idea: Extrema at Non-Differentiable Points
New ideaMediumSingle correct - 3 Apr, Shift 2Q17The shortest distance between the curves and is:
Idea: Shortest Distance Between Curves
MediumSingle correct - 4 Apr, Shift 2Q16Let be a differentiable function on such that , . Let…
Idea: Analyzing Polynomial Roots via Extrema
HardSingle correct - 4 Apr, Shift 2Q17Let . If the function attains its local maximum and minimum values at the points and …
Idea: Finding Parameters from Given Extrema
Asked the year beforeMediumSingle correct - 7 Apr, Shift 1Q17Let and be the critical points of the function , . Let and …
Idea: Closed Interval Extrema
Asked the year beforeMediumSingle correct - 7 Apr, Shift 2Q18Let be a polynomial function of degree four having extreme values at and . If…
Idea: Determining Coefficients from Extrema
MediumSingle correct
JEE Main 202415 questions in 12 shifts
- 4 Apr, Shift 1Q12Let the sum of the maximum and the minimum values of the function be , where…
Idea: Extrema of Quadratic over Quadratic
New ideaMediumSingle correct - 4 Apr, Shift 2Q7Let be a real valued function. If and are respectively the minimum and the maximum values…
Idea: Optimization via Cauchy-Schwarz Inequality
New ideaHardSingle correct - 5 Apr, Shift 1Q9Let a rectangle ABCD of sides 2 and 4 be inscribed in another rectangle PQRS such that the vertices of the rectangle ABCD lie on the sides…
Idea: Max/Min of Inscribed Geometric Figures
New ideaHardSingle correct - 6 Apr, Shift 2Q8If the function ; attains the maximum value at then :
Idea: Extrema of x^x and x^(1/x)
New ideaHardSingle correct - 8 Apr, Shift 1Q8The number of critical points of the function is
Idea: Cusp Extrema in Fractional Power Functions
New ideaMediumSingle correct - 8 Apr, Shift 1Q9Let . The number of points of local maxima of in interval is
Idea: Counting Extrema in Periodic Functions
New ideaHardSingle correct - 8 Apr, Shift 2Q10If the function , has a local maximum at and a local minimum at ,…
Idea: Finding Parameters from Given Extrema
MediumSingle correct - 8 Apr, Shift 2Q24Let A be the region enclosed by the parabola and the line . Then the maximum area of the rectangle inscribed in the…
Idea: Max/Min of Inscribed Geometric Figures
New ideaMediumNumerical value - 9 Apr, Shift 1Q7A variable line L passes through the point and intersects the positive coordinate axes at the points A and B. The minimum area of…
Idea: Optimization Problems
Asked the year beforeMediumSingle correct - 9 Apr, Shift 1Q27Let the set of all positive values of , for which the point of local minimum of the function satisfies…
Idea: First Derivative Test
MediumNumerical value - 9 Apr, Shift 2Q25Let the set of all values of , for which does not have any critical point,…
Idea: Critical vs Stationary Points
MediumNumerical value - 30 Jan, Shift 1Q7The maximum area of a triangle whose one vertex is at and the other two vertices lie on the curve at points …
Idea: Max/Min of Inscribed Geometric Figures
New ideaMediumSingle correct - 30 Jan, Shift 2Q9Let , . If and are the maximum and minimum values of , respectively in , then…
Idea: Closed Interval Extrema
Asked the year beforeMediumSingle correct - 31 Jan, Shift 1Q25Let and be defined as , Let p…
Idea: Extrema of Integral Functions (Leibniz Rule)
New ideaHardNumerical value - 31 Jan, Shift 2Q10Let a variable line passing through the centre of the circle , meet the positive co-ordinate axes at the points and…
Idea: Optimization via AM-GM Inequality
MediumSingle correct
JEE Main 20234 questions in 4 shifts
- 8 Apr, Shift 1Q23If is the greatest term in the sequence , then is equal to ____________.
Idea: Extrema of Discrete Sequences via Calculus
New ideaMediumNumerical value - 10 Apr, Shift 1Q7A square piece of tin of side 30 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to…
Idea: Optimization Problems
Asked the year beforeMediumSingle correct - 12 Apr, Shift 1Q9If the local maximum value of the function , ,…
Idea: Extrema of Variable-Base Exponentials
HardSingle correct - 13 Apr, Shift 1Q10Asked the year beforeHardSingle correct
JEE Main 202221 questions in 17 shifts
- 25 Jul, Shift 1Q6If the absolute maximum value of the function in the interval is…
Idea: Closed Interval Extrema
Asked the year beforeMediumSingle correct - 25 Jul, Shift 1Q7The curve touches the -axis at the point and cuts the -axis at the point ,…
Idea: First Derivative Test
MediumSingle correct - 25 Jul, Shift 2Q24The sum of the maximum and minimum values of the function in the interval , where …
Idea: Extrema Involving Greatest Integer Function
New ideaMediumNumerical value - 26 Jul, Shift 1Q9Let . Then the set of all…
Idea: Extrema at Piecewise Junctions
New ideaMediumSingle correct - 26 Jul, Shift 1Q24The number of distinct real roots of the equation is ___________.
Idea: Analyzing Polynomial Roots via Extrema
Asked the year beforeHardNumerical value - 26 Jul, Shift 2Q5Let P and Q be any points on the curves and , respectively. The distance between P and Q is minimum for some…
Idea: Shortest Distance Between Curves
Asked the year beforeHardSingle correct - 28 Jul, Shift 1Q17If the minimum value of , is 14, then the value of is equal to :
Idea: Optimization via AM-GM Inequality
Asked the year beforeMediumSingle correct - 28 Jul, Shift 2Q67The sum of the absolute maximum and absolute minimum values of the function in the interval is :
Idea: Closed Interval Extrema
Asked the year beforeMediumSingle correct - 29 Jul, Shift 1Q20Let , . Then which of the following statements are true ? P : is a point of local…
Idea: Points of Inflection
New ideaHardOther - 30 Jul, Shift 2Q83The number of integral values of for which has three distinct real roots is ________.
Idea: Analyzing Polynomial Roots via Extrema
Asked the year beforeMediumNumerical value - 30 Jul, Shift 2 · Q84Optimization ProblemsAsked the year beforeMedium
- 24 Jun, Shift 1 · Q12Closed Interval ExtremaAsked the year beforeHard
- 25 Jun, Shift 2 · Q28Extrema of Modulus FunctionsNew ideaHard
- 26 Jun, Shift 1 · Q8Extrema of Absolute Value FunctionsNew ideaMedium
- 26 Jun, Shift 2 · Q6Optimization ProblemsAsked the year beforeHard
- 27 Jun, Shift 1 · Q6Analyzing Polynomial Roots via ExtremaAsked the year beforeMedium
- 27 Jun, Shift 1 · Q7Optimization ProblemsAsked the year beforeMedium
- 27 Jun, Shift 2 · Q7Extrema of Integral FunctionsMedium
- 29 Jun, Shift 1 · Q14Optimization ProblemsAsked the year beforeMedium
- 29 Jun, Shift 2 · Q6First Derivative TestMedium
- 30 Jun, Shift 1 · Q8Optimization ProblemsAsked the year beforeMedium
JEE Main 202120 questions in 17 shifts
- 3 Aug, Shift 2 · Q71Finding Parameters from Given ExtremaNew ideaMedium
- 4 Aug, Shift 1 · Q85Second Derivative TestNew ideaEasy
- 4 Aug, Shift 2 · Q87Second Derivative TestNew ideaMedium
- 26 Aug, Shift 1 · Q84Optimization ProblemsMedium
- 26 Aug, Shift 2 · Q66Extrema of Variable-Base ExponentialsNew ideaMedium
- 27 Aug, Shift 1 · Q66Optimization ProblemsMedium
- 27 Aug, Shift 1 · Q85Analyzing Polynomial Roots via ExtremaAsked the year beforeMedium
- 27 Aug, Shift 2 · Q68Extrema of Trigonometric CompositionsNew ideaMedium
- 27 Aug, Shift 2 · Q69Optimization ProblemsMedium
- 31 Aug, Shift 2 · Q85Determining Coefficients from ExtremaAsked the year beforeMedium
- 24 Feb, Shift 1 · Q86Optimization via AM-GM InequalityAsked the year beforeMedium
- 24 Feb, Shift 2 · Q63Shortest Distance Between CurvesNew ideaMedium
- 25 Feb, Shift 1 · Q87Critical vs Stationary PointsNew ideaHard
- 25 Feb, Shift 2 · Q67Optimization via AM-GM InequalityAsked the year beforeMedium
- 26 Feb, Shift 1 · Q68Second Derivative TestNew ideaMedium
- 26 Feb, Shift 2 · Q75Standard Geometric Optimization ResultsNew ideaEasy
- 25 Jul, Shift 2 · Q89Optimization ProblemsMedium
- 17 Mar, Shift 2 · Q85Closed Interval ExtremaNew ideaMedium
- 18 Mar, Shift 2 · Q68Optimization ProblemsHard
- 18 Mar, Shift 2 · Q85Determining Coefficients from ExtremaAsked the year beforeMedium
JEE Main 20208 questions in 7 shifts
- 8 Jan, Shift 2 · Q73Determining Coefficients from ExtremaNew ideaMedium
- 9 Jan, Shift 2 · Q61Extrema of Integral FunctionsNew ideaMedium
- 2 Sep, Shift 1 · Q61Determining Coefficients from ExtremaNew ideaMedium
- 3 Sep, Shift 2 · Q58Analyzing Polynomial Roots via ExtremaNew ideaMedium
- 4 Sep, Shift 2 · Q60Optimization via AM-GM InequalityNew ideaMedium
- 4 Sep, Shift 2 · Q62Inscribed 2D Geometry OptimizationNew ideaMedium
- 5 Sep, Shift 1 · Q60Shortest Distance from Point to CurveNew ideaMedium
- 6 Sep, Shift 2 · Q60First Derivative TestNew ideaHard
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.