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Saturday, 31 October

JEE Main · Maths · Application of Derivatives

Optimization Problems

JEE Main asked Optimization Problems 13 times in 13 of the 108 shifts Lumi analysed, in 2017, 2021, 2022, 2023 and 2024. It belongs to Maxima and Minima, in Application of Derivatives (Maths). The longest wait between two years asking it was 4 years, across 2018 and 2019, which Lumi has no shifts for. In 2021 and 2022 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
13
in 13 shifts
Years
5 of 8
First asked
2017
last in 2024
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2017, 2021, 2022, 2023 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.510.86’170’200.17’210.18’220.07’230.05’240’250’26

Raw count: 2017: 1 in 1 shift · 2020: 0 in 12 shifts · 2021: 5 in 24 shifts · 2022: 5 in 24 shifts · 2023: 1 in 12 shifts · 2024: 1 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.

  • 20260 of 9
  • 20250 of 8
  • 20241 of 18
  • 20231 of 12
  • 20225 of 24
  • 20215 of 24
  • 20200 of 12
  • 20171 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: multi-step.

  • Minimum area of triangle cut by line
  • Maximize area under perimeter constraint

Difficulty

Easy 0Medium 11Hard 2

3 of the 13 questions had a numerical answer.

Every question

All 13 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 9 Apr 2024, Shift 1 · Q7A variable line L passes through the point (3,5)(3,5) and intersects the positive coordinate axes at the points A and B. The minimum area of…MediumSingle correct
  2. 10 Apr 2023, Shift 1 · Q7A 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…MediumSingle correct
  3. 30 Jun 2022, Shift 1 · Q8If xy4xy^4 attains maximum value at the point (x,y)(x, y) on the line passing through the points (50+α,0)(50+\alpha, 0) and (0,50+α)(0, 50+\alpha),…MediumSingle correct
  4. 29 Jun 2022, Shift 1 · Q14A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral…MediumSingle correct
  5. 27 Jun 2022, Shift 1 · Q7The lengths of the sides of a triangle are 10+x210+x^2, 10+x210+x^2 and 20−2x220-2x^2. If for x=kx=k, the area of the triangle is maximum, then…MediumSingle correct
  6. 26 Jun 2022, Shift 2 · Q6Cosider a cuboid of sides 2x2x, 4x4x and 5x5x and a closed hemisphere of radius rr. If the sum of their surface areas is a constant kk,…HardSingle correct
  7. 30 Jul 2022, Shift 2 · Q84An air duct is made of a thick metallic sheet. The duct is open from front and back. Its cross-section is a trapezium of base angles…MediumNumerical valueHas a figure
  8. 18 Mar 2021, Shift 2 · Q68Let a tangent be drawn to the ellipse x227+y2=1\frac{x^2}{27}+y^2=1 at (33cos⁡θ,sin⁡θ)(3\sqrt{3}\cos\theta,\sin\theta) where…HardSingle correct
  9. 25 Jul 2021, Shift 2 · Q89If a rectangle is inscribed in an equilateral triangle of side length 222\sqrt{2} as shown in the figure, then the square of the largest…MediumNumerical valueHas a figure
  10. 27 Aug 2021, Shift 2 · Q69A box open from top is made from a rectangular sheet of dimension a×ba \times b by cutting squares each of side xx from each of the four…MediumSingle correct
  11. 27 Aug 2021, Shift 1 · Q66A wire of length 20 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a regular hexagon.…MediumSingle correct
  12. 26 Aug 2021, Shift 1 · Q84A wire of length 36 m is cut into two pieces, one of the pieces is bent to form a square and the other is bent to form a circle. If the…MediumNumerical value
  13. 2 Apr 2017 (offline) · Q73Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the…MediumSingle correct

Shifts: 2 Apr 2017 (offline), 18 Mar 2021, Shift 2, 25 Jul 2021, Shift 2, 26 Aug 2021, Shift 1, 27 Aug 2021, Shift 2, 27 Aug 2021, Shift 1, 26 Jun 2022, Shift 2, 27 Jun 2022, Shift 1, 29 Jun 2022, Shift 1, 30 Jun 2022, Shift 1, 30 Jul 2022, Shift 2, 10 Apr 2023, Shift 1, 9 Apr 2024, Shift 1.

Same topic

Other ideas in Maxima and Minima

Maxima and Minima has 31 ideas JEE Main has asked; 14 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas