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Saturday, 31 October

JEE Main 2021 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 25 July 2021, Shift 2, Maths Q89

Question 89 of 90 in this shift, Maths question 29 of 30, Section B.

If 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 area of such a rectangle is __________.

The figure, in words

A triangle with apex at the top and a horizontal base is drawn; a rectangle is drawn inside it with its base on the triangle's base and its top side's two ends touching the two slanted sides. No labels or lengths are printed on the figure.

Official answer

3

NTA final key.

Chapter
Application of Derivatives
Topic
Maxima and Minima
Idea tested
Optimization Problems

Same idea in other shifts

Asked 13× in all
  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 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
  4. 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
  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. 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
  7. 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
  8. 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

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. This question needs a figure we do not reproduce; it is described in words above. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.