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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 27 August 2021, Shift 2, Maths Q69

Question 69 of 90 in this shift, Maths question 9 of 30, Section A.

A 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 corners and folding up the flaps. If the volume of the box is maximum, then xx is equal to :
  1. (1)a+b−a2+b2−ab6\frac{a + b - \sqrt{a^2 + b^2 - ab}}{6}Official answer
  2. (2)a+b−a2+b2−ab12\frac{a + b - \sqrt{a^2 + b^2 - ab}}{12}
  3. (3)a+b−a2+b2+ab6\frac{a + b - \sqrt{a^2 + b^2 + ab}}{6}
  4. (4)a+b+a2+b2−ab6\frac{a + b + \sqrt{a^2 + b^2 - ab}}{6}

Official answer

Option 1

NTA final key.

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

Same idea in other shifts

Asked 13× in all
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  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. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.