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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 29 June 2022, Shift 1, Maths Q14

Question 14 of 90 in this shift, Maths question 14 of 30, Section A.

A 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 triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is :
  1. (1)229+43\frac{22}{9 + 4\sqrt{3}}
  2. (2)669+43\frac{66}{9 + 4\sqrt{3}}Official answer
  3. (3)224+93\frac{22}{4 + 9\sqrt{3}}
  4. (4)664+93\frac{66}{4 + 9\sqrt{3}}

Official answer

Option 2

NTA final key (2022 Session 1).

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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  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. 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
  7. 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
  8. 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

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.