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Saturday, 31 October

JEE Main 2022 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 30 July 2022, Shift 2, Maths Q84

Question 84 of 90 in this shift, Maths question 24 of 30, Section B.

An 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 60o60^{\mathrm{o}} and area 1.5 m2\mathrm{m^2}. Its length is 1 m. (see the figure). If its height x=x0x = x_0 (in metres) so that the area of the metallic sheet used for its construction is minimum, then 16 (x0)416\,(x_0)^4 is equal to ________.

The figure, in words

3D sketch of an air duct (open at front and back) whose cross-section is a trapezium with both base angles 60 degrees; height marked x, length marked 1 m.

Official answer

27

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. 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
  4. 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
  5. 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
  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. 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.