JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 30 June 2022, Shift 1, Maths Q8

Question 8 of 90 in this shift, Maths question 8 of 30, Section A.

xy^4

attains maximum value at the point

(x, y)

on the line passing through the points

(50+\alpha, 0)

and

(0, 50+\alpha)

\alpha > 0

, then

(x, y)

also lies on the line :

(1) $y = 4x$ Official answer
(2) $x = 4y$
(3) $y = 4x + \alpha$
(4) $x = 4y - \alpha$

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

9 Apr 2024, Shift 1 · Q7A variable line L passes through the point $(3,5)$ and intersects the positive coordinate axes at the points A and B. The minimum area of…MediumSingle correct
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
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
26 Jun 2022, Shift 2 · Q6Cosider a cuboid of sides $2x$ , $4x$ and $5x$ and a closed hemisphere of radius $r$ . If the sum of their surface areas is a constant $k$ ,…HardSingle correct
27 Jun 2022, Shift 1 · Q7The lengths of the sides of a triangle are $10+x^2$ , $10+x^2$ and $20-2x^2$ . If for $x=k$ , the area of the triangle is maximum, then…MediumSingle correct
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
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
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.