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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceDiagram basedHardMulti-step

JEE Main 27 July 2022, Shift 2, Maths Q10

Question 10 of 90 in this shift, Maths question 10 of 30, Section A.

Consider a curve y=y(x)y = y(x) in the first quadrant as shown in the figure. Let the area A1A_1 is twice the area A2A_2. Then the normal to the curve perpendicular to the line 2x−12y=152x - 12y = 15 does NOT pass through the point.

The figure, in words

Graph of a curve y=y(x) in the first quadrant on X-Y axes, rising and concave down. Marked on the y-axis: 2 and y; on the x-axis: 4 and x. Region A1 (vertical hatching) lies under the curve between x=4 and x; region A2 (horizontal hatching) lies between the curve and the y-axis, between y=2 and y.
  1. (1)(6,21)(6, 21)
  2. (2)(8,9)(8, 9)
  3. (3)(10,−4)(10, -4)Official answer
  4. (4)(12,−15)(12, -15)

Official answer

Option 3

NTA final key.

Chapter
Differential Equations
Topic
Area Under Curves
Idea tested
Curves from Area Properties

Same idea in other shifts

Asked 3× in all
  1. 8 Apr 2024, Shift 1 · Q12Let f(x)f(x) be a positive function such that the area bounded by y=f(x)y=f(x), y=0y=0 from x=0x=0 to x=a>0x=a>0 is e−a+4a2+a−1e^{-a}+4a^2+a-1. Then the…HardSingle correct
  2. 26 Jul 2022, Shift 1 · Q27Let a curve y=y(x)y = y(x) pass through the point (3, 3)(3,\ 3) and the area of the region under this curve, above the xx-axis and between the…HardNumerical 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.