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Friday, 9 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 28 July 2022, Shift 1, Maths Q16

Question 16 of 90 in this shift, Maths question 16 of 30, Section A.

The foot of the perpendicular from a point on the circle x2+y2=1, z=0x^2+y^2=1,\ z=0 to the plane 2x+3y+z=62x+3y+z=6 lies on which one of the following curves ?
  1. (1)(6x+5y−12)2+4(3x+7y−8)2=1, z=6−2x−3y(6x+5y-12)^2+4(3x+7y-8)^2=1,\ z=6-2x-3y
  2. (2)(5x+6y−12)2+4(3x+5y−9)2=1, z=6−2x−3y(5x+6y-12)^2+4(3x+5y-9)^2=1,\ z=6-2x-3yOfficial answer
  3. (3)(6x+5y−14)2+9(3x+5y−7)2=1, z=6−2x−3y(6x+5y-14)^2+9(3x+5y-7)^2=1,\ z=6-2x-3y
  4. (4)(5x+6y−14)2+9(3x+7y−8)2=1, z=6−2x−3y(5x+6y-14)^2+9(3x+7y-8)^2=1,\ z=6-2x-3y

Official answer

Option 2

NTA final key (2022 Session 2).

Chapter
Three Dimensional Geometry
Topic
Point-Plane Distance
Idea tested
Foot of Perpendicular

Same idea in other shifts

Asked 2× in all
  1. 29 Jun 2022, Shift 1 · Q23Let dd be the distance between the foot of perpendiculars of the points P(1,2,−1)P(1, 2, -1) and Q(2,−1,3)Q(2, -1, 3) on the plane −x+y+z=1-x + y + z = 1.…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 42 of the 174 JEE Main shifts held from 2017 to 2026.