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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 26 June 2022, Shift 1, Maths Q15

Question 15 of 90 in this shift, Maths question 15 of 30, Section A.

Let the plane 2x+3y+z+20=02x + 3y + z + 20 = 0 be rotated through a right angle about its line of intersection with the plane x−3y+5z=8x - 3y + 5z = 8. If the mirror image of the point (2,−12,2)\left(2, -\frac{1}{2}, 2\right) in the rotated plane is B(a,b,c)(a, b, c), then :
  1. (1)a8=b5=c−4\frac{a}{8} = \frac{b}{5} = \frac{c}{-4}Official answer
  2. (2)a4=b5=c−2\frac{a}{4} = \frac{b}{5} = \frac{c}{-2}
  3. (3)a8=b−5=c4\frac{a}{8} = \frac{b}{-5} = \frac{c}{4}
  4. (4)a4=b5=c2\frac{a}{4} = \frac{b}{5} = \frac{c}{2}

Official answer

Option 1

NTA final key.

Chapter
Three Dimensional Geometry
Topic
Planes in 3D
Idea tested
Family of Planes Perpendicular to a Third Plane

Same idea in other shifts

Asked 5× in all
  1. 8 Apr 2023, Shift 1 · Q15If the equation of the plane containing the line x+2y+3z−4=0=2x+y−z+5x+2y+3z-4=0=2x+y-z+5 and perpendicular to the plane…MediumSingle correct
  2. 12 Apr 2023, Shift 1 · Q14Let the plane P: 4x−y+z=104x-y+z=10 be rotated by an angle π2\frac{\pi}{2} about its line of intersection with the plane x+y−z=4x+y-z=4. If α\alpha…HardSingle correct
  3. 26 Jun 2022, Shift 2 · Q14If the plane 2x+y−5z=02x + y - 5z = 0 is rotated about its line of intersection with the plane 3x−y+4z−7=03x - y + 4z - 7 = 0 by an angle of…MediumSingle correct
  4. 4 Aug 2021, Shift 2 · Q76The distance of the point (5,6,9)(5,6,9) from the plane, which passes through the line of intersection of the planes x+y−z=1x+y-z=1 and…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.