JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 12 April 2023, Shift 1, Maths Q14

Question 14 of 90 in this shift, Maths question 14 of 30, Section A.

Let the plane P:

4x-y+z=10

be rotated by an angle

\frac{\pi}{2}

about its line of intersection with the plane

x+y-z=4

. If

\alpha

is the distance of the point

(2,3,-4)

from the new position of the plane P, then

35\alpha

is equal to

(1) $85$
(2) $90$
(3) $105$
(4) $126$ Official answer

Official answer

Option 4

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

8 Apr 2023, Shift 1 · Q15If the equation of the plane containing the line $x+2y+3z-4=0=2x+y-z+5$ and perpendicular to the plane…MediumSingle correct
26 Jun 2022, Shift 1 · Q15Let the plane $2x + 3y + z + 20 = 0$ be rotated through a right angle about its line of intersection with the plane $x - 3y + 5z = 8$ . If…HardSingle correct
26 Jun 2022, Shift 2 · Q14If the plane $2x + y - 5z = 0$ is rotated about its line of intersection with the plane $3x - y + 4z - 7 = 0$ by an angle of…MediumSingle correct
4 Aug 2021, Shift 2 · Q76The distance of the point $(5,6,9)$ from the plane, which passes through the line of intersection of the planes $x+y-z=1$ 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.