JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 17 March 2021, Shift 2, Maths Q77

Question 77 of 90 in this shift, Maths question 17 of 30, Section A.

If the equation of plane passing through the mirror image of a point (2, 3, 1) with respect to line

\frac{x+1}{2}=\frac{y-3}{1}=\frac{z+2}{-1}

and containing the line

\frac{x-2}{3}=\frac{1-y}{2}=\frac{z+1}{1}

\alpha x+\beta y+\gamma z=24

, then

\alpha+\beta+\gamma

is equal to :

(1) $21$
(2) $20$
(3) $19$ Official answer
(4) $18$

Official answer

Option 3

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Plane Containing a Line and a Point

Same idea in other shifts

Asked 5× in all

8 Apr 2023, Shift 2 · Q13Let $P$ be the plane passing through the line $\frac{x-1}{1} = \frac{y-2}{-3} = \frac{z+5}{7}$ and the point $(2, 4, -3)$ . If the image of…MediumSingle correct
25 Jul 2022, Shift 1 · Q14Let $P$ be the plane containing the straight line $\frac{x-3}{9}=\frac{y+4}{-1}=\frac{z-7}{-5}$ and perpendicular to the plane containing…HardSingle correct
29 Jun 2022, Shift 2 · Q14Let Q be the mirror image of the point P(1, 2, 1) with respect to the plane $x + 2y + 2z = 16$ . Let T be a plane passing through the point…HardSingle correct
17 Mar 2021, Shift 1 · Q76The equation of the plane which contains the $y$ -axis and passes through the point $(1, 2, 3)$ is :EasySingle 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.