JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 25 July 2022, Shift 1, Maths Q14

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

Let

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 the straight lines

\frac{x}{2}=\frac{y}{3}=\frac{z}{5}

and

\frac{x}{3}=\frac{y}{7}=\frac{z}{8}

. If

d

is the distance of

P

from the point

(2,-5,11)

, then

d^2

is equal to :

(1) $\frac{147}{2}$
(2) $96$
(3) $\frac{32}{3}$ Official answer
(4) $54$

Official answer

Option 3

NTA final key (2022 Session 2).

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
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
17 Mar 2021, Shift 2 · Q77If the equation of plane passing through the mirror image of a point (2, 3, 1) with respect to line…HardSingle 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.