JEE Main 2022 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 28 June 2022, Shift 2, Maths Q16

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

Let the plane

ax+by+cz=d

pass through

(2, 3, -5)

and is perpendicular to the planes

2x+y-5z=10

and

3x+5y-7z=12

. If a, b, c, d are integers

d>0

and

\gcd(|a|, |b|, |c|, d)=1

, then the value of

a+7b+c+20d

is equal to :

(1)18
(2)20
(3)24
(4)22Official answer

Official answer

Option 4

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Plane Perpendicular to Two Planes

Same idea in other shifts

Asked 4× in all

11 Apr 2023, Shift 1 · Q8If equation of the plane that contains the point $(-2, 3, 5)$ and is perpendicular to each of the planes $2x + 4y + 5z = 8$ and…MediumSingle correct
25 Jul 2022, Shift 2 · Q15A plane $E$ is perpendicular to the two planes $2x-2y+z=0$ and $x-y+2z=4$ , and passes through the point $P(1,-1,1)$ . If the distance of…MediumSingle correct
24 Feb 2021, Shift 1 · Q76The equation of the plane passing through the point $(1, 2, -3)$ and perpendicular to the planes $3x + y - 2z = 5$ and $2x - 5y - z = 7$ ,…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.