JEE Main 2023 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 11 April 2023, Shift 1, Maths Q8

Question 8 of 90 in this shift, Maths question 8 of 30, Section A.

If equation of the plane that contains the point

(-2, 3, 5)

and is perpendicular to each of the planes

2x + 4y + 5z = 8

and

3x - 2y + 3z = 5

\alpha x + \beta y + \gamma z + 97 = 0

then

\alpha + \beta + \gamma =

(1)15Official answer
(2)16
(3)17
(4)18

Official answer

Option 1

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

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
28 Jun 2022, Shift 2 · Q16Let 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…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.