JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 6 April 2023, Shift 1, Maths Q13

Question 13 of 90 in this shift, Maths question 13 of 30, Section A.

If the equation of the plane passing through the line of intersection of the planes

2x-y+z=3

4x-3y+5z+9=0

and parallel to the line

\frac{x+1}{-2}=\frac{y+3}{4}=\frac{z-2}{5}

ax+by+cz+6=0

, then

a+b+c

is equal to

(1)12
(2)13
(3)14Official answer
(4)15

Official answer

Option 3

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Family of Planes

Same topic in other shifts

All Planes in 3D questions

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
8 Apr 2023, Shift 2 · Q14For $a, b \in \mathbb{Z}$ and $|a - b| \leq 10$ , let the angle between the plane $P: ax + y - z = b$ and the line…HardSingle correct
8 Apr 2023, Shift 2 · Q30Let $P_1$ be the plane $3x - y - 7z = 11$ and $P_2$ be the plane passing through the points $(2, -1, 0)$ , $(2, 0, -1)$ , and $(5, 1, 1)$ .…HardNumerical value
11 Apr 2023, Shift 1 · Q2Let $(\alpha, \beta, \gamma)$ be the image of the point $P(2, 3, 5)$ in the plane $2x + y - 3z = 6$ . Then $\alpha + \beta + \gamma$ is…MediumSingle correct
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
13 Apr 2023, Shift 2 · Q14The plane, passing through the points $(0,-1,2)$ and $(-1,2,1)$ and parallel to the line passing through $(5,1,-7)$ and $(1,-1,-1)$ , also…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 42 of the 174 JEE Main shifts held from 2017 to 2026.