JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 10 April 2023, Shift 1, Maths Q13

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

Let two vertices of a triangle ABC be

(2,4,6)

and

(0,-2,-5)

, and its centroid be

(2,1,-1)

. If the image of the third vertex in the plane

x+2y+4z=11

(\alpha,\beta,\gamma)

, then

\alpha\beta+\beta\gamma+\gamma\alpha

is equal to

(1) $70$
(2) $72$
(3) $74$ Official answer
(4) $76$

Official answer

Option 3

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Point-Plane Distance
Idea tested: Image of a Point

Same idea in other shifts

Asked 8× in all

25 Jun 2022, Shift 1 · Q17Let Q be the mirror image of the point P(1, 0, 1) with respect to the plane S : $x+y+z=5$ . If a line L passing through $(1,-1,-1)$ ,…MediumSingle correct
27 Jun 2022, Shift 1 · Q30Let the mirror image of the point $(a, b, c)$ with respect to the plane $3x-4y+12z+19=0$ be $(a-6, \beta, \gamma)$ . If $a+b+c=5$ , then…MediumNumerical value
29 Jun 2022, Shift 1 · Q3If the mirror image of the point $(2, 4, 7)$ in the plane $3x - y + 4z = 2$ is $(a, b, c)$ , then $2a + b + 2c$ is equal to :EasySingle correct
27 Aug 2021, Shift 2 · Q87Let S be the mirror image of the point $Q(1, 3, 4)$ with respect to the plane $2x - y + z + 3 = 0$ and let $R(3, 5, \gamma)$ be a point of…MediumNumerical value
26 Feb 2021, Shift 2 · Q61If the mirror image of the point $(1, 3, 5)$ with respect to the plane $4x-5y+2z=8$ is $(\alpha, \beta, \gamma)$ , then…EasySingle correct
18 Mar 2021, Shift 2 · Q88Let the mirror image of the point $(1, 3, a)$ with respect to the plane $\vec{r}\cdot\left(2\hat{i}-\hat{j}+\hat{k}\right)-b=0$ be…MediumNumerical value
2 Apr 2017 (offline) · Q83If the image of the point $P(1,-2,3)$ in the plane, $2x+3y-4z+22=0$ measured parallel to the line, $\frac{x}{1}=\frac{y}{4}=\frac{z}{5}$ …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 108 of the 174 JEE Main shifts held from 2017 to 2026.