If the mirror image of the point $(1, 3, 5)$ with respect to the plane $4x-5y+2z=8$ is $(\alpha, \beta, \gamma)$, then $5(\alpha+\beta+\gamma)$ equals :

JEE Main 2021 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 26 February 2021, Shift 2, Maths Q61

Question 61 of 90 in this shift, Maths question 1 of 30, Section A.

If the mirror image of the point

(1, 3, 5)

with respect to the plane

4x-5y+2z=8

(\alpha, \beta, \gamma)

, then

5(\alpha+\beta+\gamma)

equals :

(1) $39$
(2) $41$
(3) $43$
(4) $47$ Official answer

Official answer

Option 4

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

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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
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.