JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 3 August 2021, Shift 2, Maths Q77

Question 77 of 90 in this shift, Maths question 17 of 30, Section A.

A plane intersects the

yz

-plane at

x = 0,\ 2y - 3z = 5

and it intersects the

xy

-plane at

z = 0,\ 7x + 4y = 10

. Then the distance of the point

(1, -2, -1)

from this plane is

(1) $\frac{1}{\sqrt{101}}$
(2) $\frac{3}{\sqrt{101}}$
(3) $\frac{5}{\sqrt{101}}$ Official answer
(4) $\frac{7}{\sqrt{101}}$

Official answer

Option 3

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Point-Plane Distance
Idea tested: Distance from Point

Same topic in other shifts

All Point-Plane Distance questions

4 Apr 2026, Shift 1 · Q15The square of the distance of the point $(-2,-8,6)$ from the line $\frac{x-1}{1}=\frac{y-1}{2}=\frac{z}{-1}$ along the line…MediumSingle correct
28 Jul 2022, Shift 1 · Q16The foot of the perpendicular from a point on the circle $x^2+y^2=1,\ z=0$ to the plane $2x+3y+z=6$ lies on which one of the following…HardSingle correct
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
29 Jun 2022, Shift 1 · Q23Let $d$ be the distance between the foot of perpendiculars of the points $P(1, 2, -1)$ and $Q(2, -1, 3)$ on the plane $-x + y + z = 1$ .…MediumNumerical value
16 Mar 2021, Shift 2 · Q83If the distance of the point (1, $-2$ , 3) from the plane $x+2y-3z+10=0$ measured parallel to the line,…MediumNumerical value
18 Mar 2021, Shift 1 · Q86The equation of the planes parallel to the plane $x-2y+2z-3=0$ which are at unit distance from the point $(1,2,3)$ is $ax+by+cz+d=0$ . If…MediumNumerical value

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.