JEE Main 2023 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 15 April 2023, Shift 1, Maths Q15

Question 15 of 90 in this shift, Maths question 15 of 30, Section A.

Let S be the set of all values of

\lambda

, for which the shortest distance between the lines

\frac{x-\lambda}{0}=\frac{y-3}{4}=\frac{z+6}{1}

and

\frac{x+\lambda}{3}=\frac{y}{-4}=\frac{z-6}{0}

is 13. Then

8\left|\sum_{\lambda\in S}\lambda\right|

is equal to

(1) $302$
(2) $304$
(3) $306$ Official answer
(4) $308$

Official answer

Option 3

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Skew Lines
Idea tested: Cartesian Shortest Distance

Same idea in other shifts

Asked 15× in all

6 Apr 2026, Shift 2 · Q14The shortest distance between the lines $\frac{x-4}{1}=\frac{y-3}{2}=\frac{z-2}{-3}$ and $\frac{x+2}{2}=\frac{y-6}{4}=\frac{z-5}{-5}$ is :EasySingle correct
7 Apr 2025, Shift 1 · Q14If the shortest distance between the lines $\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4}$ and…MediumSingle correct
8 Apr 2024, Shift 2 · Q16If the shortest distance between the lines $\frac{x-\lambda}{2} = \frac{y-4}{3} = \frac{z-3}{4}$ and…MediumSingle correct
9 Apr 2024, Shift 1 · Q16The shortest distance between the lines $\frac{x-3}{4}=\frac{y+7}{-11}=\frac{z-1}{5}$ and $\frac{x-5}{3}=\frac{y-9}{-6}=\frac{z+2}{1}$ is :EasySingle correct
1 Feb 2024, Shift 1 · Q16If the shortest distance between the lines $\frac{x-\lambda}{-2}=\frac{y-2}{1}=\frac{z-1}{1}$ and…MediumSingle correct
27 Jan 2024, Shift 1 · Q18If the shortest distance between the lines $\dfrac{x-4}{1}=\dfrac{y+1}{2}=\dfrac{z}{-3}$ and…MediumSingle correct
30 Jan 2024, Shift 1 · Q28If $d_1$ is the shortest distance between the lines $x+1=2y=-12z$ , $x=y+2=6z-6$ and $d_2$ is the shortest distance between the lines…MediumNumerical value
31 Jan 2024, Shift 2 · Q17The shortest distance, between lines $L_1$ and $L_2$ , where $L_1:\frac{x-1}{2}=\frac{y+1}{-3}=\frac{z+4}{2}$ and $L_2$ is the line,…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.