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Friday, 9 October

JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 25 July 2022, Shift 1, Maths Q30

Question 30 of 90 in this shift, Maths question 30 of 30, Section B. NTA dropped this question from the final key; it is left out of every count on this site.

The line of shortest distance between the lines x−20=y−11=z1\frac{x-2}{0}=\frac{y-1}{1}=\frac{z}{1} and x−32=y−52=z−11\frac{x-3}{2}=\frac{y-5}{2}=\frac{z-1}{1} makes an angle of cos⁡−1(227)\cos^{-1}\left(\sqrt{\frac{2}{27}}\right) with the plane P:ax−y−z=0P:ax-y-z=0, (a>0)(a>0). If the image of the point (1,1,−5)(1,1,-5) in the plane PP is (α,β,γ)(\alpha,\beta,\gamma), then α+β−γ\alpha+\beta-\gamma is equal to ______.

Official answer

Dropped by NTA (marks given to all)

NTA final key (2022 Session 2).

Chapter
Three Dimensional Geometry
Topic
Skew Lines
Idea tested
No close match in our taxonomy

Same topic in other shifts

All Skew Lines questions
  1. 4 Apr 2026, Shift 2 · Q13The shortest distance between the lines…EasySingle correct
  2. 6 Apr 2026, Shift 2 · Q14The shortest distance between the lines x−41=y−32=z−2−3\frac{x-4}{1}=\frac{y-3}{2}=\frac{z-2}{-3} and x+22=y−64=z−5−5\frac{x+2}{2}=\frac{y-6}{4}=\frac{z-5}{-5} is :EasySingle correct
  3. 2 Apr 2025, Shift 2 · Q15The line L1L_1 is parallel to the vector a⃗=−3i^+2j^+4k^\vec{a} = -3\hat{i} + 2\hat{j} + 4\hat{k} and passes through the point (7,6,2)(7, 6, 2) and the line…EasySingle correct
  4. 3 Apr 2025, Shift 1 · Q14Line L1\mathrm{L}_1 passes through the point (1,2,3)(1, 2, 3) and is parallel to zz-axis. Line L2\mathrm{L}_2 passes through the point…MediumSingle correct
  5. 4 Apr 2025, Shift 2 · Q14Let the values of p, for which the shortest distance between the lines x+13=y4=z5\frac{x+1}{3}=\frac{y}{4}=\frac{z}{5} and…MediumSingle correct
  6. 7 Apr 2025, Shift 1 · Q14If the shortest distance between the lines x−12=y−23=z−34\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4} and…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.