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Friday, 9 October

JEE Main 2026 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 6 April 2026, Shift 1, Maths Q15

Question 15 of 75 in this shift, Maths question 15 of 25, Section A.

Let the image of the point P(1,6,a)\mathrm{P}(1,6,a) in the line L:x1=y−12=z−a+1b\mathrm{L}:\frac{x}{1}=\frac{y-1}{2}=\frac{z-a+1}{b}, b>0b>0, be (a3,0,a+c)\left(\frac{a}{3},0,a+c\right). If S(α,β,γ)\mathrm{S}(\alpha,\beta,\gamma), α>0\alpha>0, is the point on L such that the distance of S from the foot of perpendicular from the point P on L is 2142\sqrt{14}, then α+β+γ\alpha+\beta+\gamma is equal to:
  1. (1)19
  2. (2)20
  3. (3)21Official answer
  4. (4)22

Official answer

Option 3

NTA final key.

Chapter
Three Dimensional Geometry
Topic
Lines in 3D
Idea tested
Image of a Point in a Line

Same idea in other shifts

Asked 8× in all
  1. 4 Apr 2026, Shift 2 · Q14If (2α+1, α2−3α, α−12)\left(2\alpha+1,\,\alpha^2-3\alpha,\,\frac{\alpha-1}{2}\right) is the image of (α,2α,1)(\alpha,2\alpha,1) in the line…MediumSingle correct
  2. 5 Apr 2026, Shift 2 · Q15If the distance of the point (a,2,5)(a, 2, 5) from the image of the point (1,2,7)(1, 2, 7) in the line x1=y−11=z−22\frac{x}{1}=\frac{y-1}{1}=\frac{z-2}{2} is…MediumSingle correct
  3. 6 Apr 2026, Shift 2 · Q24Let the image of the point P(0,−5,0)(0,-5,0) in the line x−12=y1=z+1−2\frac{x-1}{2}=\frac{y}{1}=\frac{z+1}{-2} be the point R and the image of the point…HardNumerical value
  4. 2 Apr 2025, Shift 2 · Q14If the image of the point P(1,0,3)P(1, 0, 3) in the line joining the points A(4,7,1)A(4, 7, 1) and B(3,5,3)B(3, 5, 3) is Q(α,β,γ)Q(\alpha, \beta, \gamma), then…MediumSingle correct
  5. 6 Apr 2024, Shift 2 · Q17Let P(α,β,γ)P(\alpha,\beta,\gamma) be the image of the point Q(3,−3,1)Q(3,-3,1) in the line x−01=y−31=z−1−1\frac{x-0}{1}=\frac{y-3}{1}=\frac{z-1}{-1} and RR be the…HardSingle correct
  6. 9 Apr 2024, Shift 2 · Q29The square of the distance of the image of the point (6,1,5)(6, 1, 5) in the line x−13=y2=z−24\frac{x-1}{3}=\frac{y}{2}=\frac{z-2}{4}, from the origin is…MediumNumerical value
  7. 31 Jan 2024, Shift 2 · Q16Let (α,β,γ)(\alpha,\beta,\gamma) be the mirror image of the point (2,3,5)(2,3,5) in the line x−12=y−23=z−34\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}. Then,…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.