JEE Main 2026 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 4 April 2026, Shift 2, Maths Q14

Question 14 of 75 in this shift, Maths question 14 of 25, Section A.

\left(2\alpha+1,\,\alpha^2-3\alpha,\,\frac{\alpha-1}{2}\right)

is the image of

(\alpha,2\alpha,1)

in the line

\frac{x-2}{3}=\frac{y-1}{2}=\frac z1

, then the possible value(s) of

\alpha

is (are)

(1)Only 3Official answer
(2)Only 3 and $-1$
(3)Only 3, $\frac14$ and $-1$
(4)Only 3 and $\frac14$

Official answer

Option 1

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

5 Apr 2026, Shift 2 · Q15If the distance of the point $(a, 2, 5)$ from the image of the point $(1, 2, 7)$ in the line $\frac{x}{1}=\frac{y-1}{1}=\frac{z-2}{2}$ is…MediumSingle correct
6 Apr 2026, Shift 1 · Q15Let the image of the point $\mathrm{P}(1,6,a)$ in the line $\mathrm{L}:\frac{x}{1}=\frac{y-1}{2}=\frac{z-a+1}{b}$ , $b>0$ , be…HardSingle correct
6 Apr 2026, Shift 2 · Q24Let the image of the point P $(0,-5,0)$ in the line $\frac{x-1}{2}=\frac{y}{1}=\frac{z+1}{-2}$ be the point R and the image of the point…HardNumerical value
2 Apr 2025, Shift 2 · Q14If the image of the point $P(1, 0, 3)$ in the line joining the points $A(4, 7, 1)$ and $B(3, 5, 3)$ is $Q(\alpha, \beta, \gamma)$ , then…MediumSingle correct
6 Apr 2024, Shift 2 · Q17Let $P(\alpha,\beta,\gamma)$ be the image of the point $Q(3,-3,1)$ in the line $\frac{x-0}{1}=\frac{y-3}{1}=\frac{z-1}{-1}$ and $R$ be the…HardSingle correct
9 Apr 2024, Shift 2 · Q29The square of the distance of the image of the point $(6, 1, 5)$ in the line $\frac{x-1}{3}=\frac{y}{2}=\frac{z-2}{4}$ , from the origin is…MediumNumerical value
31 Jan 2024, Shift 2 · Q16Let $(\alpha,\beta,\gamma)$ be the mirror image of the point $(2,3,5)$ in the line $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ . 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.