JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 3 April 2025, Shift 2, Maths Q14

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

Each of the angles

\beta

and

\gamma

that a given line makes with the positive

y

- and

z

-axes, respectively, is half of the angle that this line makes with the positive

x

-axes. Then the sum of all possible values of the angle

\beta

(1) $\pi$
(2) $\frac{3\pi}{2}$
(3) $\frac{3\pi}{4}$ Official answer
(4) $\frac{\pi}{2}$

Official answer

Option 3

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Lines in 3D
Idea tested: Direction Cosines Squares Identity

Same topic in other shifts

All Lines in 3D questions

2 Apr 2026, Shift 1 · Q13If the point of intersection of the lines $\frac{x+1}{3}=\frac{y+a}{5}=\frac{z+b+1}{7}$ and $\frac{x-2}{1}=\frac{y-b}{4}=\frac{z-2a}{7}$ …MediumSingle correct
2 Apr 2026, Shift 1 · Q15Let a line L passing through the point $(1, 1, 1)$ be perpendicular to both the vectors $2\hat i+2\hat j+\hat k$ and…MediumSingle correct
2 Apr 2026, Shift 2 · Q15Let the point $A$ be the foot of perpendicular drawn from the point $P(a, b, 0)$ on the line…MediumSingle correct
4 Apr 2026, Shift 1 · Q14A line with direction ratios $1,-1,2$ intersects the lines $\frac{x}{2}=\frac{y}{3}=\frac{z+1}{3}$ and…MediumSingle correct
4 Apr 2026, Shift 2 · Q14If $\left(2\alpha+1,\,\alpha^2-3\alpha,\,\frac{\alpha-1}{2}\right)$ is the image of $(\alpha,2\alpha,1)$ in the line…MediumSingle correct
5 Apr 2026, Shift 1 · Q13The square of the distance of the point $P(5, 6, 7)$ from the line $\frac{x-2}{2}=\frac{y-5}{3}=\frac{z-2}{4}$ is equal to:EasySingle 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.