JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 3 April 2025, Shift 2, Maths Q10

Question 10 of 75 in this shift, Maths question 10 of 25, Section A.

Consider the lines

x(3\lambda + 1) + y(7\lambda + 2) = 17\lambda + 5

\lambda

being a parameter, all passing through a point P. One of these lines (say

L

) is farthest from the origin. If the distance of

L

from the point

(3, 6)

d

, then the value of

d^2

(1)20Official answer
(2)10
(3)30
(4)15

Official answer

Option 1

NTA final key.

Chapter: Straight Lines
Topic: Straight Line Distance
Idea tested: Extremum Distance to a Family of Lines

Same topic in other shifts

All Straight Line Distance questions

2 Apr 2026, Shift 1 · Q9Let the mid points of the sides of a triangle ABC be $\left(\frac{5}{2}, 7\right)$ , $\left(\frac{5}{2}, 3\right)$ and $(4, 5)$ . If its…MediumSingle correct
2 Apr 2026, Shift 2 · Q10Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines…MediumSingle correct
4 Apr 2026, Shift 1 · Q11Let the line $L_1: x+3=0$ intersect the lines $L_2: x-y=0$ and $L_3: 3x+y=0$ at the points A and B, respectively. Let the bisector of the…MediumSingle correct
5 Apr 2026, Shift 2 · Q22From the point $(-1, -1)$ , two rays are sent making angles of $45^\circ$ with the line $x+y=0$ . These rays get reflected from the mirror…HardNumerical value
6 Apr 2026, Shift 1 · Q22Let the centre of the circle $x^2+y^2+2gx+2fy+25=0$ be in the first quadrant and lie on the line $2x-y=4$ . Let the area of an equilateral…MediumNumerical value
2 Apr 2025, Shift 2 · Q10Let the area of the triangle formed by a straight line $L : x + by + c = 0$ with co-ordinate axes be 48 square units. If the perpendicular…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.