Straight Lines

15 JEE Main questions · Maths

MathsJEE Main 21 Jan 2026, Shift 1·Q4·MCQ·Moderate
Open
Distance between parallel lines
Let a point $A$ lie between the parallel lines $L_1$ and $L_2$ such that its distances from $L_1$ and $L_2$ are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral triangle $ABC$ , where the points $B$ and $C$ lie on the lines $L_1$ and $L_2$ respectively, is:
1. (1) $15\sqrt6$
2. (2)27
3. (3) $21\sqrt3$
4. (4) $12\sqrt2$
MathsJEE Main 21 Jan 2026, Shift 2·Q25·Numerical·Moderate
Open
Image of point in line
If $P$ is a point on the circle $x^2 + y^2 = 4$ , $Q$ is a point on the straight line $5x + y + 2 = 0$ and $x - y + 1 = 0$ is the perpendicular bisector of $PQ$ , then 13 times the sum of abscissa of all such point $P$ is .
MathsJEE Main 22 Jan 2026, Shift 2·Q7·MCQ·Moderate
Open
Orthocentre and concurrent lines
Among the statements
- (S1): If $A(5, -1)$ and $B(-2, 3)$ are two vertices of a triangle, whose orthocentre is $(0, 0)$ , then its third vertex is $(-4, -7)$ and
- (S2): If positive numbers $2a$ , $b$ , $c$ are three consecutive terms of an A.P., then the lines $ax + by + c = 0$ are concurrent at $(2, -2)$ ,
1. (1)Only (S1) is correct
2. (2)Only (S2) is correct
3. (3)Both are incorrect
4. (4)Both are correct
MathsJEE Main 23 Jan 2026, Shift 1·Q4·MCQ·Easy–moderate
Open
Perpendicular line and point distance
A rectangle is formed by the lines $x = 0$ , $y = 0$ , $x = 3$ and $y = 4$ . Let the line $L$ be perpendicular to $3x + y + 6 = 0$ and divide the area of the rectangle into two equal parts. Then the distance of the point $\left(\dfrac12, -5\right)$ from the line $L$ is equal to:
1. (1) $2\sqrt5$
2. (2) $3\sqrt{10}$
3. (3) $\sqrt{10}$
4. (4) $2\sqrt{10}$
MathsJEE Main 23 Jan 2026, Shift 2·Q4·MCQ·Easy–moderate
Open
Diagonals of a rhombus
Let $A(1, 2)$ and $C(-3, -6)$ be two diagonally opposite vertices of a rhombus, whose sides $AD$ and $BC$ are parallel to the line $7x - y = 14$ . If $B(\alpha, \beta)$ and $D(\gamma, \delta)$ are the other two vertices, then $\lvert\alpha + \beta + \gamma + \delta\rvert$ is equal to:
1. (1)9
2. (2)3
3. (3)6
4. (4)1
We corrected a printing error in the original paper
Source printed “sides AD an BC”.
MathsJEE Main 24 Jan 2026, Shift 1·Q13·MCQ·Easy–moderate
Open
Angle bisector equation
Let $A(1, 0)$ , $B(2, -1)$ and $C\left(\dfrac73, \dfrac43\right)$ be three points. If the equation of the bisector of the angle $ABC$ is $\alpha x + \beta y = 5$ , then the value of $\alpha^2 + \beta^2$ is
1. (1)8
2. (2)5
3. (3)13
4. (4)10
MathsJEE Main 24 Jan 2026, Shift 2·Q3·MCQ·Moderate
Open
Parametric form of a line
Let the angles made with the positive $x$ -axis by two straight lines drawn from the point $P(2, 3)$ and meeting the line $x + y = 6$ at a distance $\sqrt{\dfrac23}$ from the point $P$ be $\theta_1$ and $\theta_2$ . Then the value of $(\theta_1 + \theta_2)$ is:
1. (1) $\dfrac{\pi}{12}$
2. (2) $\dfrac{\pi}{6}$
3. (3) $\dfrac{\pi}{2}$
4. (4) $\dfrac{\pi}{3}$
MathsJEE Main 28 Jan 2026, Shift 1·Q6·MCQ·Moderate
Open
Orthocentre of equilateral triangle
Let $ABC$ be an equilateral triangle with orthocenter at the origin and the side $BC$ on the line $x + 2\sqrt2\,y = 4$ . If the co-ordinates of the vertex $A$ are $(\alpha, \beta)$ , then the greatest integer less than or equal to $\lvert\alpha + \sqrt2\,\beta\rvert$ is
1. (1)2
2. (2)3
3. (3)5
4. (4)4
MathsJEE Main 2 Apr 2026, Shift 1·Q9·MCQ·Moderate
Open
Incentre of a triangle
Let the mid points of the sides of a triangle $ABC$ be $\left(\dfrac52, 7\right)$ , $\left(\dfrac52, 3\right)$ and $(4, 5)$ . If its incentre is $(h, k)$ , then $3h + k$ is equal to:
1. (1)11
2. (2)12
3. (3)13
4. (4)14
MathsJEE Main 4 Apr 2026, Shift 1·Q11·MCQ·Moderate
Open
Angle bisectors of two lines
Let 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 obtuse angle between the lines $L_2$ and $L_3$ intersect the line $L_1$ at the point $C$ . Then $BC^2 : AC^2$ is equal to:
1. (1) $5 : 1$
2. (2) $1 : 5$
3. (3) $2 : 3$
4. (4) $3 : 2$
MathsJEE Main 4 Apr 2026, Shift 1·Q12·MCQ·Moderate
Open
Centroid and circumcentre of triangle
Let the vertex $A$ of a triangle $ABC$ be $(1, 2)$ , and the mid-point of the side $AB$ be $(5, -1)$ . If the centroid of this triangle is $(3, 4)$ and its circumcenter is $(\alpha, \beta)$ , then $21(\alpha + \beta)$ is equal to:
1. (1)309
2. (2)403
3. (3)497
4. (4)524
MathsJEE Main 4 Apr 2026, Shift 2·Q23·Numerical·Moderate
Open
Angle bisector of two lines
Let $A$ , $B$ be points on the two half-lines $x - \sqrt3\,\lvert y\rvert = \alpha$ , $\alpha > 0$ at a distance of $\alpha$ from their point of intersection $P$ . The line segment $AB$ meets the angle bisector of the given half-lines at the point $Q$ . If $PQ = \dfrac92$ and $R$ is the radius of the circumcircle of $\triangle PAB$ , then $\dfrac{\alpha^2}{R}$ is equal to .
MathsJEE Main 5 Apr 2026, Shift 1·Q11·MCQ·Easy–moderate
Open
Orthocentre of equilateral triangle
In an equilateral triangle $PQR$ , let the vertex $P$ be at $(3, 5)$ and the side $QR$ be along the line $x + y = 4$ . If the orthocentre of the triangle $PQR$ is $(\alpha, \beta)$ , then $9(\alpha + \beta)$ is equal to:
1. (1)16
2. (2)27
3. (3)36
4. (4)48
MathsJEE Main 5 Apr 2026, Shift 2·Q22·Numerical·Tough
Open
Reflection of a line
From 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 $x + 2y = 1$ . If the equations of the reflected rays are $ax + by = 9$ and $cx + dy = 7$ , $a, b, c, d \in \mathbb{Z}$ , then the value of $ad + bc$ is .
MathsJEE Main 8 Apr 2026, Shift 2·Q10·MCQ·Moderate
Open
Locus of midpoint of intercepts
If a straight line drawn through the point of intersection of the lines $4x + 3y - 1 = 0$ and $3x + 4y - 1 = 0$ , meets the co-ordinate axes at the points $P$ and $Q$ , then the locus of the mid point of $PQ$ is:
1. (1) $x + y - 7 = 0$
2. (2) $x + y - 14xy = 0$
3. (3) $2x + y + 14xy = 0$
4. (4) $x + 2y - 14xy = 0$
We corrected a printing error in the original paper
Source printed “a straight line … meet the co-ordinate axes” (subject-verb agreement).