Straight Lines JEE Main PYQs PDF, 2020–2026

Straight Lines questions per year

in the free PDF asked, not in the PDFThe PDF only has questions we can print in full with a checked answer, so it holds 123 of the 130 asked.

Topic-wise weightage by year

How many Straight Lines questions each topic had in every JEE Main year (all shifts), counting every question asked, including ones not in the PDF. Darker cells mean more questions.

Swipe the table sideways for older years.

Newest questions (2026)

The 12 newest of the 14 JEE Main 2026 Straight Lines questions in the free PDF, latest shift first.

1. JEE Main 2026 · 8 Apr · Shift 2 · Family of Lines

   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 :

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2. JEE Main 2026 · 5 Apr · Shift 1 · Distance and Section Formula

   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:

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3. JEE Main 2026 · 5 Apr · Shift 2 · Forms 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 ${\mathrm{a}}x+{\mathrm{b}}y=9$ and $cx+dy=7,a,b,c,d\in {\mathbf{Z}}$, then the value of $ad+bc$ is $\_\_\_\_$ .

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4. JEE Main 2026 · 4 Apr · Shift 1 · Angle Between Lines

   Let the line ${\mathrm{L}}_{1}:x+3=0$ intersect the lines ${\mathrm{L}}_{2}:x-y=0$ and ${\mathrm{L}}_{3}:3x+y=0$ 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:

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5. JEE Main 2026 · 4 Apr · Shift 2 · Angle Between Lines

   Let ${\mathrm{A}},{\mathrm{B}}$ be points on the two half-lines $x-\sqrt{3}|y|=\alpha,\alpha>0$ 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 $PQ=\frac{9}{2}$ and $R$ is the radius of the circumcircle of $\triangle {\mathrm{PAB}}$, then $\frac{\alpha^{2}}{R}$ is equal to $\_\_\_\_$

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6. JEE Main 2026 · 4 Apr · Shift 1 · Distance and Section Formula

   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 :

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7. JEE Main 2026 · 2 Apr · Shift 1 · Distance and Section Formula

   Let 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 incentre is $(h,k)$, then $3h+k$ is equal to :

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8. JEE Main 2026 · 28 Jan · Shift 1 · Distance from a Point to a Line

   Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the line $x+2\sqrt{2}y=4$. If the co-ordinates of the vertex A are $(\alpha,\beta)$, then the greatest integer less than or equal to $|\alpha+\sqrt{2}\beta|$ is

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9. JEE Main 2026 · 24 Jan · Shift 1 · Angle Between Lines

   Let $A(1,0),B(2,-1)$ and $C\left(\frac{7}{3},\frac{4}{3}\right)$ 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

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10. JEE Main 2026 · 24 Jan · Shift 2 · Angle Between Lines

    Let the angles made with the positive $x$-axis by two straight lines drawn from the point ${\mathrm{P}}(2,3)$ and meeting the line $x+y=6$ at a distance $\sqrt{\frac{2}{3}}$ from the point P be $\theta_{1}$ and $\theta_{2}$. Then the value of $(\theta_{1}+\theta_{2})$ is:

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11. JEE Main 2026 · 23 Jan · Shift 1 · Distance from a Point to a Line

    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 $\left(\frac{1}{2},-5\right)$ from the line $L$ is equal to :

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12. JEE Main 2026 · 23 Jan · Shift 2 · Forms of a Line

    Let ${\mathrm{A}}(1,2)$ and ${\mathrm{C}}(-3,-6)$ be two diagonally opposite vertices of a rhombus, whose sides AD and BC are parallel to the line $7x-y=14$. If ${\mathrm{B}}(\alpha,\beta)$ and ${\mathrm{D}}(\gamma,\delta)$ are the other two vertices, then $|\alpha+\beta+\gamma+\delta|$ is equal to :

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Practise the 2026 Straight Lines questions online

Sample questions from recent papers

The free PDF above has all 123 questions grouped by topic, with an answer key.

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