Parabola JEE Main PYQs PDF, 2020–2026

Parabola 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 104 of the 107 asked.

Topic-wise weightage by year

How many Parabola 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 13 JEE Main 2026 Parabola questions in the free PDF, latest shift first.

1. JEE Main 2026 · 8 Apr · Shift 2 · Parametric Form

   Let O be the vertex of the parabola $y^{2}=4x$ and its chords OP and OQ are perpendicular to each other. If the locus of the mid-point of the line segment PQ is a conic C , then the length of its latus rectum is :

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2. JEE Main 2026 · 6 Apr · Shift 1 · Parametric Form

   Let chord PQ of length $3\sqrt{13}$ of the parabola $y^{2}=12x$ be such that the ordinates of points P and Q are in the ratio 1:2. If the chord PQ subtends an angle $\alpha$ at the focus of the parabola, then $\sin \alpha$ is equal to :

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3. JEE Main 2026 · 5 Apr · Shift 2 · Focal Chord

   Let the directrix of the parabola ${\mathrm{P}}:y^{2}=8x$, cut $x$-axis at the point A . Let ${\mathrm{B}}(\alpha,\beta),\alpha>1$, be a point on $P$ such that the slope of $AB$ is $3/5$. If $BC$ is a focal chord of $P$, then six times the area of $\triangle ABC$ is :

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4. JEE Main 2026 · 4 Apr · Shift 2 · Parametric Form

   Let ${\mathrm{A}},{\mathrm{B}}$ and C be the vertices of a variable right angled triangle inscribed in the parabola $y^{2}=16x$. Let the vertex $B$ containing the right angle be $(4,8)$ and the locus of the centroid of $\triangle ABC$ be a conic $C_{0}$. Then three times the length of latus rectum of ${\mathrm{C}}_{0}$ is $\_\_\_\_$

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5. JEE Main 2026 · 2 Apr · Shift 2 · Parametric Form

   Let the parabola $y=x^{2}+px+q$ passing through the point $(1,-1)$ be such that the distance between its vertex and the $x$-axis is minimum. Then the value of $p^{2}+q^{2}$ is :

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6. JEE Main 2026 · 28 Jan · Shift 2 · Parametric Form

   Let A be the focus of the parabola $y^{2}=8x$. Let the line $y=mx+c$ intersect the parabola at two distinct points B and C. If the centroid of the triangle ABC is $\left(\frac{7}{3},\frac{4}{3}\right)$, then $(BC)^{2}$ is equal to :

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7. JEE Main 2026 · 24 Jan · Shift 2 · Parametric Form

   Let the image of parabola $x^{2}=4y$, in the line $x-y=1$ be $(y+a)^{2}=b(x-c)$, $a,b,c\in {\ \mathrm{N}}$. Then $a+b+c$ is equal to

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8. JEE Main 2026 · 23 Jan · Shift 2 · Parametric Form

   An equilateral triangle OAB is inscribed in the parabola $y^{2}=4x$ with the vertex O at the vertex of the parabola. Then the minimum distance of the circle having $AB$ as a diameter from the origin is

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9. JEE Main 2026 · 22 Jan · Shift 1 · Parametric Form

   If the chord joining the points ${\mathrm{P}}_{1}(x_{1},y_{1})$ and ${\mathrm{P}}_{2}(x_{2},y_{2})$ on the parabola $y^{2}=12x$ subtends a right angle at the vertex of the parabola, then $x_{1}x_{2}-y_{1}y_{2}$ is equal to

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10. JEE Main 2026 · 22 Jan · Shift 2 · Parametric Form

    Let the locus of the mid-point of the chord through the origin $O$ of the parabola $y^{2}=4x$ be the curve S . Let P be any point on S . Then the locus of the point, which internally divides OP in the ratio 3 : 1, is :

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11. JEE Main 2026 · 21 Jan · Shift 2 · Focal Chord

    Let one end of a focal chord of the parabola $y^{2}=16x$ be $(16,16)$. If $P(\alpha,\ \beta)$ divides this focal chord internally in the ratio $5:2$, then the minimum value of $\alpha+\beta$ is equal to:

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12. JEE Main 2026 · 21 Jan · Shift 1 · Chord of Contact

    Let O be the vertex of the parabola $x^{2}=4y$ and Q be any point on it. Let the locus of the point P , which divides the line segment OQ internally in the ratio $2:3$ be the conic C . Then the equation of the chord of $C$, which is bisected at the point $(1,2)$, is :

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Practise the 2026 Parabola questions online

Sample questions from recent papers

The free PDF above has all 104 questions grouped by topic, with an answer key.

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JEE Main PYQs by year: 2026 · 2025 · 2024 · 2023 · 2022 · 2021 · 2020