Circles JEE Main PYQs PDF, 2020–2026

Circles questions per year

Topic-wise weightage by year

How many Circles 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 15 JEE Main 2026 Circles questions in the free PDF, latest shift first.

1. JEE Main 2026 · 8 Apr · Shift 2 · Equation of a Circle

   Consider the circle C : $x^{2}+y^{2}-6x-8y-11=0$. Let a variable chord AB of the circle C subtend a right angle at the origin. If the locus of the foot of the perpendicular drawn from the origin on the chord AB is the circle $x^{2}+y^{2}-\alpha x-\beta y-\gamma=0$, then $\alpha+\beta+2\gamma$ is equal to $\_\_\_\_$ .

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2. JEE Main 2026 · 6 Apr · Shift 2 · Equation of a Circle

   Let the line $x-y=4$ intersect the circle ${\mathrm{C}}:(x-4)^{2}+(y+3)^{2}=9$ at the points Q and R . If ${\mathrm{P}}(\alpha,\beta)$ is a point on C such that ${\mathrm{PQ}}={\mathrm{PR}}$, then $(6\alpha+8\beta)^{2}$ is equal to $\_\_\_\_$ .

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3. JEE Main 2026 · 6 Apr · Shift 2 · Intersection of Two Circles

   Let C be a circle having centre in the first quadrant and touching the $x$-axis at a distance of 3 units from the origin. If the circle $C$ has an intercept of length $6\sqrt{3}$ on $y$-axis, then the length of the chord of the circle C on the line $x-y=3$ is :

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4. JEE Main 2026 · 6 Apr · Shift 1 · Intersection of Two Circles

   Let the centre of the circle $x^{2}+y^{2}+2{\ \mathrm{g}}x+2fy+25=0$ be in the first quadrant and lie on the line $2x-y=4$. Let the area of an equilateral triangle inscribed in the circle be $27\sqrt{3}$. Then the square of the length of the chord of the circle on the line $x=1$ is $\_\_\_\_$ .

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5. JEE Main 2026 · 5 Apr · Shift 2 · Equation of a Circle

   Let the point P be the vertex of the parabola $y=x^{2}-6x+12$. If a line passing through the point P intersects the circle $x^{2}+y^{2}-2x-4y+3=0$ at the points R and S , then the maximum value of $({\mathrm{PR}}+{\mathrm{PS}})^{2}$ is :

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6. JEE Main 2026 · 5 Apr · Shift 1 · Equation of a Circle

   Let P be a moving point on the circle $x^{2}+y^{2}-6x-8y+21=0$. Then, the maximum distance of P from the vertex of the parabola $x^{2}+6x+y+13=0$ is equal to:

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7. JEE Main 2026 · 4 Apr · Shift 1 · Chord of Contact

   Suppose that two chords, drawn from the point $(1,2)$ on the circle $x^{2}+y^{2}+x-3y=0$ are bisected by the $y$-axis. If the other ends of these chords are R and S , and the mid point of the line segment RS is $(\alpha,\beta)$, then $6(\alpha+\beta)$ is equal to :

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8. JEE Main 2026 · 2 Apr · Shift 2 · Intersection of Two Circles

   Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines $x+(k-1)y+3=0$ and $2x+k^{2}y-4=0$. If the line $x-y+2=0$ intersects the circle at the points A and B, then $(AB)^{2}$ is equal to :

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9. JEE Main 2026 · 2 Apr · Shift 1 · Intersection of Two Circles

   Let a circle C have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts from the coordinate axes. If the length of the chord of C on the line $x+y=1$ is $\sqrt{14}$, then the square of the radius of C is ________.

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10. JEE Main 2026 · 28 Jan · Shift 1 · Equation of a Circle

    Let $y=x$ be the equation of a chord of the circle ${\mathrm{C}}_{1}$ (in the closed half-plane $x\geq 0$ ) of diameter 10 passing through the origin. Let ${\mathrm{C}}_{2}$ be another circle described on the given chord as its diameter. If the equation of the chord of the circle ${\mathrm{C}}_{2}$, which passes through the point $(2,3)$ and is farthest from the center of ${\mathrm{C}}_{2}$, is $x+ay+b=0$, then $a-b$ is equal to

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11. JEE Main 2026 · 28 Jan · Shift 2 · Equation of a Circle

    Let the circle $x^{2}+y^{2}=4$ intersect x-axis at the points A$(a,0)$, $a>0$ and B$(b,0)$. Let $P(2\cos \alpha,2\sin \alpha)$, $0<\alpha<\frac{\pi}{2}$ and $Q(2\cos \beta,2\sin \beta)$ be two points such that $(\alpha-\beta)=\frac{\pi}{2}$. Then the point of intersection of AQ and BP lies on :

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12. JEE Main 2026 · 24 Jan · Shift 1 · Family of Circles

    Let a circle of radius 4 pass through the origin O , the points ${\mathrm{A}}(-\sqrt{3}a,0)$ and ${\mathrm{B}}(0,-\sqrt{2}b)$, where $a$ and $b$ are real parameters and $ab\neq 0$. Then the locus of the centroid of $\triangle {\mathrm{OAB}}$ is a circle of radius

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Sample questions from recent papers

The free PDF above has all 117 questions grouped by topic, with an answer key.

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