Circles

JEE Main · Mathematics · 12 past questions

These are the board's own papers. 134 more board questions reprinted in the books we use in class are for signed-in students: sign in.

1. Q1 2026 2 Apr Shift 1

   Let a circle C have its centre in the first quadrant, intersect the coordinate axes at exactly three points…

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2. Q2 2026 2 Apr Shift 2

   Let the circles $C_1 : |z| = r$ and $C_2 : |z-3-4i| = 5$, $z \in \mathbb{C}$, be such that $C_2$ lies within…

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3. Q3 2026 2 Apr Shift 2

   Let a circle pass through the origin and its centre be the point of intersection of two mutually…

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4. Q4 2026 4 Apr Shift 1

   Suppose that two chords, drawn from the point $(1, 2)$ on the circle $x^2+y^2+x-3y=0$ are bisected by the…

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5. Q5 2026 4 Apr Shift 2

   Let $A = \begin{bmatrix} 1 & 2 & 7 \\ 4 & -2 & 8 \\ 3 & 8 & -7 \end{bmatrix}$ and $\det(A - \alpha I) = 0$…

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6. Q6 2026 4 Apr Shift 2

   Let $P(3\cos\alpha, 2\sin\alpha)$, $\alpha \neq 0$, be a point on the ellipse…

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7. Q7 2026 5 Apr Shift 1

   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…

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8. Q8 2026 5 Apr Shift 2

   Let the point P be the vertex of the parabola $y = x^2 - 6x + 12$. If a line passing through the point P…

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9. Q9 2026 6 Apr Shift 1

   Let the centre of the circle $x^2+y^2+2gx+2fy+25=0$ be in the first quadrant and lie on the line $2x-y=4$.…

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10. Q10 2026 6 Apr Shift 2

    Let C be a circle having centre in the first quadrant and touching the $x$-axis at a distance of 3 units from…

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11. Q11 2026 6 Apr Shift 2

    Let the line $x-y=4$ intersect the circle $C: (x-4)^2+(y+3)^2=9$ at the points Q and R. If $P(\alpha,\beta)$…

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12. Q12 2026 8 Apr Shift 2

    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…

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