JEE MAIN Circle Previous Year Question Paper and Solution with PDF

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Previous Year Questions

JEE MAIN
Previous Year Questions
JEE MAIN

JEE MAIN Previous Year Questions (PYQs)

JEE MAIN Circle PYQ

Qus : 1 JEE MAIN PYQ

If the angle of intersection at a point where two circles with radii $5\text{ cm}$ and $12\text{ cm}$ intersect is $90^\circ$, then the length (in cm) of their common chord is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 April Morning Shift) PYQ

Solution

Qus : 2 JEE MAIN PYQ

Let the arc $AC$ of a circle subtend a right angle at the centre $O$. If the point $B$ on the arc $AC$ divides the arc $AC$ such that $\dfrac{\text{length of arc }AB}{\text{length of arc }BC}=\dfrac{1}{5}$, and $\overrightarrow{OC}=\alpha\,\overrightarrow{OA}+\beta\,\overrightarrow{OB}$, then $\alpha+\sqrt{2}\,(\sqrt{3}-1)\,\beta$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (23 January Morning Shift) PYQ

Solution

Qus : 3 JEE MAIN PYQ

Let $P$ and $Q$ be any points on the curves $(x-1)^{2}+(y+1)^{2}=1$ and $y=x^{2}$, respectively. The distance between $P$ and $Q$ is minimum for some value of the abscissa of $P$ in the interval:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (26 July Evening Shift) PYQ

Solution

Qus : 4 JEE MAIN PYQ

Let the abscissae of the two points $P$ and $Q$ on a circle be the roots of $x^{2}-4x-6=0$ and the ordinates of $P$ and $Q$ be the roots of $y^{2}+2y-7=0$. If $PQ$ is a diameter of the circle $x^{2}+y^{2}+2ax+2by+c=0$, then the value of $(a+b-c)$ is _________. (A)

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (26 July Evening Shift) PYQ

Solution

Qus : 5 JEE MAIN PYQ

Let $C$ be a circle with radius $\sqrt{10}$ units and centre at the origin. Let the line $x+y=2$ intersect the circle $C$ at the points $P$ and $Q$. Let $MN$ be a chord of $C$ of length $2$ units and slope $-1$. Then, the distance (in units) between the chord $PQ$ and the chord $MN$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (4 April Evening Shift) PYQ

Solution

Qus : 6 JEE MAIN PYQ

If the area of an equilateral triangle inscribed in the circle $x^{2}+y^{2}+10x+12y+c=0$ is $27\sqrt{3}$ sq units, then $c$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 January Evening Shift) PYQ

Solution

Qus : 7 JEE MAIN PYQ

Let $A = \begin{pmatrix} 1 & 2 \\ -2 & -5 \end{pmatrix}$. Let $\alpha, \beta \in \mathbb{R}$ be such that $\alpha A^2 + \beta A = 2I$. Then $\alpha + \beta$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (27 July Morning Shift) PYQ

Solution

Qus : 8 JEE MAIN PYQ

A circle touching the $x$-axis at $(3,0)$ and making an intercept of length $8$ on the $y$-axis passes through the point:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 April Evening Shift) PYQ

Solution

Qus : 9 JEE MAIN PYQ

Let $C_1$ be the circle in the third quadrant of radius 3 , that touches both coordinate axes. Let $C_2$ be the circle with centre $(1,3)$ that touches $\mathrm{C}_1$ externally at the point $(\alpha, \beta)$. If $(\beta-\alpha)^2=\frac{m}{n}$ , $\operatorname{gcd}(m, n)=1$, then $m+n$ is equal to

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (7 April Morning Shift) PYQ

Solution

Qus : 10 JEE MAIN PYQ

A square is inscribed in the circle $x^{2}+y^{2}-6x+8y-103=0$ with its sides parallel to the coordinate axes. Then the distance of the vertex of this square which is nearest to the origin is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (11 January Morning Shift) PYQ

Solution

Qus : 11 JEE MAIN PYQ

If the circle $x^{2} + y^{2} - 2gx + 6y - 19c = 0,; g,c \in \mathbb{R}$ passes through the point $(6,1)$ and its centre lies on the line $x - 2cy = 8$, then the length of intercept made by the circle on $x$-axis is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (27 July Morning Shift) PYQ

Solution

Qus : 12 JEE MAIN PYQ

Let a circle $C$ of radius $1$ and closer to the origin be such that the lines passing through the point $(3,2)$ and parallel to the coordinate axes touch it. Then the shortest distance of the circle $C$ from the point $(5,5)$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (5 April Morning Shift) PYQ

Solution

Qus : 13 JEE MAIN PYQ

The straight line $x+2y=1$ meets the coordinate axes at $A$ and $B$. A circle is drawn through $A$, $B$ and the origin. Then the sum of perpendicular distances from $A$ and $B$ on the tangent to the circle at the origin is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (11 January Morning Shift) PYQ

Solution

Qus : 14 JEE MAIN PYQ

Let the system of equations :$ \begin{aligned} & 2 x+3 y+5 z=9 \\ & 7 x+3 y-2 z=8 \\ & 12 x+3 y-(4+\lambda) z=16-\mu \end{aligned}$$

have infinitely many solutions. Then the radius of the circle centred at $(\lambda, \mu)$ and touching the line $4 x=3 y$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (7 April Morning Shift) PYQ

Solution

Qus : 15 JEE MAIN PYQ

Let $\mathbb{N}$ be the set of natural numbers and a relation $R$ on $\mathbb{N}$ be defined by \[ R=\{(x,y)\in \mathbb{N}\times \mathbb{N} : x^{3}-3x^{2}y-xy^{2}+3y^{3}=0\}. \] Then the relation $R$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (27 July Evening Shift) PYQ

Solution

Qus : 16 JEE MAIN PYQ

Consider a circle C which touches the y-axis at (0, 6) and cuts off an intercept $6\sqrt 5 $ on the x-axis. Then the radius of the circle C is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (27 July Evening Shift) PYQ

Solution

Qus : 17 JEE MAIN PYQ

Let the line $2x+3y-k=0,\ k>0$ intersect the $x$-axis and $y$-axis at points $A$ and $B$, respectively. If the circle having $AB$ as a diameter is $x^{2}+y^{2}-3x-2y=0$ and the length of the latus rectum of the ellipse $x^{2}+9y^{2}=k^{2}$ is $\dfrac{m}{n}$, where $m$ and $n$ are coprime, then $2m+n$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (5 April Morning Shift) PYQ

Solution

Qus : 18 JEE MAIN PYQ

Let the circle $C_1: x^2+y^2-2(x+y)+1=0$ and $C_2$ be a circle with centre $(-1,0)$ and radius $2$. If the line of the common chord of $C_1$ and $C_2$ meets the $y$-axis at the point $P$, then the square of the distance of $P$ from the centre of $C_1$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (5 April Evening Shift) PYQ

Solution

Qus : 19 JEE MAIN PYQ

If a line along a chord of the circle 4x² + 4y² + 120x + 675 = 0, passes through the point ($-$30, 0) and is tangent to the parabola y² = 30x, then the length of this chord is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (26 August Morning Shift) PYQ

Solution

Qus : 20 JEE MAIN PYQ

Let $C$ be the centre of the circle $x^{2}+y^{2}-x+2y=\dfrac{11}{4}$ and $P$ be a point on the circle. A line passes through the point $C$, makes an angle of $\dfrac{\pi}{4}$ with the line $CP$ and intersects the circle at the points $Q$ and $R$. Then the area of the triangle $PQR$ (in unit$^{2}$) is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 July Morning Shift) PYQ

Solution

Qus : 21 JEE MAIN PYQ

Four distinct points $(2k,3k)$, $(1,0)$, $(0,1)$ and $(0,0)$ lie on a circle for $k$ equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (27 January Morning Shift) PYQ

Solution

Qus : 22 JEE MAIN PYQ

Let $ABCD$ and $AEFG$ be squares of side $4$ and $2$ units, respectively. The point $E$ is on the line segment $AB$ and the point $F$ is on the diagonal $AC$. Then the radius $r$ of the circle passing through the point $F$ and touching the line segments $BC$ and $CD$ satisfies:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (5 April Evening Shift) PYQ

Solution

Qus : 23 JEE MAIN PYQ

For $t\in(0,2\pi)$, if $\triangle ABC$ is an equilateral triangle with vertices $A(\sin t,-\cos t)$, $B(\cos t,\sin t)$ and $C(a,b)$ such that its orthocentre lies on a circle with centre $\left(1,\tfrac{1}{3}\right)$, then $(a^{2}-b^{2})$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 July Morning Shift) PYQ

Solution

Qus : 24 JEE MAIN PYQ

Let circle $C$ be the image of $x^2 + y^2 - 2x + 4y - 4 = 0$ in the line $2x - 3y + 5 = 0$ and $A$ be the point on $C$ such that $OA$ is parallel to $x$-axis and $A$ lies on the right hand side of the centre $O$ of $C$. If $B(\alpha,\beta)$, with $\beta < 4$, lies on $C$ such that the length of the arc $AB$ is $(1/6)^{\text{th}}$ of the perimeter of $C$, then $\beta - \sqrt{3},\alpha$ is equal to

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (24 January Morning Shift) PYQ

Solution

Qus : 25 JEE MAIN PYQ

A circle C touches the line x = 2y at the point (2, 1) and intersects the circle C₁ : x² + y² + 2y $-$ 5 = 0 at two points P and Q such that PQ is a diameter of C₁. Then the diameter of C is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (26 August Evening Shift) PYQ

Solution

Qus : 26 JEE MAIN PYQ

A circle cuts a chord of length $4a$ on the $x$-axis and passes through a point on the $y$-axis, distant $2b$ from the origin. Then the locus of the centre of this circle, is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (11 January Evening Shift) PYQ

Solution

Qus : 27 JEE MAIN PYQ

Let $\left(5,\dfrac{9}{4}\right)$ be the circumcenter of a triangle with vertices $A(a,-2)$, $B(a,6)$ and $C\!\left(\dfrac{a}{4},-2\right)$. Let $\alpha$ denote the circumradius, $\beta$ denote the area and $\gamma$ denote the perimeter of the triangle. Then $\alpha+\beta+\gamma$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (29 January Morning Shift) PYQ

Solution

Qus : 28 JEE MAIN PYQ

Let $C$ be the circle of minimum area touching the parabola $y=6-x^{2}$ and the lines $y=\sqrt{3},|x|$. Which of the following points lies on $C$?

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (6 April Morning Shift) PYQ

Solution

Qus : 29 JEE MAIN PYQ

In the circle given below, let OA = 1 unit, OB = 13 unit and PQ $ \bot $ OB. Then, the area of the triangle PQB (in square units) is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (26 February Morning Shift) PYQ

Solution

Qus : 30 JEE MAIN PYQ

Let A(1, 4) and B(1, $-$5) be two points. Let P be a point on the circle (x $-$ 1)² + (y $-$ 1)² = 1 such that (PA)² + (PB)² have maximum value, then the points, P, A and B lie on :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (26 February Evening Shift) PYQ

Solution

Qus : 31 JEE MAIN PYQ

Let the equation of the circle, which touches $x$-axis at the point $(a,0)$, $a>0$, and cuts off an intercept of length $b$ on $y$-axis be $x^{2}+y^{2}-\alpha x+\beta y+\gamma=0$. If the circle lies below $x$-axis, then the ordered pair $(2a,,b^{2})$ is equal to

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (28 January Morning Shift) PYQ

Solution

Qus : 32 JEE MAIN PYQ

A line segment $AB$ of length $\lambda$ moves such that the points $A$ and $B$ remain on the periphery of a circle of radius $\lambda$. Then the locus of the point that divides the line segment $AB$ in the ratio $2:3$ is a circle of radius:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (10 April Morning Shift) PYQ

Solution

Qus : 33 JEE MAIN PYQ

If the locus of the mid-point of the line segment from the point (3, 2) to a point on the circle, x² + y² = 1 is a circle of radius r, then r is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (26 February Evening Shift) PYQ

Solution

Qus : 34 JEE MAIN PYQ

Let $A$ be the point $(1, 2)$ and $B$ be any point on the curve $x^2 + y^2 = 16$. If the centre of the locus of the point $P$, which divides the line segment $AB$ in the ratio $3 : 2$, is the point $C(\alpha, \beta)$, then the length of the line segment $AC$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (10 April Evening Shift) PYQ

Solution

Qus : 35 JEE MAIN PYQ

If a circle $C$, whose radius is $3$, touches externally the circle $x^{2}+y^{2}+2x-4y-4=0$ at the point $(2,2)$, then the length of the intercept cut by this circle $C$ on the $x$-axis is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

Solution

Qus : 36 JEE MAIN PYQ

The locus of the midpoints of the chord of the circle, x² + y² = 25 which is tangent to the hyperbola, ${{{x^2}} \over 9} - {{{y^2}} \over {16}} = 1$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (16 March Morning Shift) PYQ

Solution

Qus : 37 JEE MAIN PYQ

If the locus of a point whose distances from $(2,1)$ and $(1,3)$ are in the ratio $5:4$ is $ax^{2}+by^{2}+cxy+dx+ey+170=0$, then the value of $a^{2}+2b+3c+4d+e$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (6 April Evening Shift) PYQ

Solution

Qus : 38 JEE MAIN PYQ

If the circles $(x+1)^2+(y+2)^2=r^2$ and $x^2+y^2-4x-4y+4=0$ intersect at exactly two distinct points, then:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (30 January Morning Shift) PYQ

Solution

Qus : 39 JEE MAIN PYQ

Let the circles $C_1:(x-\alpha)^2+(y-\beta)^2=r_1^2$ and $C_2:(x-8)^2+\left(y-\dfrac{15}{2}\right)^2=r_2^2$ touch each other externally at the point $(6,6)$. If the point $(6,6)$ divides the line segment joining the centres of the circles $C_1$ and $C_2$ internally in the ratio $2:1$, then $(\alpha+\beta)+4\left(r_1^2+r_2^2\right)$ equals:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (8 April Morning Shift) PYQ

Solution

Qus : 40 JEE MAIN PYQ

Let $(5, \tfrac{a}{4})$ be the circumcenter of a triangle with vertices $A(a, -2)$, $B(a, 6)$ and $C\left(\tfrac{a}{4}, -2\right)$. Let $\alpha$ denote the circumradius, $\beta$ denote the area and $\gamma$ denote the perimeter of the triangle. Then $\alpha + \beta + \gamma$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (29 January Morning Shift) PYQ

Solution

Qus : 41 JEE MAIN PYQ

The locus of the mid-points of the chords of the circle $C_{1} : (x-4)^{2}+(y-5)^{2}=4$ which subtend an angle $\theta_{i}$ at the centre of the circle $C_{1}$, is a circle of radius $r_{i}$. If $\theta_{1}=\dfrac{\pi}{3}$, $\theta_{3}=\dfrac{2\pi}{3}$ and $r_{1}^{2}=r_{2}^{2}+r_{3}^{2}$, then $\theta_{2}$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (24 January Evening Shift) PYQ

Solution

Qus : 42 JEE MAIN PYQ

Let the lengths of intercepts on x-axis and y-axis made by the circle x² + y² + ax + 2ay + c = 0, (a < 0) be 2${\sqrt 2 }$ and 2${\sqrt 5 }$, respectively. Then the shortest distance from origin to a tangent to this circle which is perpendicular to the line x + 2y = 0, is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (16 March Evening Shift) PYQ

Solution

Qus : 43 JEE MAIN PYQ

The sum of the squares of the lengths of the chords intercepted on the circle $x^{2}+y^{2}=16$, by the lines $x+y=n,\ n\in\mathbb{N}$, where $\mathbb{N}$ is the set of all natural numbers, is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (8 April Morning Shift) PYQ

Solution

Qus : 44 JEE MAIN PYQ

In a triangle PQR, the co-ordinates of the points P and Q are ($-$2, 4) and (4, $-$2) respectively. If the equation of the perpendicular bisector of PR is 2x $-$ y + 2 = 0, then the centre of the circumcircle of the $\Delta $PQR is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (17 March Morning Shift) PYQ

Solution

Qus : 45 JEE MAIN PYQ

If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the center and subtend angles $\cos^{-1}\left(\dfrac{1}{7}\right)$ and $\sec^{-1}(7)$ at the center respectively, then the distance between these chords, is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2017 (8 April Morning Shift) PYQ

Solution

Qus : 46 JEE MAIN PYQ

The set of values of k, for which the circle $C:4{x^2} + 4{y^2} - 12x + 8y + k = 0$ lies inside the fourth quadrant and the point $\left( {1, - {1 \over 3}} \right)$ lies on or inside the circle C, is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (27 June Evening Shift) PYQ

Solution

Qus : 47 JEE MAIN PYQ

The points of intersection of the line $ax+by=0,\ (a\ne b)$ and the circle $x^{2}+y^{2}-2x=0$ are $A(\alpha,0)$ and $B(1,\beta)$. The image of the circle with $AB$ as a diameter in the line $x+y+2=0$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (25 January Morning Shift) PYQ

Solution

Qus : 48 JEE MAIN PYQ

If a point P has co-ordinates (0,-2) and Q is any point on the circle $x^{2}+y^{2}-5x-y+5=0$, then the maximum value of $(PQ)^{2}$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2017 (8 April Morning Shift) PYQ

Solution

Qus : 49 JEE MAIN PYQ

If the image of the point $(-4,5)$ in the line $x+2y=2$ lies on the circle $(x+4)^{2}+(y-3)^{2}=r^{2}$, then $r$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (8 April Evening Shift) PYQ

Solution

Qus : 50 JEE MAIN PYQ

The two adjacent sides of a cyclic quadrilateral are $2$ and $5$ and the angle between them is $60^\circ$. If the area of the quadrilateral is $4\sqrt{3}$, then the perimeter of the quadrilateral is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2017 (9 April Morning Shift) PYQ

Solution

Qus : 51 JEE MAIN PYQ

Let a circle passing through $(2, 0)$ have its centre at the point $(h, k)$. Let $(x_c, y_c)$ be the point of intersection of the lines $3x + 5y = 1$ and $(2 + c)x + 5c^{2}y = 1$. If $h = \lim_{c \to 1} x_c$ and $k = \lim_{c \to 1} y_c$, then the equation of the circle is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (9 April Morning Shift) PYQ

Solution

Qus : 52 JEE MAIN PYQ

A line drawn through the point $P(4,7)$ cuts the circle $x^{2} + y^{2} = 9$ at the points $A$ and $B$. Then $PA \cdot PB$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2017 (9 April Morning Shift) PYQ

Solution

Qus : 53 JEE MAIN PYQ

For the four circles M, N, O and P, following four equations are given :Circle M : x² + y² = 1, Circle N : x² + y² $-$ 2x = 0 ,Circle O : x² + y² $-$ 2x $-$ 2y + 1 = 0, Circle P : x² + y² $-$ 2y = 0

If the centre of circle M is joined with centre of the circle N, further center of circle N is joined with centre of the circle O, centre of circle O is joined with the centre of circle P and lastly, centre of circle P is joined with centre of circle M, then these lines form the sides of a :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (18 March Morning Shift) PYQ

Solution

Qus : 54 JEE MAIN PYQ

Let the tangents at the points $A(4,-11)$ and $B(8,-5)$ on the circle $x^{2}+y^{2}-3x+10y-15=0$, intersect at the point $C$. Then the radius of the circle, whose centre is $C$ and the line joining $A$ and $B$ is its tangent, is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (29 January Morning Shift) PYQ

Solution

Qus : 55 JEE MAIN PYQ

If one of the diameters of the circle $x^{2}+y^{2}-10x+4y+13=0$ is a chord of another circle $C$, whose center is the point of intersection of the lines $2x+3y=12$ and $3x-2y=5$, then the radius of the circle $C$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (31 January Morning Shift) PYQ

Solution

Qus : 56 JEE MAIN PYQ

A rectangle is inscribed in a circle with a diameter lying along the line $3y=x+7$. If the two adjacent vertices of the rectangle are $(-8,5)$ and $(6,5)$, then the area of the rectangle (in sq. units) is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (9 April Evening Shift) PYQ

Solution

Qus : 57 JEE MAIN PYQ

If one of the diameters of the circle, given by the equation, $ x^{2} + y^{2} - 4x + 6y - 12 = 0 $, is a chord of a circle $S$, whose centre is at $(-3, 2)$, then the radius of $S$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

Qus : 58 JEE MAIN PYQ

A circle passes through $(-2,4)$ and touches the $y$-axis at $(0,2)$. Which one of the following equations can represent a diameter of this circle?

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

Qus : 59 JEE MAIN PYQ

Let a triangle ABC be inscribed in the circle ${x^2} - \sqrt 2 (x + y) + {y^2} = 0$ such that $\angle BAC = {\pi \over 2}$. If the length of side AB is $\sqrt 2 $, then the area of the $\Delta$ABC is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (29 June Evening Shift) PYQ

Solution

Qus : 60 JEE MAIN PYQ

A circle $C$ of radius $2$ lies in the second quadrant and touches both the coordinate axes. Let $r$ be the radius of a circle that has centre at the point $(2,5)$ and intersects the circle $C$ at exactly two points. If the set of all possible values of $r$ is the interval $(\alpha,\beta)$, then $3\beta-2\alpha$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (22 January Morning Shift) PYQ

Solution

Qus : 61 JEE MAIN PYQ

Let $C:\ x^{2}+y^{2}=4$ and $C':\ x^{2}+y^{2}-4\lambda x+9=0$ be two circles. If the set of all values of $\lambda$ for which the circles $C$ and $C'$ intersect at two distinct points is $\mathbb{R}\setminus [a,b]$, then the point $(\,8a+12,\ 16b-20\,)$ lies on the curve:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (1 February Morning Shift) PYQ

Solution

Qus : 62 JEE MAIN PYQ

Let the circle S : 36x² + 36y² $-$ 108x + 120y + C = 0 be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, x $-$ 2y = 4 and 2x $-$ y = 5 lies inside the circle S, then :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (22 July Evening Shift) PYQ

Solution

Qus : 63 JEE MAIN PYQ

Let the locus of the centre $(\alpha,\beta)$, $\beta>0$, of the circle which touches the circle $x^2+(y-1)^2=1$ externally and also touches the $x$-axis be $L$. Then the area bounded by $L$ and the line $y=4$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (25 July Morning Shift) PYQ

Solution

Qus : 64 JEE MAIN PYQ

Let the locus of the midpoints of the chords of the circle $x^{2}+(y-1)^{2}=1$ drawn from the origin intersect the line $x+y=1$ at $P$ and $Q$. Then, the length of $PQ$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (1 February Evening Shift) PYQ

Solution

Qus : 65 JEE MAIN PYQ

If the four distinct points $(4,6)$, $(-1,5)$, $(0,0)$ and $(k,3k)$ lie on a circle of radius $r$, then $10k+r^2$ is equal to

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (3 April Evening Shift) PYQ

Solution

Qus : 66 JEE MAIN PYQ

A square is inscribed in the circle $x^2 + y^2 - 10x - 6y + 30 = 0$. One side of this square is parallel to $y = x + 3$. If $(x_i, y_i)$ are the vertices of the square, then $\displaystyle \sum \big(x_i^2 + y_i^2\big)$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (4 April Morning Shift) PYQ

Solution

Qus : 67 JEE MAIN PYQ

Consider the sets $A={(x,y)\in\mathbb{R}\times\mathbb{R}:x^{2}+y^{2}=25}$, $B={(x,y)\in\mathbb{R}\times\mathbb{R}:x^{2}+9y^{2}=144}$, $C={(x,y)\in\mathbb{Z}\times\mathbb{Z}:x^{2}+y^{2}\le 4}$ and $D=A\cap B$. The total number of one-one functions from the set $D$ to the set $C$ is

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (4 April Morning Shift) PYQ

Solution

Qus : 68 JEE MAIN PYQ

The set of all values of $a^{2}$ for which the line $x+y=0$ bisects two distinct chords drawn from a point $P\!\left(\dfrac{1+a}{2},\,\dfrac{1-a}{2}\right)$ on the circle $2x^{2}+2y^{2}-(1+a)x-(1-a)y=0$, is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (31 January Evening Shift) PYQ

Solution

Qus : 69 JEE MAIN PYQ

If the length of the chord of the circle,x² + y² = r² (r > 0) along the line, y – 2x = 3 is r,then r² is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 5 September 2020 (Evening) PYQ

Solution

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