Q JEE MAIN 2022

The tangents at the points $A(1,3)$ and $B(1,-1)$ on the parabola $y^2-2 x-2 y=1$ meet at the point $P$. Then...

JEE Main Mathematics Easy

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Q JEE MAIN 2026

Let $O$ be the vertex of the parabola $y^2=4 x$ and its chords $O P$ and $O Q$ are perpendicular...

JEE Main Mathematics Medium

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Q JEE MAIN 2026

Let chord PQ of length $3 \sqrt{13}$ of the parabola $y^2=12 x$ be such that the ordinates of points P...

JEE Main Mathematics Medium

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Q JEE MAIN 2026

Let the directrix of the parabola $\mathrm{P}: y^2=8 x$, cut $x$-axis at the point A . Let $\mathrm{B}(\alpha, \beta), \alpha>1$,...

JEE Main Mathematics Medium

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Q JEE MAIN 2026

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

JEE Main Mathematics Medium

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Q JEE MAIN 2026

Let one root of the quadratic equation in $x$ : $$ \left(k^2-15 k+27\right) x^2+9(k-1) x+18=0 $$ be twice the other....

JEE Main Physics Medium

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Q JEE MAIN 2026

Let $\mathrm{A}, \mathrm{B}$ and C be the vertices of a variable right angled triangle inscribed in the parabola $y^2=16 x$....

JEE Main Mathematics Easy

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Q JEE MAIN 2026

Let P be a moving point on the circle $x^2+y^2-6 x-8 y+21=0$. Then, the maximum distance of P from the...

JEE Main Mathematics Easy

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Q JEE Main 2024

Let a line perpendicular to the line $2 x-y=10$ touch the parabola $y^2=4(x-9)$ at the point $P$. The distance of...

JEE Main Mathematics Easy

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Q JEE Main 2024

Let $\mathrm{A}, \mathrm{B}$ and C be three points on the parabola $y^2=6 x$ and let the line segment $A B$...

JEE Main Mathematics Easy

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Q JEE Main 2024

Consider the circle $C: x^2+y^2=4$ and the parabola $P: y^2=8 x$. If the set of all values of $\alpha$, for...

JEE Main Mathematics Easy

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Q JEE Main 2024

Let P Q be a chord of the parabola $y^2=12 x$ and the midpoint of PQ be at $(4,1)$. Then,...

JEE Main Mathematics Easy

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Q Jee Main 2024

Let $\mathrm{P}(\alpha, \beta)$ be a point on the parabola $\mathrm{y}^2=4 \mathrm{x}$. If P also lies on the chord of the...

JEE Main Mathematics Medium

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Q JEE MAIN 2026

Let A be the focus of the parabola $y^2=8 x$. Let the line $y=m x+c$ intersect the parabola at two...

JEE Main Mathematics Medium

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Q JEE MAIN 2026

The probability distribution of a random variable X is given below : If $E(X)=\frac{263}{15}$, then $P(X

JEE Main Mathematics Easy

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Q JEE MAIN 2026

An equilateral triangle OAB is inscribed in the parabola $y^2=4 x$ with the vertex O at the vertex of the...

JEE Main Mathematics Easy

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Q JEE MAIN 2026

Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One...

JEE Main Mathematics Easy

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Q JEE MAIN 2026

Let the locus of the mid-point of the chord through the origin O of the parabola $y^2=4 x$ be the...

JEE Main Mathematics Easy

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Q JEE MAIN_2026_

If the chord joining the points $\mathrm{P}_1\left(x_1, y_1\right)$ and $\mathrm{P}_2\left(x_2, y_2\right)$ on the parabola $y^2=12 x$ subtends a right angle...

JEE Main Mathematics Medium

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Q JEE MAIN 2026

Let one end of a focal chord of the parabola $y^2=16 x$ be $(16,16)$. If $\mathrm{P}(\alpha, \beta)$ divides this focal...

JEE Main Mathematics Easy

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Q JEE MAIN 2026

Let $y^2=12 x$ be the parabola with its vertex at O . Let P be a point on the parabola...

JEE Main Mathematics Easy

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Q JEE MAIN 2026

Let O be the vertex of the parabola $x^2=4 y$ and Q be any point on it. Let the locus...

JEE Main Mathematics Easy

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Q JEE MAIN 2019

If one end of a focal chord of the parabola, $y^2$ = 16x is at (1, 4), then the length...

JEE Main Mathematics Easy

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Q JEE MAIN 2020

Let $E^C$ denote the complement of an event $E$. Let $E_1, E_2$ and $E_3$ be any pairwise independent events with...

JEE Main Mathematics Hard

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Q JEE MAIN 2019

JEE Main Mathematics Medium

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Q JEE MAIN 2019

Let $\mathrm{A}(4,-4)$ and $\mathrm{B}(9,6)$ be points on the parabola, $\mathrm{y}^2=4 \mathrm{x}$. Let C be chosen on the arc AOB of...

JEE Main Mathematics Medium

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Q JEE MAIN 2019

The equation of a tangent to the parabola, $x^2=8 y$, which makes an angle $\theta$ with the positive direction of...

JEE Main Mathematics Easy

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Q JEE MAIN 2019

In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair...

JEE Main Mathematics Medium

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Q JEE MAIN 2019

In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC...

JEE Main Mathematics Easy

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Q JEE MAIN 2020

Let $L_1$ be a tangent to the parabola $y^2=4(x+1)$ and $L_2$ be a tangent to the parabola $y^2=8(x+2)$ such that...

JEE Main Mathematics Medium

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Q JEE MAIN 2020

The centre of the circle passing through the point $(0,1)$ and touching the parabola $\mathrm{y}=\mathrm{x}^2$ at the point $(2,4)$ is...

JEE Main Mathematics Medium

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Q JEE MAIN 2019

Let $\mathrm{A}(4,-4)$ and $\mathrm{B}(9,6)$ be points on the parabola, $\mathrm{y}^2=4 \mathrm{x}$. Let C be chosen on the arc AOB of...

JEE Main Mathematics Easy

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Q JEE MAIN 2020

The locus of a point which divides the line segment joining the point $(0,-1)$ and a point on the parabola,...

JEE Main Mathematics Easy

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Q JEE MAIN 2019

If the line $a x+y=c$, touches both the curves $x^2+y^2=1$ and $y^2=4 \sqrt{2} x$, then $|c|$ is equal to :

JEE Main Mathematics Medium

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Q JEE Main 2019

If the parabolas $y^2=4 b(x-c)$ and $y \quad l=8 a x$ have a common normal, then which one of the...

JEE Main Mathematics Medium

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Q JEE MAIN_2021

If two tangents drawn from a point $P$ to the parabola $y^2=16(x-3)$ are at right angles, then the locus of...

JEE Main Mathematics Medium

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Q JEE MAIN 2020

If one end of a focal chord AB of the parabola $\mathrm{y}^2= 8 x$ is at $A\left(\frac{1}{2},-2\right)$, then the equation...

JEE Main Mathematics Easy

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Q JEE MAIN 2020

Let a line y=m x(m>0) intersect the parabola, $y^2=x$ at a point $P$, other than the origin. Let the tangent...

JEE Main Mathematics Medium

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Q JEE MAIN 2019

If the area of the triangle whose one vertex is at the vertex of the parabola, $y^2+4\left(x-a^2\right)=0$ and the other...

JEE Main Mathematics Easy

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Q JEE MAIN 2019

A circle cuts a chord of length 4a on the x-axis and passes through a point on the y-axis, distant...

JEE Main Mathematics Easy

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Q JEE-MAIN 2020

Let the latus ractum of the parabola $y^2=4 x$ be the common chord to the circles $C_1$ and $C_2$ each...

JEE Main Mathematics Easy

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Q JEE MAIN 2019

The area (in sq. units) of the smaller of the two circles that touch the parabola, $y^2=4 x$ at the...

JEE Main Mathematics Hard

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Q JEE Main 2021

A tangent line L is drawn at the point $(2,-4)$ on the parabola $\mathrm{y}^2=8 \mathrm{x}$. If the line L is...

JEE Main Mathematics Easy

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Q JEE MAIN 2020

If $y=m x+4$ is a tangent to both the parabolas, $y^2 =4 x$ and $x^2=2 b y$, then $b$ is...

JEE Main Mathematics Medium

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Q JEE MAIN 2021

The length of the latus rectum of a parabola, whose vertex and focus are on the positive $x$-axis at a...

JEE Main Mathematics Easy

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Q JEE MAIN 2019

The length of the chord of the parabola $x^2=4 y$ having equation $x-\sqrt{2} y+4 \sqrt{2}=0$ is

JEE Main Mathematics Medium

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Q JEE MAIN 2021

A tangent and a normal are drawn at the point $\mathrm{P}(2,-4)$ on the parabola $\mathrm{y}^2=8 \mathrm{x}$, which meet the directrix...

JEE Main Mathematics Medium

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Q JEE Main 2021

If a line along a chord of the circle $4 x^2+4 y^2+120 x+675=0$, passes through the point $(-30,0)$ and is...

JEE Main Mathematics Medium

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Q JEE Main 2019

Equation of a common tangent to the circle, $x^2+y^2-6 x=0$ and the parabola, $y^2=4 x$, is:

JEE Main Mathematics Medium

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Q JEE Main 2019

Axis of a parabola lies along x-axis. If its vertex and focus are at distances 2 and 4 respectively from...

JEE Main Mathematics Easy

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Q JEE MAIN 2019

The shortest distance between the line $\mathrm{y}=\mathrm{x}$ and the curve $y^2=x-2$ is :

JEE Main Mathematics Medium

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Q JEE MAIN 2021

Consider the parabola with vertex $\left(\frac{1}{2}, \frac{3}{4}\right)$ and the directrix $y=\frac{1}{2}$. Let $P$ be the point where the parabola meets...

JEE Main Mathematics Medium

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Q _JEE MAIN_2021_

Let a parabola P be such that its vertex and focus lie on the positive x -axis at a distance...

JEE Main Mathematics Easy

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Q JEE MAIN 2019

Let $\mathrm{S}(\alpha)=\left\{(\mathrm{x}, \mathrm{y}): \mathrm{y}^2 \leq \mathrm{x}, 0 \leq \mathrm{x} \leq \alpha\right\}$ and $\mathrm{A}(\alpha)$ is area of the region $\mathrm{S}(\alpha)$. If...

JEE Main Mathematics Medium

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Q JEE MAIN 2019

The tangent to the parabola $\mathrm{y}^2=4 \mathrm{x}$ at the point where it intersects the circle $\mathrm{x}^2+\mathrm{y}^2=5$ in the first quadrant,...

JEE Main Mathematics Easy

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Q JEE MAIN 2021

A seven-digit number is formed using digits 3, 3, 4, 4, 4, 5, 5. The probability, that number so formed...

JEE Main Mathematics Medium

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Q JEE MAIN 2021

Let $y=m x+c, m>0$ be the focal chord of $y^2=-64 x$, which is tangent to $(x+10)^2+y^2=4$. Then, the value of...

JEE Main Mathematics Medium

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Q JEE MAIN 2021

Let the tangent to the parabola $\mathrm{S}: \mathrm{y}^2=2 \mathrm{x}$ at the point $\mathrm{P}(2,2)$ meet the x -axis at Q and...

JEE Main Mathematics Easy

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Q JEE MAIN 2021

A line is a common tangent to the circle $(x-3)^2+ y^2=9$ and the parabola $y^2=4 x$. If the two points...

JEE Main Mathematics Hard

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Q JEE MAIN 2021

Let $P$ be a variable point on the parabola $y=4 x^2+1$. Then, the locus of the mid-point of the point...

JEE Main Mathematics Medium

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Q JEE MAIN 2021

The locus of the mid-point of the line segment joining the focus of the parabola $y^2=4 a x$ to a...

JEE Main Mathematics Medium

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Q JEE MAIN 2021

If the three normasl drawn to the prabola, $y^2=2 x$ pass through the point $(a, 0) a \neq 0$, then...

JEE Main Mathematics Easy

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Q JEE MAIN 2021

A tangent is drawn to the parabola $y^2=6 x$ which is perpendicular to the line $2 x+y=1$. Which of the...

JEE Main Mathematics Medium

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Q JEE MAIN 2022

The sum of diameters of the circles that touch (i) the parabola $75 x^2=64(5 y-3)$ at the point $\left(\frac{8}{5}, \frac{6}{5}\right)$...

JEE Main Mathematics Medium

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Q JEE MAIN 2022

Let P1 be a parabola with vertex (3, 2) and focus (4, 4) and P2 be its mirror image with...

JEE Main Mathematics Medium

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Q JEE MAIN 2022

If vertex of a parabola is (2, –1) and the equation of its directrix is 4x – 3y = 21,...

JEE Main Mathematics Easy

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Q JEE MAIN 2022

Let $P: y^2=4 a x, a>0$ be a parabola with focus $S$. Let the tangents to the parabola $P$ make...

JEE Main Mathematics Easy

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Q JEE MAIN 2022

If the equation of the parabola, whose vertex is at $(5,4)$ and the directrix is $...

JEE Main Mathematics Medium

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Q JEE MAIN 2022

If the line $y=4+k x, k>0$, is the tangent to the parabola $y=x-x^2$ at the point $P$ and $V$ is...

JEE Main Mathematics Medium

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Q JEE MAIN 2022

A particle is moving in the xy-plane along a curve C passing through the point (3, 3). The tangent to...

JEE Main Mathematics Medium

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Q JEE MAIN 2022

A circle of radius 2 unit passes through the vertex and the focus of the parabola $y^2=2 x$ and touches...

JEE Main Mathematics Medium

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Q JEE MAIN 2022

Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability...

JEE Main Mathematics Medium

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Q JEE MAIN 2022

Let $x=2 t, y=\frac{t^2}{3}$ be a conic. Let $S$ be the focus and $B$ be the point on the axis...

JEE Main Mathematics Medium

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Q JEE MAIN 2022

If $y=m_1 x+c_1$ and $y=m_2 x+c_2, m_1 \neq m_2$ are two common tangents of circle $x^2+y^2=2$ and parabola $y^2=x$, then...

JEE Main Mathematics Easy

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Q JEE MAIN 2025

Let $r$ be the radius of the circle, which touches $x$ - axis at point $(a, 0), a

JEE Main Mathematics Medium

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Q JEE MAIN 2023

Let a die be rolled $n$ times. Let the probability of getting odd numbers seven times be equal to the...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Let the point P of the focal chord PQ of the parabola $y^2=16 x$ be $(1,-4)$. If the focus of...

JEE Main Mathematics Easy

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Q JEE MAIN 2025

The axis of a parabola is the line $y=x$ and its vertex and focus are in the first quadrant at...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

The shortest distance between the curves $y^2=8 x$ and $x^2+y^2+12 y+35=0$ is:

JEE Main Mathematics Medium

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Q JEE MAIN 2023

A bag contains 6 white and 4 black balls. A die is rolled once and the number of balls equal...

JEE Main Mathematics Medium

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Q JEE MAIN 2023

Let P Q be a focal chord of the parabola $y^2=36 x$ of length 100 , making an acute angle...

JEE Main Mathematics Medium

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Q JEE MAIN 2023

A coin is biased so that the head is 3 times as likely to occur as tail. This coin is...

JEE Main Mathematics Medium

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Q JEE MAIN 2023

Let a common tangent to the curves $y^2=4 x$ and $(x-4)^2+y^2=16$ touch the curves at the points $P$ and $Q$....

JEE Main Mathematics Easy

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Q JEE MAIN 2023

Let R be the focus of the parabola $\mathrm{y}^2=20 \mathrm{x}$ and the line $\mathrm{y}=m \mathrm{x}+c$ intersect the parabola at two...

JEE Main Mathematics Hard

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Q JEE-Main 2024

Let $L_1, L_2$ be the lines passing through the point $P(0,1)$ and touching the parabola $9 x^2+12 x+18 y- 14=0$....

JEE Main Mathematics Hard

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Q JEE MAIN 2024

Suppose $A B$ is a focal chord of the parabola $y^2=12 x$ of length $l$ and slope $m

JEE Main Mathematics Medium

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Q JEE MAIN 2024

Let the length of the focal chord $P Q$ of the parabola $\mathrm{y}^2=12 \mathrm{x}$ be 15 units. If the distance...

JEE Main Mathematics Medium

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Q JEE-Main 2024

Let C be the circle of minimum area touching the parabola $y=6-x^2$ and the lines y=√3|x|. Then, which one of...

JEE Main Mathematics Medium

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Q JEE MAIN 2024

If the shortest distance of the parabola $y^2=4 x$ from the centre of the circle $x^2+y^2-4 x-16 y+64=0$ is d...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Let $y^{2}=12 x$ be the parabola and $S$ be its focus. Let PQ be a focal chord of the parabola...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Let $A$ and $B$ be the two points of intersection of the line $y+5=0$ and the mirror image of the...

JEE Main Mathematics Easy

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Q JEE MAIN 2025

Let P be the parabola, whose focus is (-2, 1) and directrix is $2x + y + 2 = 0$....

JEE Main Mathematics Medium

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Q JEE MAIN 2025

The radius of the smallest circle which touches the parabolas $...

JEE Main Mathematics Hard

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Q JEE MAIN 2025

If the equation of the parabola with vertex $\mathrm{V}\left(\frac{3}{2}, 3\right)$ and the directrix $x+2 y=0$ is $...

JEE Main Mathematics Easy

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Q JEE MAIN 2025

Let the focal chord PQ of the parabola ${y^2} = 4x$ make an angle of ${60^\circ}$ with the positive axis,...

JEE Main Mathematics Hard

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Q JEE MAIN 2025

The focus of the parabola $y^{2}=4 x+16$ is the centre of the circle $C$ of radius 5 . If the...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Let the shortest distance from ( $\mathrm{a}, 0$ ), $\mathrm{a}>0$, to the parabola $y^{2}=4 x$ be 4 . Then the...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Two parabolas have the same focus (4, 3) and their directrices are the x-axis and the y-axis, respectively. If these...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Let ABCD be a trapezium whose vertices lie on the parabola ${{\rm{y}}^2} = 4{\rm{x}}$. Let the sides AD and BC...

JEE Main Mathematics Easy

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Q JEE MAIN 2025

Let the parabola $y={{x}^{2}}+\text{p}x-3$ , meet the coordinate axes at the points P,Q and R. If the circle C with...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Let $\mathrm{P}(4,4 \sqrt{3})$ be a point on the parabola $y^2=4 \mathrm{ax}$ and PQ be a focal chord of the parabola....

JEE Main Mathematics Medium

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