Q JEE MAIN 2026

Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the line $...

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Q JEE MAIN 2026

Let $A(1,2)$ and $C(-3,-6)$ be two diagonally opposite vertices of a rhombus, whose sides AD and BC are parallel to...

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Q JEE MAIN 2026

Let $A(1,0), B(2,-1)$ and $C\left(\frac{7}{3}, \frac{4}{3}\right)$ be three points. If the equation of the bisector of the angle A B...

JEE Main Mathematics Easy

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Q JEE MAIN_2026

A rectangle is formed by the lines $x=0, y=0, x=3$ and $y=4$. Let the line L be perpendicular to $...

JEE Main Mathematics Medium

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Q JEE MAIN 2026

Among the statements (S1) : If $\mathrm{A}(5,-1)$ and $\mathrm{B}(-2,3)$ are two vertices of a triangle, whose orthocentre is $(0,0)$, then...

JEE Main Mathematics Medium

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Q JEE MAIN 2026

Let a point A lie between the parallel lines $L_1$ and $L_2$ such that its distances from $L_1$ and $L_2$...

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Q JEE MAIN_2019_

The region represented by $|x-y| \leq 2$ and $|x+y| \leq 2$ is bounded by a:

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Q JEE MAIN 2019

Slope of a line passing through P(2, 3) and intersecting the line, x + y = 7 at a distance...

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Q JEE MAIN 2019

A triangle has a vertex at (1, 2) and the mid points of the two sides through it are (–1,...

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Q JEE MAIN 2020

The set of all possible values of  in the interval (0, ) for which the points (1, 2) and...

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Q JEE-MAIN 2019

If the straight line, $2 x-3 y+17=0$ is perpendicular to the line passing through the points $(7,17)$ and $(15, \beta)$,...

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Q JEE MAIN 2019

Let the equations of two sides of a triangle be 3x – 2y + 6 = 0 and 4x +...

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Q JEE MAIN 2019

Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the...

JEE Main Mathematics Medium

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Q JEE MAIN 2020

Let C be the centroid of the triangle with vertices (3, –1), (1, 3) and (2, 4). Let P be...

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Q JEE MAIN 2019

If a straight line passing through the point P(–3, 4) is such that its intercepted portion between the coordinate axes...

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Q JEE MAIN 2020

If $\sum_{i=1}^n\left(x_i-a\right)=n$ and $\sum_{i=1}^n\left(x_i-a\right)^2=n a,(n, a>1)$ then the standard deviation of $n$ observations $x_1, x_2, \ldots, x_n$ is :

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Q JEE MAIN 2020

Let L denote the line in the xy-plane with x and y intercepts as 3 and 1 respectively. Then the...

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Q JEE MAIN 2020

A ray of light coming from the point $(2,2 \sqrt{3})$ is incident at an angle $30^{\circ}$ on the line $x=1$...

JEE Main Mathematics Hard

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Q JEE MAIN 2019

Let the equations of two sides of a triangle be $3 x-2 y+6=0$ and $4 x+5 y-20=0$. If the orthocentre...

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Q JEE MAIN 2020

Let two points be $\mathrm{A}(1,-1)$ and $\mathrm{B}(0,2)$. If a point $\mathrm{P}\left(\mathrm{x}^{\prime}, \mathrm{y}^{\prime}\right)$ be such that the area of $\Delta \mathrm{PAB}=5$...

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Q JEE MAIN 2019

Lines are drawn parallel to the line $4 x-3 y+2=0$, at a distance $\frac{3}{5}$ from the origin. Then which one...

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Q JEE MAIN_2021_

Two poles, $A B$ of length a metres and $C D$ of length $a+b(b \neq a)$ metres are erected at...

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Q JEE Main 2019

A point $P$ moves on the line $2 x-3 y+4=0$. If $Q(1,4)$ and $R(3,-2)$ are fixed points, then the locus...

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Q JEE MAIN_2021_

Let $A(a, 0), B(b, 2 b+1)$ and $C(0, b), b \neq 0,|b| \neq 1$, be points such that the area...

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Q JEE MAIN 2020

A triangle $A B C$ lying in the first quadrant has two vertices as $\mathrm{A}(1,2)$ and $\mathrm{B}(3,1)$. If $\angle \mathrm{BAC}=90^{\circ}$,...

JEE Main Mathematics Medium

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Q JEE MAIN 2020

If the perpendicular bisector of the line segment joining the points P(1, 4) and Q(k, 3) has y-intercept equal to...

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Q JEE MAIN 2020

If a $\Delta$ABC has vertices A(–1, 7), B(–7, 1) and C(5, –5), then its orthocentre has coordinates

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Q JEE MAIN 2019

If in a parallelogram ABDC, the coordinates of A, B and C are respectively (1, 2), (3, 4) and (2,...

JEE Main Mathematics Easy

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Q JEE MAIN 2020

The length of the perpendicular from the origin, on the normal to the curve, $x^2+2 x y-3 y^2=0$ at the...

JEE Main Mathematics Medium

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Q JEE MAIN 2019

Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the...

JEE Main Mathematics Easy

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Q JEE MAIN 2020

Let $\mathrm{A}(1,0), \mathrm{B}(6,2)$ and $\mathrm{C}\left(\frac{3}{2}, 6\right)$ be the vertices of a triangle $A B C$. If $P$ is a point...

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Q JEE MAIN 2019

If the two lines $x+(a-1) y=1$ and $2 x+a^2 y=1(a \in R-\{0,1\})$ are perpendicular, then the distance of their point...

JEE Main Mathematics Medium

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Q JEE Main 2021

Let A be the set of all points $(\alpha, \beta)$ such that the area of triangle formed by the points...

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Q JEE MAIN 2019

Two vertices of a triangle are (0, 2) and (4, 3). If its orthocentre is at the origin, then its...

JEE Main Mathematics Easy

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Q JEE MAIN 2021

If $p$ and $q$ are the lengths of the perpendiculars from the origin on the lines, $...

JEE Main Mathematics Medium

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Q JEE MAIN 2019

Two sides of a parallelogram are along the lines, $x+y=3$ and $x-y+3=0$. If its diagonals intersect at (2,4) then one...

JEE Main Mathematics Medium

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Q JEE MAIN 2021

Let A be a fixed point (0, 6) and B be a moving point (2t, 0), Let M be the...

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Q JEE Main 2021

Let $A B C$ be a triangle with $A(-3,1)$ and $\angle A C B=\theta, 0

JEE Main Mathematics Medium

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Q JEE MAIN 2021

Let n be an odd natural number such that the variance of 1, 2, 3, 4, ...., n is 14....

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Q JEE MAIN 2019

Let $\mathrm{O}(0,0)$ and $\mathrm{A}(0,1)$ be two fixed points. Then the locus of a point P such that the perimeter of...

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Q JEE MAIN 2019

A point on the straight line, 3x + 5y = 15 which is equidistant from the coordinate axes will lie...

JEE Main Mathematics Medium

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Q JEE MAIN 2021

A man starts walking from the point $P(-3,4)$, touches the $x$-axis at $R$, and then turns to reach at the...

JEE Main Mathematics Medium

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Q JEE MAIN 2021

Let the points of intersections of the lines x – y + 1 = 0, x – 2y + 3...

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Q JEE MAIN 2021 S2

Two sides of a parallelogram are along the lines $4 x+5 y=0$ and $7 x+2 y=0$. If the equation of...

JEE Main Mathematics Medium

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Q JEE MAIN 2019

Suppose that the points $(h, k),(1,2)$ and $(-3,4)$ lie on the line $L_1$. If a line $L_2$ passing through the...

JEE Main Mathematics Easy

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Q JEE MAIN 2021 S2

The point P (a,b) undergoes the following three transformations successively : (a) reflection about the line $\mathrm{y}=\mathrm{x}$.: (b) translation through...

JEE Main Mathematics Medium

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Q JEE MAIN 2021

Let the equation of the pair of lines, $y=p x$ and $y=q x$, can be written as $(y-p x)(y-q x)=0$....

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Q JEE-MAIN 2021

Let $\tan \alpha, \tan \beta$ and $\tan \gamma, \alpha, \beta, \gamma \neq \frac{(2 \mathrm{n}-1) \pi}{2}, \mathrm{n} \in \mathrm{N}$ be the...

JEE Main Mathematics Easy

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Q JEE MAIN 2021

If the curve $x^2+2 y^2=2$ intersects the line $x+y=1$ at two points $P$ and $Q$, then the angle subtended by...

JEE Main Mathematics Easy

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Q JEE MAIN 2021

Consider a triangle having vertices $\mathrm{A}(-2,3), \mathrm{B}(1,9)$ and $\mathrm{C}(3,8)$. If a line L passing through the circum-centre of triangle $...

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Q JEE MAIN 2021

Let $A(-1,1), B(3,4)$ and $C(2,0)$ be given three points. A line $y=m x, m>0$, intersects lines $A C$ and BC...

JEE Main Mathematics Medium

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Q JEE MAIN 2021

Let C be the locus of the mirror image of a point on the parabola $\mathrm{y}^2=4 \mathrm{x}$ with respect to...

JEE Main Mathematics Easy

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Q JEE MAIN_2021_

In a triangle PQR , the co-ordinates of the points P and $Q$ are ( $-2,4$ ) and ( $4,-2$...

JEE Main Mathematics Medium

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Q JEE Main 2019

Consider the set of all lines $p x+q y+r=0$ such that $3 p+2 q+4 r=0$. Which one of the following...

JEE Main Mathematics Medium

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Q JEE MAIN 2021

The equation of one of the straight lines which passes through the point $(1,3)$ and makes an angles $...

JEE Main Mathematics Easy

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Q JEE MAIN 2021

The number of integral values of m so that the abscissa of point of intersection of lines 3x + 4y...

JEE Main Mathematics Easy

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Q JEE MAIN 2021

The intersection of three lines x – y = 0, x + 2y = 3 and 2x + y =...

JEE Main Mathematics Medium

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Q JEE MAIN 2021

A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line...

JEE Main Mathematics Medium

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Q JEE MAIN 2021

The image of the point (3, 5) in the line x – y + 1 = 0, lies on :

JEE Main Mathematics Easy

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Q JEE MAIN_2022

The equations of the sides $A B, B C$ and $C A$ of a triangle $A B C$ are $...

JEE Main Mathematics Medium

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Q _JEE MAIN_2022

A point P moves so that the sum of squares of its distances from the points (1, 2) and (–2,...

JEE Main Mathematics Medium

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Q JEE MAIN 2022

A line, with the slope greater than one, passes through the point $A(4,3)$ and intersects the line $x-y-2=0$ at the...

JEE Main Mathematics Medium

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Q JEE MAIN 2022

If the system of linear equations $2 x-3 y=\gamma+5, \alpha x+5 y=\beta+1$ where $\alpha, \beta, \gamma \in \mathbf{R}$ has infinitely...

JEE Main Mathematics Easy

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Q JEE MAIN 2022

The distance of the origin from the centroid of the triangle whose two sides have the equations $x-2 y+1=0$ and...

JEE Main Mathematics Easy

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Q JEE MAIN 2022

Let a triangle be bounded by the lines $L_{1 i} 2 x+5 y=10 ; L_{2 i}-4 x+3 y=12$ and the...

JEE Main Mathematics Easy

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Q JEE MAIN 2022

Let the area of the triangle with vertices $\mathrm{A}(1, \alpha), \mathrm{B}(\alpha, 0)$ and $\mathrm{C}(0, \alpha)$ be 4 sq. units. If...

JEE Main Mathematics Easy

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Q JEE MAIN 2022

The distance between the two points $A$ and $A^{\prime}$ which lie on $y=2$ such that both the line segments $...

JEE Main Mathematics Easy

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Q JEE MAIN 2022

A ray of light passing through the point $P(2,3)$ reflects on the $x$-axis at point $A$ and the reflected ray...

JEE Main Mathematics Medium

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Q JEE MAIN 2022

In an isosceles triangle $A B C$, the vertex $A$ is $(6,1)$ and the equation of the base $B C$...

JEE Main Mathematics Medium

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Q JEE MAIN 2022

Let $A\left(\frac{3}{\sqrt{a}}, \sqrt{a}\right) a>0$ be a fixed point in the $x y$-plane. The image of $A$ in $y$-axis be $B$...

JEE Main Mathematics Medium

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Q JEE MAIN 2023

Let the equations of two adjacent sides of a parallelogram ABCD be $2 \mathrm{x}-3 \mathrm{y}=-23$ and $5 \mathrm{x}+4 \mathrm{y}=23$. If...

JEE Main Mathematics Medium

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Q JEE MAIN 2023

Let $(\alpha, \beta)$ be the centroid of the triangle formed by the lines $15 x-y=82,6 x-5 y=-4$ and $...

JEE Main Mathematics Easy

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Q JEE MAIN 2025

A line passing through the point $P(a, 0)$ makes an acute angle $\alpha$ with the positive $x$-axis. Let this line...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Let $A(4,-2), B(1,1)$ and $C(9,-3)$ be the vertices of a triangle ABC . Then the maximum area of the parallelogram...

JEE Main Mathematics Hard

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Q JEE MAIN 2025

Let $a$ be the length of a side of a square OABC with O being the origin. Its side OA...

JEE Main Mathematics Medium

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Q JEE MAIN_2025

If the orthocenter of the triangle formed by the lines $y=x+1, y=4 x-8$ and $y=m x+c$ is at $(3,-1)$ ,...

JEE Main Physics Easy

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Q JEE MAIN 2025

Let the area of the triangle formed by a straight line $L: x+b y+c=0$ with co-ordinate axes be 48 square...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Let the equation $x(x+2)(12-k)=2$ have equal roots. Then the distance of the point $\left(k, \frac{k}{2}\right)$ from the line $...

JEE Main Mathematics Easy

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Q JEE MAIN 2025

Consider the lines $x(3 \lambda+1)+y(7 \lambda+2)=17 \lambda+5, \lambda$ being a parameter, all passing through a point P : One of...

JEE Main Mathematics Medium

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Q JEE MAIN 2023

Consider the triangles with vertices $A(2,1) B(0,0)$ and $C(t, 4), t \in[0,4]$. It the maximum and the minimum perimeters of...

JEE Main Mathematics Hard

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Q JEE MAIN 2023

If $(\alpha, \beta)$ is the orthocentre of the triangle ABC with vertices $\mathrm{A}(3,-7), \mathrm{B}(-1,2)$ and $\mathrm{C}(4,5)$, then $9 \alpha-6 \beta+60$...

JEE Main Mathematics Medium

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Q JEE-Main 2023

The straight lines $I_1$ and $I_2$ pass through the origin and trisect the line segment of the line L: 9x...

JEE Main Mathematics Medium

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Q JEE MAIN 2023

If the point $\left(\alpha, \frac{7 \sqrt{3}}{3}\right)$ lies on the curve traced by the mid-points of the line segments of the...

JEE Main Mathematics Medium

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Q JEE-Main 2023

The straight lines l1 and l2 pass through the origin and trisect the line segment of the line L: 9x...

JEE Main Mathematics Medium

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Q JEE MAIN 2024

If the orthocentre of the triangle formed by the lines 2x+3y-1=0,x+2y-1=0 and ax + by -1=0, is the centroid of...

JEE Main Mathematics Medium

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Q JEE MAIN

A ray of light coming from the point P(1,2) gets reflected from the point Q on the x-axis and then...

JEE Main Mathematics Medium

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Q JEE MAIN 2024

The equations of two sides AB and AC of a triangle $A B C$ are $4 x+y=14$ and $...

JEE Main Mathematics Medium

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Q JEE MAIN 2024

Let λ,μ∈R. If the system of equations 3x+5y+λz=3 7x+11y-9z=2 97x+155y-189z=μ has infinitely many solutions, then μ+2λ is equal to :

JEE Main Mathematics Medium

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Q

Let two straight lines drawn from the origin O intersect the line 3x+4y=12 at the points P and Q such...

JEE Main Mathematics Medium

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Q JEE MAIN 2024

Let a rectangle ABCD of sides 2 and 4 be inscribed in another rectangle PQRS such that the vertices of...

JEE Main Mathematics Hard

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Q JEE MAIN 2024

The vertices of a triangle are A(-1,3),B(-2,2) and C(3,-1). A new triangle is formed by shifting the sides of the...

JEE Main Mathematics Hard

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Q JEE MAIN 2024

Let d be the distance of the point of intersection of the lines x+63=y2=z+11 and x-74=y-93=z-42 from the point (7,8,9)....

JEE Main Mathematics Hard

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Q JEE-Main 2024

Let $A=\{1,2,3, \ldots 20\}$. Let $R_1$ and $R_2$ two relation on A such that $\mathrm{R}_1=\{(\mathrm{a}, \mathrm{b}): \mathrm{b}$ is divisible by...

JEE Main Mathematics Medium

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Q JEE MAIN 2024

Let $\alpha, \beta, \gamma, \delta \in \mathrm{Z}$ and let $\mathrm{A}(\alpha, \beta), \mathrm{B}(1,0), \mathrm{C}(\gamma, \delta)$ and $D(1,2)$ be the vertices of...

JEE Main Mathematics Easy

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Q JEE MAIN

Let $\left(5, \frac{a}{4}\right)$, be the circumcenter of a triangle with vertices $A(a,-2), B(a, 6)$ and $C\left(\frac{a}{4},-2\right)$. Let $\alpha$ denote the...

JEE Main Mathematics Medium

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Q JEE MAIN

In a △ABC, suppose y=x is the equation of the bisector of the angle B and the equation of the...

JEE Main Mathematics Easy

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Q JEE MAIN 2024

A line passing through the point  makes an angle of  with the positive direction of -axis. If this line is...

JEE Main Mathematics Easy

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Q JEE MAIN 2024

The portion of the line $4 x+5 y=20$ in the first quadrant is trisected by the lines $\mathrm{L}_1$ and $\mathrm{L}_2$...

JEE Main Mathematics Easy

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Q JEE MAIN 2025

Let the line $x+y=1$ meet the axes of $x$ and $y$ at $A$ and $B$, respectively. A right angled triangle...

JEE Main Mathematics Easy

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Q JEE MAIN 2025

Two equal sides of an isosceles triangle are along $-x+2 y=4$ and $x+y=4$. If m is the slope of its...

JEE Main Mathematics Easy

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Q JEE MAIN 2025

Let ABC be the triangle such that the equations of lines AB and AC be $3y - x = 2$...

JEE Main Mathematics Easy

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Q JEE MAIN 2025

Let the three sides of a triangle are on the lines $...

JEE Main Mathematics Easy

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Q JEE MAIN 2025

A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines $...

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Q JEE MAIN 2025

Let the points $\left(\frac{11}{2}, \alpha\right)$ lie on or inside the triangle with sides $x+y=11, x+2 y=16$ and $2 x+3 y=29$....

JEE Main Mathematics Easy

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Q

The variance of the numbers 8, 21, 34, 47, .............., 320 is._______.

JEE Main Mathematics Medium

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Q JEE MAIN 2025

A rod of length eight units moves such that its ends $A$ and $B$ always lie on the lines $x-y+2=0$...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Let $\mathrm{A}=\{(x, y) \in \mathbf{R} \times \mathbf{R}:|x+y| \geqslant 3\}$ and $\mathrm{B}=\{(x, y) \in \mathbf{R} \times \mathbf{R}:|x|+|y| \leq 3\}$. If $...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Let ABC be a triangle formed by the lines $...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Let the lines $3x - 4y - \alpha = 0,8x - 11y - 33 = 0$, and $...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Let the area of a $\Delta PQR$ with vertices $P(5,4),Q( - 2,4)$ and $R(a,b)$ be 35 square units. If its...

JEE Main Mathematics Medium

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Q JEE MAIN 2025

If the line $3x-2y+12=0$ intersects the parabola $4y=3{{x}^{2}}$ at the points A and B, then at the vertex of the...

JEE Main Mathematics Easy

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Q JEE MAIN 2025

Let $A(6,8), B(10 \cos \alpha,-10 \sin \alpha)$ and $C(-10 \sin \alpha, 10 \cos \alpha)$, be the vertices of a triangle....

JEE Main Mathematics Medium

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Q JEE MAIN 2025

Let the distance between two parallel lines be 5 units and a point $P$ lie between the lines at a...

JEE Main Mathematics Easy

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Q JEE MAIN 2025

Let the triangle PQR be the image of the triangle with vertices (1,3)(3,1) and (2,4) in the line $x+2y=2$. If...

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