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JEE Straight Lines PYQs with Solutions

497 previous year questions from Straight Lines (JEE Main & Advanced Mathematics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

497 questionsMathematics2007–2026Answers + solutions

About Straight Lines PYQs

Straight Lines has 497 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 220 questions in this list come from JEE Main (198) and JEE Advanced (22), spanning 2007 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2026: 15
  • 2025: 20
  • 2024: 31
  • 2023: 17
  • 2022: 18
  • 2021: 23
  • 2020: 12
  • 2019: 19
  • 2018: 5
  • 2017: 3
  • 2016: 6
  • 2015: 5

Straight Lines questions with solutions

1

If a straight line drawn through the point of intersection of the lines 4x+3y-1=0 and 3x+4y-1=0 , meets the co-ordinate axes at the points P and Q, then the locus of the mid point

JEE Main 2026 Solution View → 2

From the point (-1, -1) , two rays are sent making angles of 45° with the line x + y = 0 . These rays get reflected from the mirror x + 2y = 1 . If the equations of the reflected

JEE Main 2026 Solution View → 3

In an equilateral triangle PQR , let the vertex P be at (3, 5) and the side QR be along the line x + y = 4 . If the orthocentre of the triangle PQR is (α, β) , then 9(α + β) is

JEE Main 2026 Solution View → 4

Let P(3 α, 2 α) , α ≠ 0 , be a point on the ellipse (x^2)/(9)+(y^2)/(4)=1 , Q be a point on the circle x^2+y^2-14x-14y+82=0 and R be a point on the line x+y=5 such that the

JEE Main 2026 Solution View → 5

Let A,B be points on the two half-lines x- 3 |y|=α , α>0 at a distance of α from their point of intersection P . The line segment AB meets the angle bisector of the given

JEE Main 2026 Solution View → 6

Let the line L_1 : x + 3 = 0 intersect the lines L_2 : x - y = 0 and L_3 : 3x + y = 0 at the points A and B , respectively. Let the bisector of the obtuse angle between the lines

JEE Main 2026 Solution View → 7

Let the vertex A of a triangle ABC be (1, 2) , and the mid-point of the side AB be (5, -1) . If the centroid of this triangle is (3, 4) and its circumcenter is (α, β) , then 21(α

JEE Main 2026 Solution View → 8

Let the mid points of the sides of a triangle ABC be ((5)/(2), 7) , ((5)/(2), 3) and (4, 5). If its incentre is (h, k) , then 3h + k is equal to :

JEE Main 2026 Solution View → 9

Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the line x+2 2 y=4 . If the co-ordinates of the vertex A are (α, β) , then the greatest

JEE Main 2026 Solution View → 10

Let the angles made with the positive x -axis by two straight lines drawn from the point P(2,3) and meeting the line x+y=6 at a distance (2)/(3) from the point P be θ_ 1 and θ_ 2

JEE Main 2026 Solution View → 11

Let A(1,0), B(2,-1) and C((7)/(3), (4)/(3)) be three points. If the equation of the bisector of the angle ABC is α x+β y=5 , then the value of α^ 2 +β^ 2 is

JEE Main 2026 Solution View → 12

Let A(1,2) and C(-3,-6) be two diagonally opposite vertices of a rhombus, whose sides AD and BC are parallel to the line 7 x-y=14 . If B(α, β) and D(γ, δ) are the other two

JEE Main 2026 Solution View → 13

A rectangle is formed by the lines x=0, y=0, x=3 and y=4 . Let the line L be perpendicular to 3 x+y+6=0 and divide the area of the rectangle into two equal parts. Then the

JEE Main 2026 Solution View → 14

Among the statements (S 1) : If A(5,-1) and B(-2,3) are two vertices of a triangle, whose orthocentre is (0,0) , then its third vertex is (-4,-7) and (S2) : If positive numbers

JEE Main 2026 Solution View → 15

Let a point A lie between the parallel lines L_ 1 and L_ 2 such that its distances from L_ 1 and L_ 2 are 6 and 3 units, respectively. Then the area (in sq. units) of the

JEE Main 2026 Solution View → 16

A line passing through the point P(a, θ) makes an acute angle α with the positive x -axis. Let this line be rotated about the point P through an angle (α)/(2) in the clock-wise

JEE Main 2025 Solution View → 17

Let a be the length of a side of a square OABC with O being the origin. Its side OA makes an acute angle α with the positive x -axis and the equations of its diagonals are ( 3 +1)

JEE Main 2025 Solution View → 18

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

JEE Main 2025 Solution View → 19

Let ABC be the triangle such that the equations of lines A B and A C be 3 y-x=2 and x+y=2 , respectively, and the points B and C lie on x -axis. If P is the orthocentre of the

JEE Main 2025 Solution View → 20

Let the three sides of a triangle are on the lines 4 x-7 y+10=0, x+y=5 and 7 x+4 y=15 . Then the distance of its orthocentre from the orthocentre of the triangle formed by the

JEE Main 2025 Solution View → 21

Let the equation x(x+2)(12-k)=2 have equal roots. Then the distance of the point (k, k 2 ) from the line 3 x+4 y+5=0 is

JEE Main 2025 Solution View → 22

Consider the lines x(3 λ+1)+y(7 λ+2)=17 λ+5 , λ being a parameter, all passing through a point P . One of these lines (say L) is farthest from the origin. If the distance of L

JEE Main 2025 Solution View → 23

A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines L_1: 2 x+y+6=0 and L_2: 4 x+2 y-p=0, p 0 , at the points A and B

JEE Main 2025 Solution View → 24

Let A(4,-2), B(1,1) and C(9,-3) be the vertices of a triangle A B C . Then the maximum area of the parallelogram AFDE , formed with vertices D, E and F on the sides BC, CA and AB

JEE Main 2025 Solution View → 25

Let the area of the triangle formed by a straight Line L: x+by+c=0 with co-ordinate axes be 48 square units. If the perpendicular drawn from the origin to the line L makes an

JEE Main 2025 Solution View → 26

Let the line x+y=1 meet the axes of x and y at A and B, respectively. A right angled triangle AMN is inscribed in the triangle OAB , where O is the origin and the points M and N

JEE Main 2025 Solution View → 27

Let \(A B C\) be a triangle formed by the lines \(7 x-6 y+3=0, x+2 y-31=0\) and \(9 x-2 y-19=0\). Let the point \((h, k)\) be the image of the centroid of \(Δ A B C\) in the line

JEE Main 2025 Solution View → 28

Two equal sides of an isosceles triangle are along -x+2 y=4 and x+y=4 . If m is the slope of its third side, then the sum, of all possible distinct values of m , is :

JEE Main 2025 Solution View → 29

Let ^ n C_ r-1 =28, ^ n C_ r =56 and ^ n C_ r+1 =70 . Let A(4 t, 4 t), B(2 t,-2 t) and C(3 r-n, r^2-n-1) be the vertices of a triangle A B C , where t is a parameter. If (3

JEE Main 2025 Solution View → 30

Let the points ((11)/(2), α) lie on or inside the triangle with sides x+y=11, x+2 y=16 and 2 x+3 y=29 . Then the product of the smallest and the largest values of α is equal to :

JEE Main 2025 Solution View → 31

Let the lines 3 x-4 y-α=0,8 x-11 y-33=0 , and 2 x-3 y+λ=0 be concurrent. If the image of the point (1,2) in the line 2 x-3 y+λ=0 is ((57)/(13), (-40)/(13)) , then |α λ| is equal to

JEE Main 2025 Solution View → 32

A rod of length eight units moves such that its ends A and B always lie on the lines x-y+2=0 and y+2=0 , respectively. If the locus of the point P , that divides the rod A B

JEE Main 2025 Solution View → 33

Let the area of a P Q R with vertices P(5,4), Q(-2,4) and R(a, b) be 35 square units. If its orthocenter and centroid are O(2, (14)/(5)) and C(c, d) respectively, then c+2 d is

JEE Main 2025 Solution View → 34

Let A(6,8), B(10 α,-10 α) and C(-10 α, 10 α) , be the vertices of a triangle. If L(a, 9) and G(h, k) be its orthocenter and centroid respectively, then (5 a-3 h+6 k+100 2 α) is

JEE Main 2025 Solution View → 35

Let the triangle PQR be the image of the triangle with vertices (1,3),(3,1) and (2,4) in the line x+2 y=2 . If the centroid of PQR is the point (α, β) , then 15(α-β) is equal to :

JEE Main 2025 Solution View → 36

Let ℝ^2 denote ℝ × ℝ. Let S= \ (a, b, c): a, b, c ∈ ℝ and a x^2+2 b x y+c y^2>0 for all (x, y) ∈ ℝ^2- \ (0,0)\ \ . Then which of the following statements is (are) TRUE?

JEE Advanced 2024 Solution View → 37

Two vertices of a triangle ABC are A(3,-1) and B(-2,3) , and its orthocentre is P(1,1) . If the coordinates of the point C are (α, β) and the centre of the of the circle

JEE Main 2024 Solution View → 38

A ray of light coming from the point P(1,2) gets reflected from the point Q on the x -axis and then passes through the point R(4,3) . If the point S(h, k) is such that PQRS is a

JEE Main 2024 Solution View → 39

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

JEE Main 2024 Solution View → 40

If the line segment joining the points (5,2) and (2, a) subtends an angle (π)/(4) at the origin, then the absolute value of the product of all possible values of a is :

JEE Main 2024 Solution View → 41

Let a ray of light passing through the point (3,10) reflects on the line 2 x+y=6 and the reflected ray passes through the point (7,2) . If the equation of the incident ray is a

JEE Main 2024 Solution View → 42

The equations of two sides AB and AC of a triangle ABC are 4 x+y=14 and 3 x-2 y=5 , respectively. The point (2,-(4)/(3)) divides the third side BC internally in the ratio 2: 1 .

JEE Main 2024 Solution View → 43

If the orthocentre of the triangle formed by the lines 2 x+3 y-1=0, x+2 y-1=0 and a x+b y-1=0 , is the centroid of another triangle, whose circumcentre and orthocentre

JEE Main 2024 Solution View → 44

If P(6,1) be the orthocentre of the triangle whose vertices are A(5,-2), B(8,3) and C(h, k) , then the point C lies on the circle:

JEE Main 2024 Solution View → 45

If the locus of the point, whose distances from the point (2,1) and (1,3) are in the ratio 5: 4 , is a x^2+b y^2+c x y+d x+e y+170=0 , then the value of a^2+2 b+3 c+4 d+e is equal

JEE Main 2024 Solution View → 46

Let a variable line of slope m>0 passing through the point (4,-9) intersect the coordinate axes at the points A and B . The minimum value of the sum of the distances of A and B

JEE Main 2024 Solution View → 47

If A(3,1,-1), B((5)/(3), (7)/(3), (1)/(3)), C(2,2,1) and D((10)/(3), (2)/(3), (-1)/(3)) are the vertices of a quadrilateral A B C D , then its area is

JEE Main 2024 Solution View → 48

Let A(-1,1) and B(2,3) be two points and P be a variable point above the line A B such that the area of PAB is 10 . If the locus of P is a x+b y=15 , then 5 a+2 ~b is :

JEE Main 2024 Solution View → 49

Let two straight lines drawn from the origin O intersect the line 3 x+4 y=12 at the points P and Q such that OPQ is an isosceles triangle and ∠ POQ=90^ ∘ . If l=OP^2+PQ^2+QO^2

JEE Main 2024 Solution View → 50

If A(1,-1,2), B(5,7,-6), C(3,4,-10) and D(-1,-4,-2) are the vertices of a quadrilateral A B C D , then its area is :

JEE Main 2024 Solution View → 51

Consider a triangle ABC having the vertices A(1,2), B(α, β) and C(γ, δ) and angles ∠ A B C=(π)/(6) and ∠ B A C=(2 π)/(3) . If the points B and C lie on the line y=x+4 , then

JEE Main 2024 Solution View → 52

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 triangle by one unit inwards. Then the equation of the side of

JEE Main 2024 Solution View → 53

Let ABC be an isosceles triangle in which A is at (- 1, 0), ∠ A = (2π)/(3), AB = AC and B is on the positive x - axis. If BC = 4 3 and the line BC intersects the line y = x + 3 at

JEE Main 2024 Solution View → 54

Let A (a, b), B (3, 4) and (- 6, - 8) respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point P (2a + 3, 7b + 5) from the

JEE Main 2024 Solution View → 55

Let A (- 2, - 1) , B (1, 0) , C (α, β) and D (γ, δ) be the vertices of a parallelogram ABCD . If the point C lies on 2x - y = 5 and the point D lies on 3x - 2y = 6, then the value

JEE Main 2024 Solution View → 56

Let α, β, γ, δ ∈ Z and let A(α, β), B(1, 0), C(γ, δ) and D(1, 2) be the vertices of a parallelogram ABCD . If AB = 10 and the points A and C lie on the line 3y = 2x + 1 , then 2(α

JEE Main 2024 Solution View → 57

If x ^ 2 - y ^ 2 + 2hxy + 2gx + 2fy + c = 0 is the locus of a point, which moves such that it is always equidistant from the lines x + 2y + 7 = 0 and 2x - y + 8 = 0 , then the

JEE Main 2024 Solution View → 58

A line passing through the point A ( 9, 0 ) makes an angle of 30 ° with the positive direction of x -axis. If this line is rotated about A through an angle of 15 ° in the

JEE Main 2024 Solution View → 59

Let A be the point of intersection of the lines 3x + 2y = 14, 5x - y = 6 and B be the point of intersection of the lines 4x + 3y = 8, 6x + y = 5 . The distance of the point P ( 5

JEE Main 2024 Solution View → 60

The distance of the point ( 2, 3 ) from the line 2x - 3y + 28 = 0 , measured parallel to the line 3 x - y + 1 = 0 , is equal to

JEE Main 2024 Solution View → 61

Let (5, (a)/(4)) , be the circumcenter of a triangle with vertices A ( a, - 2 ) , B ( a, 6 ) and C ((a)/(4), - 2) . Let α denote the circumradius, β denote the area and γ denote

JEE Main 2024 Solution View → 62

In a ∆ ABC , suppose y = x is the equation of the bisector of the angle B and the equation of the side AC is 2x - y = 2 . If 2AB = BC and the point A and B are respectively ( 4, 6

JEE Main 2024 Solution View → 63

Let A and B be two finite sets with m and n elements respectively. The total number of subsets of the set A is 56 more than the total number of subsets of B . Then the distance of

JEE Main 2024 Solution View → 64

If the sum of squares of all real values of α , for which the lines 2x - y + 3 = 0, 6x + 3y + 1 = 0 and α x + 2y - 2 = 0 do not form a triangle is p , then the greatest integer

JEE Main 2024 Solution View → 65

Let R be the interior region between the lines 3x - y + 1 = 0 and x + 2y - 5 = 0 containing the origin. The set of all values of a , for which the points ( a ^ 2 , a + 1) lie in R

JEE Main 2024 Solution View → 66

The portion of the line 4x + 5y = 20 in the first quadrant is trisected by the lines L _ 1 and L _ 2 passing through the origin. The tangent of an angle between the lines L _ 1

JEE Main 2024 Solution View → 67

If (α, β) is the orthocenter of the triangle ABC with vertices A (3, – 7), B (– 1, 2) and C (4, 5), then 9α - 6β + 60 is equal to

JEE Main 2023 Solution View → 68

Consider the triangles with vertices A(2, 1), B(0, 0) and C(t, 4), t = [0, 4] . If the maximum and the minimum perimeters of such triangles are obtained at t = α and t = β

JEE Main 2023 Solution View → 69

Let ( α, β ) be the centroid of the triangle formed by the lines 15x - y = 82, 6x - 5y = - 4 and 9x + 4y = 17 . Then α + 2β and 2α - β are the roots of the equation

JEE Main 2023 Solution View → 70

If the point (α, 7 3 3 ) lies on the curve traced by the mid-points of the line segments of the lines xcosθ + ysinθ = 7, θ ∈ (0, (π)/(2)) between the co-ordinates axes, then α is

JEE Main 2023 Solution View → 71

In a triangle ABC , if cosA + 2cosB + cosC = 2 and the lengths of the sides opposite to the angles A and C are 3 and 7 respectively, then cosA - cosC is equal to

JEE Main 2023 Solution View → 72

If the line l _ 1 : 3y - 2x = 3 is the angular bisector of the lines l _ 2 : x - y + 1 = 0 and l _ 3 : + + 17 = 0 , then α ^ 2 + β ^ 2 - α - β is equal to ............

JEE Main 2023 Solution View → 73

Let the equations of two adjacent sides of a parallelogram ABCD be 2x - 3y = - 23 and 5x + 4y = 23 . If the equation of its one diagonal AC is 3x + 7y = 23 and the distance of A

JEE Main 2023 Solution View → 74

Let A ( 0, 1 ) , B ( 1, 1 ) and C ( 1, 0 ) be the mid-points of the sides of a triangle with incentre at the point D . If the focus of the parabola y ^ 2 = 4ax passing through D

JEE Main 2023 Solution View → 75

Let C ( α, β ) be the circumcentre of the triangle formed by the lines 4x + 3y = 69 , 4y - 3x = 17 , and x + 7y = 61 . Then ( α - β ) ^ 2 + α + β is equal to

JEE Main 2023 Solution View → 76

The straight lines l _ 1 and l _ 2 pass through the origin and trisect the line segment of the line L: 9x + 5y = 45 between the axes. If m _ 1 and m _ 2 are the slopes of the

JEE Main 2023 Solution View → 77

The combined equation of the two lines ax + by + c = 0 and a ^ ' x + b ^ ' y + c ^ ' = 0 can be written as (ax + by + c)( a ^ ' x + b ^ ' y + c ^ ' ) = 0 . The equation of the

JEE Main 2023 Solution View → 78

If the orthocentre of the triangle, whose vertices are (1, 2), (2, 3) and (3, 1) is (α, β), then the quadratic equation whose roots are α + 4β and 4α + β , is

JEE Main 2023 Solution View → 79

A straight line cuts off the intercepts OA=a and OB=b on the positive directions of x -axis and y- axis respectively. If the perpendicular from origin O to this line makes an

JEE Main 2023 Solution View → 80

A light ray emits from the origin making an angle 30 ° with the positive x -axis. After getting reflected by the line x + y = 1 , if this ray intersects x-axis at Q, then the

JEE Main 2023 Solution View → 81

Let B and C be the two points on the line y + x =0 such that B and C are symmetric with respect to the origin. Suppose A is a point on y - 2x = 2 such that ∆ ABC is an equilateral

JEE Main 2023 Solution View → 82

A triangle is formed by X -axis, Y -axis and the line 3x + 4y = 60 . Then the number of points P(a, b) which lie strictly inside the triangle, where a is an integer and b is a

JEE Main 2023 Solution View → 83

The equations of the sides AB, BC and CA of a triangle ABC are 2x + y = 0 , x + py = 21a (a ≠ 0) and x - y = 3 respectively. LetP (2, a) be the centroid of the triangle ABC , then

JEE Main 2023 Solution View → 84

Let PQRS be a quadrilateral in a plane, where QR = 1, ∠ PQR = ∠ QRS = 70 ° , ∠ PQS = 15 ° and ∠ PRS = 40 ° . If ∠ RPS = θ ° , PQ = α and PS = β , then the interval(s) that

JEE Advanced 2022 Solution View → 85

Let m _ 1 , m _ 2 be the slopes of two adjacent sides of a square of side a such that a ^ 2 + 11a + 3( m _ 1 ^ 2 + m _ 2 ^ 2 ) = 220 . If one vertex of the square is (10(cosα

JEE Main 2022 Solution View → 86

Let A (α, - 2), B (α, 6) and C((α)/(4), - 2) be vertices of a ∆ ABC . If (5, (α)/(4)) is the circumcentre of ∆ ABC , then which of the following is NOT correct about ∆ ABC

JEE Main 2022 Solution View → 87

Let the circumcentre of a triangle with vertices A(a, 3), B(b, 5) and C(a, b), ab > 0 be P(1, 1) . If the line AP intersects the line BC at the point Q( k _ 1 , k _ 2 ) , then k _

JEE Main 2022 Solution View → 88

For t ∈ (0, 2π), if ABCis an equilateral triangle with vertices A(sint, - cost) , B (cost, sint) and C (a, b) such that its orthocentre lies on a circle with centre (1, (1)/(3))

JEE Main 2022 Solution View → 89

The equations of the sides AB, BC and CA of a triangle ABC are 2x + y = 0, x + py = 39 and x - y = 3 respectively and P(2, 3) is its circumcentre. Then which of the following is

JEE Main 2022 Solution View → 90

Let A(1, 1), B(- 4, 3), C(- 2, - 5) be vertices of a triangle ABC, P be a point on side BC , and Δ _ 1 and Δ _ 2 be the areas of triangle APB and ABC . Respectively. If Δ _ 1 : Δ

JEE Main 2022 Solution View → 91

The equations of the sides AB, BC and CA of a triangle ABC are 2x + y = 0, x + py = 15a and x - y = 3 respectively. If its orthocentre is (2, a) , - (1)/(2) < a < 2 , then p is

JEE Main 2022 Solution View → 92

Let the point P(α, β) be at a unit distance from each of the two lines L _ 1 : 3x - 4y + 12 = 0 , and L _ 2 : 8x + 6y + 11 = 0 . If P lies below L _ 1 and above L _ 2 , then 100(α

JEE Main 2022 Solution View → 93

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 point B . If the length of the line segment AB is 29 3

JEE Main 2022 Solution View → 94

The distance of the origin from the centroid of the triangle whose two sides have the equations x - 2y + 1 = 0 and 2x - y - 1 = 0 and whose orthocenter is ((7)/(3), (7)/(3)) is:

JEE Main 2022 Solution View → 95

The distance between the two points A and A ^ ' which lie on y = 2 such that both the line segments AB and A ^ ' B (where B is the point (2, 3) ) subtend angle (π)/(4) at the

JEE Main 2022 Solution View → 96

Let a triangle be bounded by the lines L _ 1 : 2x + 5y = 10 ; L _ 2 : - 4x + 3y = 12 and the line L _ 3 , which passes through the point P(2, 3) , intersect L _ 2 at A and L _ 1

JEE Main 2022 Solution View → 97

A ray of light passing through the point P(2, 3) reflects on the X -axis at point A and the reflected ray passes through the point Q (5, 4) . Let R be the point that divides the

JEE Main 2022 Solution View → 98

In an isosceles triangle ABC , the vertex A is (6, 1) and the equation of the base BC is 2x + y = 4 . Let the point B lie on the line x + 3y = 7 . If (α, β) is the centroid∆ ABC

JEE Main 2022 Solution View → 99

Let R be the point (3, 7) and let P and Q be two points on the line x + y = 5 such that PQR is an equilateral triangle. Then the area of ∆ PQR is

JEE Main 2022 Solution View → 100

Let the area of the triangle with vertices A (1, α), B (α, 0) and C(0, α) be 4 sq. units. If the points (α, - α), (- α, α) and ( α ^ 2 , β) are collinear, then β is equal to

JEE Main 2022 Solution View → 101

Let A( 3 a , a ), a > 0 , be a fixed point in the xy -plane. The image of A in y -axis be B and the image of B in x -axis be C . If D(3cosθ, asinθ) , is a point in the fourth

JEE Main 2022 Solution View → 102

Consider a triangle Δ whose two sides lie on the x -axis and the line x + y + 1 = 0 . If the orthocenter of Δ is ( 1, 1 ) , then the equation of the circle passing through the

JEE Advanced 2021 Solution View → 103

Consider the lines L_ 1 and L_ 2 defined by L_ 1 : x 2 + y-1=0 and L_ 2 : x 2 - y+1=0 For a fixed constant λ , let C be the locus of a point P such that the product of the

JEE Advanced 2021 Solution View → 104

Consider the lines L_ 1 and L_ 2 defined by L_ 1 : x 2 + y-1=0 and L_ 2 : x 2 - y+1=0 For a fixed constant λ , let C be the locus of a point P such that the product of the

JEE Advanced 2021 Solution View → 105

Let the points of intersections of the lines x - y + 1 = 0, x - 2y + 3 = 0 and 2x - 5y + 11 = 0 are the mid points of the sides of a triangle ABC . Then the area of the triangle

JEE Main 2021 Solution View → 106

A man starts walking from the point P ( - 3, 4 ) , touches the x -axis at R, and then turns to reach at the point Q ( 0, 2 ) , The man is walking at a constant speed. If the man

JEE Main 2021 Solution View → 107

Let Abe the set of all points (α, β) such that the area of triangle formed by the points (5, 6) , (3, 2) and (α, β) is 12 square units. Then the least possible length of a line

JEE Main 2021 Solution View → 108

If p and q are the lengths of the perpendiculars from the origin on the lines, x cosec α - ysecα = kcot2α and xsinα + ycosα = ksin2α respectively, then k ^ 2 is equal to :

JEE Main 2021 Solution View → 109

Let A ( a, 0 ) , B ( b, 2b + 1 ) and C ( 0, b ) , b ≠ 0, | b | ≠ 1 , be points such that the area of triangle ABC is 1 sq. unit, then the sum of all possible values of a is:

JEE Main 2021 Solution View → 110

Let A be a fixed point ( 0, 6 ) and B be a moving point ( 2t, 0 ) . Let M be the mid-point of AB and the perpendicular bisector of AB meets the y - axis at C . The locus of the

JEE Main 2021 Solution View → 111

Let ABC be a triangle with A ( - 3, 1 ) and ∠ ACB = θ, 0 < θ < (π)/(2) . If the equation of the median through B is 2x + y - 3 = 0 and the equation of angle bisector of C is 7x

JEE Main 2021 Solution View → 112

The point P(a, b) undergoes the following three transformations successively: (a) reflection about the line y = x . (b) translation through 2 units along the positive direction of

JEE Main 2021 Solution View → 113

Two sides of a parallelogram are along the lines 4x + 5y = 0 and 7x + 2y = 0 . If the equation of one of the diagonals of the parallelogram is 11x + 7y = 9, then other diagonal

JEE Main 2021 Solution View → 114

Let the equation of the pair of lines, y = px and y = qx, can be written as (y - px)(y - qx) = 0 . Then the equation of the pair of the angle bisectors of the lines x ^ 2 - 4xy

JEE Main 2021 Solution View → 115

Consider a triangle having vertices A ( - 2, 3 ) , B ( 1, 9 ) and C ( 3, 8 ) . If a line L passing through the circum-centre of triangle ABC, bisects line BC, and intersects y

JEE Main 2021 Solution View → 116

Let the centroid of an equilateral triangle ABC be at the origin. Let one of the sides of the equilateral triangle be along the straight line x + y = 3 . If R and r be the radius

JEE Main 2021 Solution View → 117

The number of integral values of m so that the abscissa of point of intersection of lines 3x + 4y = 9 and y = mx + 1 is also an integer, is:

JEE Main 2021 Solution View → 118

The equation of one of the straight lines which passes through the point ( 1, 3 ) and makes an angles ^ - 1 ( 2 ) with the straight line, y + 1 = 3 2 x is

JEE Main 2021 Solution View → 119

Let tanα, tanβ and tanγ; α, β, γ ≠ (( 2n - 1 ) π)/(2), n ∈ N be the slopes of the three line segments OA, OB and OC, respectively, where O is origin. If circumcentre of coincides

JEE Main 2021 Solution View → 120

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

JEE Main 2021 Solution View → 121

Let A(- 1, 1), B(3, 4) and C(2, 0) be given three points. A line y = mx, m > 0 , intersects lines AC and BC at point P and Q respectively. Let A _ 1 and A _ 2 be the areas of and

JEE Main 2021 Solution View → 122

The intersection of three lines x - y = 0, x + 2y = 3 and 2x + y = 6 is a/an

JEE Main 2021 Solution View → 123

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

JEE Main 2021 Solution View → 124

Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point (- 5, 0) . If the locus of the point P is a circle of radius r, then 4 r ^

JEE Main 2021 Solution View → 125

Let O be the center of the circle x ^ 2 + y ^ 2 = r ^ 2 , where r > 5 2 . Suppose PQ is a chord of this circle and the equation of the line passing through P and Q is 2x + 4y = 5

JEE Advanced 2020 Solution View → 126

Let L denote the line in the xy -plane with x and y intercepts as 3 and 1 respectively. Then the image of the point (- 1, - 4) in the line is :

JEE Main 2020 Solution View → 127

A ray of light coming from the point ( 2, 2 3 ) is incident at an angle 30 ° on the line x = 1 at the point A . The ray gets reflected on the line x = 1 and meets x -axis at the

JEE Main 2020 Solution View → 128

If the line, 2x - y + 3 = 0 is at a distance 1 5 and 2 5 from the lines 4x - 2y + α = 0 and 6x - 3y + β = 0 respectively, then the sum of all possible values of α and β is

JEE Main 2020 Solution View → 129

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

JEE Main 2020 Solution View → 130

Let PQ be a diameter of the circle x ^ 2 + y ^ 2 = 9 . If α and β are the lengths of the perpendiculars from P and Q on the straight line, x + y = 2 respectively, then the maximum

JEE Main 2020 Solution View → 131

A triangle ABC lying in the first quadrant has two vertices as A(1, 2) and B(3, 1) . If ∠ BAC = 90 ^ o , and ar ( ) = 5 5 sq. units, then the abscissa of the vertex C is :

JEE Main 2020 Solution View → 132

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

JEE Main 2020 Solution View → 133

The set of all possible values of θ in the interval (0, π) for which the points (1, 2) and (sinθ, cosθ) lie on the same side of the line x + y = 1 is?

JEE Main 2020 Solution View → 134

Let two points be A(1, - 1) and B(0, 2) . If a point P(x', y') be such that the area of ∆ PAB = 5 sq. units and it lies on the line 3x + y - 4λ = 0, then a value of λ is

JEE Main 2020 Solution View → 135

The locus of the mid-points of the perpendiculars drawn from points on the line x = 2y , to the line x = y , is.

JEE Main 2020 Solution View → 136

Let A (1, 0), B (6, 2) and C((3)/(2), 6) be the vertices of a triangle ABC . If P is a point inside the triangle ABC such that the triangles APC, APB and BPC have equal areas

JEE Main 2020 Solution View → 137

Let the point B be the reflection of the point A(2, 3) with respect to the line 8x - 6y - 23 = 0 . Let T _ A and T _ B be circle of radii 2 and 1 with centres A and B

JEE Advanced 2019 Solution View → 138

A triangle has a vertex at ( 1, 2 ) and the mid points of the two sides through it are ( - 1, 1 ) and ( 2, 3 ) . Then the centroid of this triangle is:

JEE Main 2019 Solution View → 139

A straight line L at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes an angle of 60

JEE Main 2019 Solution View → 140

Lines are drawn parallel to the line 4x - 3y + 2 = 0, at a distance (3)/(5) units from the origin. Then which one of the following points lies on any of these lines?

JEE Main 2019 Solution View → 141

If the two lines x + (a - 1)y = 1 and 2x + a ^ 2 y = 1, (a ∈ R - \ 0,1\ ) are perpendicular, then the distance of their point of intersection from the origin is

JEE Main 2019 Solution View → 142

Slope of a line passing through P ( 2, 3 ) and intersecting the line x + y = 7 at a distance of 4 units from P, is

JEE Main 2019 Solution View → 143

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 points (h, k) and (4, 3) is perpendicular to L _ 1 , then (k)/(h) e

JEE Main 2019 Solution View → 144

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

JEE Main 2019 Solution View → 145

If a straight line passing through the point P(- 3, 4) is such that its intercepted portion between the coordinate axes is bisected at P , then its equation is :

JEE Main 2019 Solution View → 146

If the straight line 2x - 3y + 17 = 0 is perpendicular to the line passing through the points (7, 17) and (15, β), then β equals :

JEE Main 2019 Solution View → 147

If in a parallelogram ABDC , the coordinates of A, B and C are respectively (1,2),(3,4) and (2,5), then the equation of the diagonal AD is :

JEE Main 2019 Solution View → 148

In a triangle, the sum of lengths of two sides is x and the product of the lengths of the same two sides is y . if x^ 2 -c^ 2 =y, where c is the length of the third side of the

JEE Main 2019 Solution View → 149

Two vertices of a triangle are (0, 2) and (4, 3) . If its orthocenter is at the origin, then its third vertex lies in which quadrant?

JEE Main 2019 Solution View → 150

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 of its vertex is:

JEE Main 2019 Solution View → 151

If the line 3x + 4y - 24 = 0 intersects the x -axis is at the point A and the y -axis at the point B, then the incentre of the triangle OAB, where O is the origin, is:

JEE Main 2019 Solution View → 152

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

JEE Main 2019 Solution View → 153

Let S be the set of all triangles in the xy -plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each

JEE Main 2019 Solution View → 154

Let the equations of two sides of a triangle be 3x - 2y + 6 = 0 and 4x + 5y - 20 = 0 . If the orthocenter of this triangle is at (1, 1) then the equation of it&#39;s third side is:

JEE Main 2019 Solution View → 155

Consider the set of all lines px + qy + r = 0 such that 3p + 2q + 4r = 0 . Which one of the following statements is true?

JEE Main 2019 Solution View → 156

The locus of the point of intersection of the lines 2 x - y + 4 2 k = 0 and 2 kx + ky - 4 2 = 0 ( k is any non-zero real parameter) is

JEE Main 2018 Solution View → 157

The foot of the perpendicular drawn from the origin, on the line, 3 x+y=λ(λ ≠ 0) is P . If the line meets x -axis at A and y -axis at B , then the ratio B P : P A is

JEE Main 2018 Solution View → 158

The sides of a rhombus A B C D are parallel to the lines, x-y+2=0 and 7 x-y+3=0 . If the diagonals of the rhombus intersect at P(1,2) and the vertex A (different from the origin)

JEE Main 2018 Solution View → 159

In a triangle A B C , coordianates of A are (1,2) and the equations of the medians through B and C are x+y=5 and x=4 respectively. Then area of A B C (in sq. units) is

JEE Main 2018 Solution View → 160

A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q . If O is the origin and the rectangle OPRQ is completed, then the locus of

JEE Main 2018 Solution View → 161

A square, of each side 2 , lies above the x -axis and has one vertex at the origin. If one of the sides passing through the origin makes an angle 30 ° with the positive direction

JEE Main 2017 Solution View → 162

The locus of the point of intersection of the straight lines, tx - 2y - 3t = 0 and x - 2ty + 3 = 0(t ∈ R), is:

JEE Main 2017 Solution View → 163

Let k be an integer such that the triangle with vertices (k, - 3k), (5, k) and (- k, 2) has area 28 sq. units. Then the orthocenter of this triangle is at the point:

JEE Main 2017 Solution View → 164

Paragraph: Let F_ 1 (x_ 1 , 0) and F_ 2 (x_ 2 , 0) , for x_ 1 0 , be the foci of the ellipse x^ 2 9 + y^ 2 8 =1 . Suppose a parabola having vertex at the origin and focus at F_ 2

JEE Advanced 2016 Solution View → 165

A straight line through origin O meets the lines 3y = 10 - 4x and 8x + 6y + 5 = 0 at points A and B respectively. Then, O divides the segment AB in the ratio

JEE Main 2016 Solution View → 166

A ray of light is incident along a line which meets another line 7x - y + 1 = 0 at the point (0, 1) . The ray is then reflected from this point along the line y + 2x = 1 . Then

JEE Main 2016 Solution View → 167

If a variable line drawn through the intersection of the lines (x)/(3) + (y)/(4) = 1 and (x)/(4) + (y)/(3) = 1 , meets the coordinate axes at A and B , (A ≠ B), then the locus of

JEE Main 2016 Solution View → 168

The point (2, 1) is translated parallel to the line L: x - y = 4 by 2 3 units. If the new point Q lies in the third quadrant, then the equation of the line passing through Q and

JEE Main 2016 Solution View → 169

Two sides of a rhombus are along the lines, x - y + 1 = 0 and 7x - y - 5 = 0 . If its diagonals intersect at (- 1, - 2) , then which one of the following is a vertex of this

JEE Main 2016 Solution View → 170

Let the curve C be the mirror image of the parabola y ^ 2 = 4x with respect to the line x + y + 4 = 0 . If A and B are the points of intersection of C with the line y = - 5, then

JEE Advanced 2015 Solution View → 171

A straight line L through the point ( 3, - 2 ) is inclined at an angle of 60 ° to the line 3 x + y = 1 . If L also intersects the X -axis, then the equation of L is:

JEE Main 2015 Solution View → 172

Let L be the line passing through the point P(1, 2) such that its intercepted segment between the co-ordinate axes is bisected at P . If L _ 1 is the line perpendicular to L and

JEE Main 2015 Solution View → 173

The points (0, (8)/(3)), (1, 3) and (82, 30)

JEE Main 2015 Solution View → 174

Locus of the image of the point ( 2, 3 ) in the line (2 x - 3 y + 4) + k (x - 2 y + 3) = 0 , k ∈ R , is a

JEE Main 2015 Solution View → 175

For a point P in the plane, let d _ 1 (P) and d _ 2 (P) be the distances of the point P from the lines x - y = 0 and x + y = 0 respectively. The area of the region R consisting of

JEE Advanced 2014 Solution View → 176

If a line L is perpendicular to the line 5x - y = 1, and the area of the triangle formed by the line L and the coordinate axes is 5 sq units, then the distance of the line L from

JEE Main 2014 Solution View → 177

The circumcentre of a triangle lies at the origin and its centroid is the midpoint of the line segment joining the points ( a ^ 2 + 1, a ^ 2 + 1 ) and (2a , - 2 a), a ≠ 0 . Then

JEE Main 2014 Solution View → 178

If a line intercepted between the coordinate axes is trisected at a point A(4,3) , which is nearer to x -axis, then its equation is:

JEE Main 2014 Solution View → 179

If the three distinct lines x+2 a y+a=0, x+3 b y +b=0 and x+4 a y+a=0 are concurrent, then the point (a, b) lies on a :

JEE Main 2014 Solution View → 180

The base of an equilateral triangle is along the line given by 3 x+4 y=9 . If a vertex of the triangle is (1,2) , then the length of a side of the triangle is:

JEE Main 2014 Solution View → 181

Given three points P, Q, R with P(5, 3) and R lies on the x - axis. If the equation of RQ is x - 2y = 2 and PQ is parallel to the x - axis, then the centroid of Δ PQR lies on the

JEE Main 2014 Solution View → 182

Let a and b be any two numbers satisfying 1 a ^ 2 + 1 b ^ 2 = (1)/(4). Then, the foot of perpendicular from the origin on the variable line (x)/(a) + (y)/(b) = 1 lies on :

JEE Main 2014 Solution View → 183

Let PS be the median of the triangle with vertices P ( 2, 2 ) , Q ( 6, - 1 ) and R ( 7, 3 ) . The equation of the line passing through ( 1, - 1 ) and parallel to PS is

JEE Main 2014 Solution View → 184

Let a, b, c and d be non-zero numbers. If the point of intersection of the lines 4ax + 2ay + c = 0 and 5bx + 2by + d = 0 lies in the fourth quadrant and is equidistant from the

JEE Main 2014 Solution View → 185

Paragraph: Let S=S_ 1 ∩ S_ 2 ∩ S_ 3 , where S_ 1 =\ z ∈ ℂ:|z| 0\ and S_ 3 =\ z ∈ ℂ: Re z>0\ . Question: Area of S=

JEE Advanced 2013 Solution View → 186

Paragraph: Let S=S_ 1 ∩ S_ 2 ∩ S_ 3 , where S_ 1 =\ z ∈ ℂ:|z| 0\ and S_ 3 =\ z ∈ ℂ: Re z>0\ . Question: _ z ∈ S |1-3 i-z|=

JEE Advanced 2013 Solution View → 187

For a > b > c > 0, the distance between (1, 1) and the point of intersection of the lines ax + by + c = 0 and bx + ay + c = 0 is less than 2 2 .Then

JEE Advanced 2013 Solution View → 188

If the image of point P(2,3) in a line L is Q(4,5) , then the image of point R(0,0) in the same line is:

JEE Main 2013 Solution View → 189

Let x ∈(0,1) . The set of all x such that ^ -1 x> ^ -1 x , is the interval:

JEE Main 2013 Solution View → 190

If two lines L_1 and L_2 in space, are defined by aligned & L_1=\ x= λ y+( λ - 1), & z=( λ - 1) y+ λ \ and & L_2=\ x= μ y+(1- μ ), aligned z=(1- μ ) y+ μ \ then L_1 is

JEE Main 2013 Solution View → 191

Let θ_1 be the angle between two lines 2 x+3 y+ c_1=0 and -x+5 y+c_2=0 and θ_2 be the angle between two lines 2 x+3 y+c_1=0 and -x+5 y+ c_3=0 , where c_1, c_2, c_3 are any real

JEE Main 2013 Solution View → 192

If the x -intercept of some line L is double as that of the line, 3 x+4 y=12 and the y -intercept of L is half as that of the same line, then the slope of L is :

JEE Main 2013 Solution View → 193

The acute angle between two lines such that the direction cosines l, m, n , of each of them satisfy the equations l+m+n=0 and l^2+m^2-n^2=0 is :

JEE Main 2013 Solution View → 194

A light ray emerging from the point source placed at P(1,3) is reflected at a point Q in the axis of x . If the reflected ray passes through the point R (6,7) , then the abscissa

JEE Main 2013 Solution View → 195

If the three lines x-3 y=p, a x+2 y=q and a x+y=r form a right-angled triangle then :

JEE Main 2013 Solution View → 196

A ray of light along x + 3 y = 3 gets reflected upon reaching X - axis, the equation of the reflected ray is

JEE Main 2013 Solution View → 197

The x - coordinate of the incentre of the triangle that has the coordinates of midpoints of its sides as (0, 1), (1, 1) and (1, 0) is

JEE Main 2013 Solution View → 198

The line parallel to x -axis and passing through the point of intersection of lines a x+2 b y+3 b=0 and b x-2 a y-3 a=0 , where (a, b) ≠(0,0) is

JEE Main 2012 Solution View → 199

Consider the straight lines aligned & L_1: x-y=1 & L_2: x+y=1 & L_3: 2 x+2 y=5 & L_4: 2 x-2 y=7 aligned The correct statement is

JEE Main 2012 Solution View → 200

Let L be the line y=2 x , in the two dimensional plane. Statement 1: The image of the point (0,1) in L is the point ((4)/(5), (3)/(5)) Statement 2: The points (0,1) and ((4)/(5)

JEE Main 2012 Solution View →
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Related JEE Mathematics chapters

Application of Derivatives (795)Three Dimensional Geometry (756)Sequences and Series (748)Functions (700)Definite Integration (692)Vector Algebra (616)Differential Equations (586)Continuity and Differentiability (576)Probability (561)Complex Number (551)Binomial Theorem (550)Quadratic Equation (517)

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