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Straight Lines — JEE Main & Advanced Mathematics PYQs

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

497 questionsMathematicsSolutions on every page
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 r

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 ( , ) , then 9( + ) is equal

JEE Main 2026 Solution View → 4

Let P(3 , 2 ) , 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 centroid of the tr

JEE Main 2026 Solution View → 5

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

JEE Main 2026 Solution View → 6

Let the line L₁ : x + 3 = 0 intersect the lines L₂ : x - y = 0 and L₃ : 3x + y = 0 at the points A and B , respectively. Let the bisector of the obtuse angle between the lines L₂ a

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 ( , ) , then 21( + )

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 ( , ) , then the greatest integer

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 ₁ and ₂ . Then the

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 x+ y=5 , then the value of ²+ 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 ( , ) and D ( , ) are the other two verti

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 distance

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 2a,

JEE Main 2026 Solution View → 15

Let a point A lie between the parallel lines L₁ and L₂ such that its distances from L₁ and L₂ are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral trian

JEE Main 2026 Solution View → 16

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

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 with the positive x -axis and the equations of its diagonals are ( 3 +1) x+

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 tria

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 line

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 +1)+ y (7 +2)=17 +5 , 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 from t

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

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

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 li

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 ( A B C ) in the line (3 x+6

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

JEE Main 2025 Solution View → 30

Let the points ( 11 2 , ) 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 is equal to :

JEE Main 2025 Solution View → 31

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

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 equal

JEE Main 2025 Solution View → 34

Let A(6,8), B(10 ,-10 ) and C(-10 , 10 ) , 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 ) is equal to

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 ( , ) , then 15( - ) 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 ( , ) and the centre of the of the circle circumsc

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 pa

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 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 x+b

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 . the

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 respectively

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 fro

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 ( , ) and C ( , ) and angles A B C= 6 and B A C= 2 3 . If the points B and C lie on the line y=x+4 , then ^2+ ^2 is equal to

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 o

JEE Main 2024 Solution View → 53

Let A B C be an isosceles triangle in which A is at − 1 , 0 , ∠ A = 2 π 3 , A B = A C and B is on the positive x - axis. If B C = 4 3 and the line B C intersects the line y = x + 3

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 2 a + 3 , 7 b + 5 from the line

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 A B C D . If the point C lies on 2 x − y = 5 and the point D lies on 3 x − 2 y = 6 , then the val

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 A B C D . If A B = 10 and the points A and C lie on the line 3 y = 2 x + 1

JEE Main 2024 Solution View → 57

If x 2 - y 2 + 2 h x y + 2 g x + 2 f y + c = 0 is the locus of a point, which moves such that it is always equidistant from the lines x + 2 y + 7 = 0 and 2 x - 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 clockwis

JEE Main 2024 Solution View → 59

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

JEE Main 2024 Solution View → 60

The distance of the point ( 2 , 3 ) from the line 2 x - 3 y + 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 the perime

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 A C is 2 x - y = 2 . If 2 A B = B C and the point A and B are respectively (

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 2 x - y + 3 = 0 , 6 x + 3 y + 1 = 0 and αx + 2 y - 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 3 x - y + 1 = 0 and x + 2 y - 5 = 0 containing the origin. The set of all values of a , for which the points a 2 , a + 1 lie in R , i

JEE Main 2024 Solution View → 66

The portion of the line 4 x + 5 y = 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 and L 2

JEE Main 2024 Solution View → 67

If α , β is the orthocenter of the triangle A B C with vertices A 3 , – 7 , B – 1 , 2 and C 4 , 5 , then 9 α - 6 β + 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 = &#94

JEE Main 2023 Solution View → 69

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

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 x cos θ + y sin θ = 7 , θ ∈ 0 , π 2 between the c

JEE Main 2023 Solution View → 71

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

JEE Main 2023 Solution View → 72

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

JEE Main 2023 Solution View → 73

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

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 = 4 a x passing through D

JEE Main 2023 Solution View → 75

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

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 : 9 x + 5 y = 45 between the axes. If m 1 and m 2 are the slopes of the lines l 1

JEE Main 2023 Solution View → 77

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

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 + 4 β and 4 α + &#9

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 - 2 x = 2 such that ∆ A B C is an equ

JEE Main 2023 Solution View → 82

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

JEE Main 2023 Solution View → 83

The equations of the sides A B , B C & C A of a triangle A B C are 2 x + y = 0 , x + p y = 21 a a ≠ 0 and x - y = 3 respectively. Let P 2 , a be the centroid of the trian

JEE Main 2023 Solution View → 84

Let P Q R S be a quadrilateral in a plane, where Q R = 1 , ∠ P Q R = ∠ Q R S = 70 ° , ∠ P Q S = 15 ° and ∠ P R S = 40 ° . If ∠ R P S =

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 + 11 a + 3 m 1 2 + m 2 2 = 220 . If one vertex of the square is 10 cos α - sin α , 1

JEE Main 2022 Solution View → 86

Let A α , - 2 , B α , 6 and C α 4 , - 2 be vertices of a ∆ A B C . If 5 , α 4 is the circumcentre of ∆ A B C , then which of the following is NOT co

JEE Main 2022 Solution View → 87

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

JEE Main 2022 Solution View → 88

For t ∈ 0 , 2 π , if A B C 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 centr

JEE Main 2022 Solution View → 89

The equations of the sides A B , B C and C A of a triangle A B C are 2 x + y = 0 , x + p y = 39 and x - y = 3 respectively and P 2 , 3 is its circumcentre. Then which of the follow

JEE Main 2022 Solution View → 90

Let A 1 , 1 , B - 4 , 3 , C - 2 , - 5 be vertices of a triangle A B C , P be a point on side B C , and Δ 1 and Δ 2 be the areas of triangle A P B and A B C . Respectively

JEE Main 2022 Solution View → 91

The equations of the sides A B , B C and C A of a triangle A B C are 2 x + y = 0 , x + p y = 15 a and x - y = 3 respectively. If its orthocentre is 2 , a , - 1 2 < a < 2 ,

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 : 3 x - 4 y + 12 = 0 , and L 2 : 8 x + 6 y + 11 = 0 . If P lies below L 1 and above L 2 , then

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 A B is 29 3 , the

JEE Main 2022 Solution View → 94

The distance of the origin from the centroid of the triangle whose two sides have the equations x - 2 y + 1 = 0 and 2 x - 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 A B and A ' B (where B is the point 2 , 3 ) subtend angle π 4 at the origin,

JEE Main 2022 Solution View → 96

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

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 lin

JEE Main 2022 Solution View → 98

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

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 P Q R is an equilateral triangle. Then the area of ∆ P Q R 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 ar

JEE Main 2022 Solution View → 101

Let A 3 a , a , a > 0 , be a fixed point in the x y -plane. The image of A in y -axis be B and the image of B in x -axis be C . If D 3 cos θ , a sin θ , is a point in

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 throu

JEE Advanced 2021 Solution View → 103

Consider the lines L₁ and L₂ defined by L₁: x 2 +y-1=0 and L₂: x 2 -y+1=0 For a fixed constant , let C be the locus of a point P such that the product of the distance of P from L₁

JEE Advanced 2021 Solution View → 104

Consider the lines L₁ and L₂ defined by L₁: x 2 +y-1=0 and L₂: x 2 -y+1=0 For a fixed constant , let C be the locus of a point P such that the product of the distance of P from L₁

JEE Advanced 2021 Solution View → 105

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

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 A be 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 len

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 - y sec α = k cot 2 α and x sin α + y cos α = k sin 2 α respe

JEE Main 2021 Solution View → 109

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

JEE Main 2021 Solution View → 110

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

JEE Main 2021 Solution View → 111

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

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 x -

JEE Main 2021 Solution View → 113

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

JEE Main 2021 Solution View → 114

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 . Then the equation of the pair of the angle bisectors of the lines x 2 - 4 x y -

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 A B C , bisects line B C , and intersect

JEE Main 2021 Solution View → 116

Let the centroid of an equilateral triangle A B C 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 3 x + 4 y = 9 and y = m x + 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 tan - 1 ( 2 ) with the straight line, y + 1 = 3 2 x is

JEE Main 2021 Solution View → 119

Let tan α , tan β and tan γ ; α , β , γ ≠ ( 2 n - 1 ) π 2 , n ∈ N be the slopes of the three line segments O A , O B and O C , respec

JEE Main 2021 Solution View → 120

In a triangle P Q R , the co-ordinates of the points P and Q are - 2 , 4 and 4 , - 2 respectively. If the equation of the perpendicular bisector of P R is 2 x - y + 2 = 0 , then th

JEE Main 2021 Solution View →
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