JEE-MAIN SERIES Mathematics
Straight Lines
56 previous year questions.
Volume: 56 Ques
Yield: High
High-Yield Trend
20
2026 2
2024 7
2023 4
2022 6
2021 4
2019 2
2018 2
2016 2
2014 7
2013 Chapter Questions 56 MCQs
01
PYQ 2013
medium
mathematics ID: jee-main
If the extremities of the base of an isosceles triangle are the points and and the equation of one of the sides is , then the area of the triangle, in square units, is :
1
2
3
4
02
PYQ 2013
easy
mathematics ID: jee-main
If the three lines and form a right-angled triangle then :
1
2
3
4
03
PYQ 2013
medium
mathematics ID: jee-main
If the x-intercept of some line is double as that of the line, and the -intercept of , is half as that of the same line, then the slope of is:
1
2
3
4
04
PYQ 2013
medium
mathematics ID: jee-main
Let and be the vertices of a triangle . If the centroid of this triangle lies on the line , then the vertex lies on the line :
1
2
3
4
05
PYQ 2013
medium
mathematics ID: jee-main
A light ray emerging from the point source placed at is reflected at a point in the axis of . If the reflected ray passes through the point , then the abscissa of is:
1
2
3
4
06
PYQ 2013
medium
mathematics ID: jee-main
The -coordinate of the incentre of the triangle that has the coordinates of mid-points of its sides as and is
1
2
3
4
07
PYQ 2013
easy
mathematics ID: jee-main
If the image of point in a line is , then the image of point in the same line is:
1
2
3
4
08
PYQ 2014
easy
mathematics ID: jee-main
If a line intercepted between the coordinate axes is trisected at a point , which is nearer to -axis, then its equation is :
1
2
3
4
09
PYQ 2014
medium
mathematics ID: jee-main
Let and be non-zero numbers. If the point of intersection of the lines and lies in the fourth quadrant and is equidistant from the two axes, then
1
2
3
4
10
PYQ 2016
medium
mathematics ID: jee-main
If a variable line drawn through the intersection of the lines and , meets the coordinate axes at and , , then the locus of the midpoint of is :
1
2
3
4
11
PYQ 2016
medium
mathematics ID: jee-main
Two sides of a rhombus are along the lines, and . If its diagonals intersect at , then which one of the following is a vertex of this rhombus?
1
(-3 , -9)
2
(-3 , -8)
3
4
12
PYQ 2018
medium
mathematics ID: jee-main
A straight line through a fixed point intersects the coordinate axes at distinct points and . If is the origin and the rectangle is completed, then the locus of is:
1
3x + 2y = 6
2
2x + 3y = xy
3
3x + 2y = xy
4
3x + 2y = 6xy
13
PYQ 2018
medium
mathematics ID: jee-main
Let the orthocenter an centroid of a triangle be and respectively. If is the circumcentre of this triangle, then the radius of the circle having line segment as diameter, is:
1
2
3
4
14
PYQ 2019
medium
mathematics ID: jee-main
If in a parallelogram , the coordinates of and are respectively and then the equation of the diagonal is :
1
5x + 3y - 11 = 0
2
3x - 5y + 7 = 0
3
3x + 5y - 13 = 0
4
5x - 3y + 1 = 0
15
PYQ 2019
medium
mathematics ID: jee-main
Let the equations of two sides of a triangle be and . If the orthocentre of this triangle is at , then the equation of its third side is :
1
2
3
4
16
PYQ 2019
medium
mathematics ID: jee-main
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
1
2
3
4
17
PYQ 2019
medium
mathematics ID: jee-main
Two vertices of a triangle are and . If its orthocentre is at the origin, then its third vertex lies in which quadrant ?
1
Fourth
2
Second
3
Third
4
First
18
PYQ 2021
medium
mathematics ID: jee-main
The equation of one of the straight lines which passes through the point (1, 3) and makes an angle tan⁻¹(√2) with the straight line, y + 1 = 3√2 x is :
1
4√2 x + 5y - (15 + 4√2) = 0
2
4√2 x - 5y - (5 + 4√2) = 0
3
5√2 x + 4y - (15 + 4√2) = 0
4
4√2 x + 5y - 4√2 = 0
19
PYQ 2021
medium
mathematics ID: jee-main
A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is . Three stones A, B and C are placed at the points (1, 1), (2, 2) and (4, 4) respectively. Then which of these stones is/are on the path of the man ?
1
A only
2
B only
3
C only
4
All the three
20
PYQ 2021
medium
mathematics ID: jee-main
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 of circumcircle and incircle respectively of ΔABC, then (R + r) is equal to :
1
2
2
9/
3
7
4
3
21
PYQ 2021
easy
mathematics ID: jee-main
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 :
1
0
2
1
3
2
4
3
22
PYQ 2021
medium
mathematics ID: jee-main
Let be a triangle with and . If the equation of the median through is and the equation of angle bisector of is , then is equal to :
1
2
3
4
2
23
PYQ 2021
medium
mathematics ID: jee-main
Two sides of a parallelogram are along the lines and . If the equation of one of the diagonals of the parallelogram is , then other diagonal passes through the point :
1
(1, 2)
2
(2, 2)
3
(2, 1)
4
(1, 3)
24
PYQ 2022
hard
mathematics ID: jee-main
The length of the perpendicular from the point on the line passing through and parallel to the line is :
1
2
3
4
1
25
PYQ 2022
easy
mathematics ID: jee-main
The slope of the tangent to a curve C : y=y(x) at any point [x, y) on it is If C passes through the points and $ then is equal to :
1
2
3
4
26
PYQ 2022
medium
mathematics ID: jee-main
If two straight lines whose direction cosines are given by the relations , are parallel, then the positive value of is :
1
6
2
4
3
3
4
2
27
PYQ 2022
hard
mathematics ID: jee-main
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(k1, k2), then k1 + k2 is equal to :
1
2
2
3
4
4
28
PYQ 2023
hard
mathematics ID: jee-main
Let and be respectively the sets of all for which the system of linear equations has unique solution and infinitely many solutions Then
1
and
2
is an infinite set and
3
and
4
and is an infinite set
29
PYQ 2023
easy
mathematics ID: jee-main
Orthocentre of triangle having vertices as A (1,2), B(3,-4), C(0,6) is
1
(-129, -37)
2
(9, -1)
3
(7, -3)
4
(28, -16)
30
PYQ 2023
hard
mathematics ID: jee-main
Let the area enclosed by the -axis, and the tangent and normal drawn to the curve at the point be . Then is equal to ______
31
PYQ 2023
medium
mathematics ID: jee-main
Let the six numbers , be in AP and If the mean of these six numbers is and their variance is , then is equal to :
1
105
2
210
3
200
4
220
32
PYQ 2023
medium
mathematics ID: jee-main
For , suppose the system of linear equations has infinitely many solutions Then and are the roots of
1
2
3
4
33
PYQ 2023
easy
mathematics ID: jee-main
A rectangle is drawn by lines x=0, x=2, y=0 and y=5. Points A and B lie on coordinate axes. If line AB divides the area of rectangle in 4:1, then the locus of mid-point of AB is?
1
Circle
2
Hyperbola
3
Ellipse
4
Straight line
34
PYQ 2023
hard
mathematics ID: jee-main
The straight lines l1 and l2 pass through the origin and trisect the line segment of the line L: 9x + 5y = 45 between the axes. If m1 and m2 are the slopes of the lines l1 and l2, then the point of intersection of the line y = (m1 + m2)x with L lies on
1
y-2x=5
2
6x-y=15
3
y-x=5
4
6x+y=10
35
PYQ 2024
medium
mathematics ID: jee-main
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 the new triangle nearest to origin is :
1
2
3
4
36
PYQ 2024
medium
mathematics ID: jee-main
If the sum of squares of all real values of , for which the lines , and do not form a triangle , then the greatest integer less than or equal to is ....
37
PYQ 2026
medium
mathematics ID: jee-main
Let the line intersect the lines and at the points A and B, respectively. Let the bisector of the obtuse angle between the lines and intersect the line at the point C. Then is equal to:
1
5:1
2
1:5
3
2:3
4
3:2
38
PYQ 2026
easy
mathematics ID: jee-main
Let be the vertex of the parabola . Let and be two points on parabola such that chords and are perpendicular to each other. If the locus of mid-point of segment is a conic , then latus rectum of is
1
1
2
2
3
3
4
4
39
PYQ 2026
medium
mathematics ID: jee-main
Let chord of length of the parabola be such that the ordinates of points and are in the ratio . If the chord subtends an angle at the focus of the parabola, then is equal to:
1
2
3
4
40
PYQ 2026
medium
mathematics ID: jee-main
Let and be two distinct roots of the equation . Let the sets
, and
.
Then is equal to:
, and
.
Then is equal to:
1
18
2
22
3
26
4
34
41
PYQ 2026
medium
mathematics ID: jee-main
Let one root of the quadratic equation in :
be twice the other. Then the length of the latus rectum of the parabola is equal to:
be twice the other. Then the length of the latus rectum of the parabola is equal to:
1
4
2
6
3
8
4
12
42
PYQ 2026
medium
mathematics ID: jee-main
Let in a , given that , mid-point of is and centroid is then circumcentre is , then the value of is :
1
305
2
315
3
351
4
350
43
PYQ 2026
easy
mathematics ID: jee-main
If the eccentricity of the hyperbola , passing through , satisfies , then the length of the latus rectum of the hyperbola is:
1
10
2
20
3
25
4
30
44
PYQ 2026
medium
mathematics ID: jee-main
The area (in square units) of the region is:
1
2
3
4
45
PYQ 2026
medium
mathematics ID: jee-main
Given vectors and . Another vector satisfy equations and , then find :
46
PYQ 2026
medium
mathematics ID: jee-main
If the ratio of y-ordinates of points on the parabola is 1 : 2 and the length of the chord joining these points is , then find the angle subtended by the chord at the focus of the parabola:
1
2
3
4
47
PYQ 2026
medium
mathematics ID: jee-main
Given two lines and . Third line is perpendicular to both lines & . Find acute angle between lines & .
1
2
3
4
48
PYQ 2026
medium
mathematics ID: jee-main
Given point satisfies the hyperbola
where eccentricity is a root of the equation . Then find the length of latus rectum of the hyperbola
1
2
3
4
49
PYQ 2026
medium
mathematics ID: jee-main
Consider the circle having centre on line and radius 6. If the line cuts the circle at A and B then is:
1
40
2
60
3
80
4
100
50
PYQ 2026
hard
mathematics ID: jee-main
If is the image of with respect to line , where . If is at a distance of from the foot of the perpendicular of Q on L, then is:
1
179
2
120
3
321
4
220
51
PYQ 2026
medium
mathematics ID: jee-main
Locus of the mid-point of chord of circle , subtending a right angle at the center is
1
2
3
4
52
PYQ 2026
medium
mathematics ID: jee-main
Let represent an ellipse. The major axis of the given ellipse is the y-axis and is a decreasing function. If the range of is , then is:
1
1
2
2
3
3
4
4
53
PYQ 2026
medium
mathematics ID: jee-main
The line passing through point of intersection of and intersects axes at P and Q, then locus of midpoint of PQ is
1
2
3
4
54
PYQ 2026
medium
mathematics ID: jee-main
If the lines \& are perpendicular and their point of intersection is the centre of a circle which passes through origin. If chord intersects this circle at \& then
1
18
2
20
3
9
4
36
55
PYQ 2026
medium
mathematics ID: jee-main
Let the angles made with the positive -axis by two straight lines drawn from the point and meeting the line at a distance from the point be and . Then the value of is
1
2
3
4
56
PYQ 2026
medium
mathematics ID: jee-main
If two lines drawn from a point intersect the line at a distance , then the angle between the lines is