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
About Straight Lines - JEE-MAIN
Straight Lines is a vital chapter for JEE-MAIN aspirants. Mastering the concepts covered in this chapter is essential for securing a top rank.
By rigorously practicing the previous year questions associated with this chapter, you can identify high-yield topics, understand the examiner's perspective, and boost your confidence during the actual exam.
Frequently Asked Questions
Why focus on Straight Lines PYQs?
Analyzing PYQs for this specific chapter reveals the most frequently tested concepts and the typical complexity of questions, allowing you to tailor your study plan efficiently.
How to best use this analysis?
Review the topic breakdown to see which sub-topics within Straight Lines carry the most weight. Then, tackle the questions iteratively to solidify your understanding.