Straight Lines and Pair of Straight Lines PYQs - Last 10 Years
JEE Main / Mathematics / Coordinate Geometry / 142 recent questions
MathematicsCoordinate Geometry2017-2026
Practice 142 JEE Main Mathematics questions from Straight Lines and Pair of Straight Lines. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
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2017-2026
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Last 10 Years Straight Lines and Pair of Straight Lines Questions
Showing 42 of 142 filtered questions.
1Straight Lines And Pair Of Straight Lines
The equation of one of the straight lines which passes through the point (1, 3) and makes an angles \({\tan ^{ - 1}}\left( {\sqrt 2 } \right)\) with the straight line, y + 1 = 3\({\sqrt 2 }\) x is :
MCQ+4 / -12021
2Straight Lines And Pair Of Straight Lines
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 \(\Delta\)ABC, th...
MCQ+4 / -12021
3Straight Lines And Pair Of Straight Lines
The maximum value of z in the following equation z = 6xy + y2, where 3x + 4y \(\le\) 100 and 4x + 3y \(\le\) 75 for x \(\ge\) 0 and y \(\ge\) 0 is __________.
INTEGER+4 / -12021
4Straight Lines And Pair Of Straight Lines
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 centre of the circumcircle of the \(\Delta\)PQR is :
MCQ+4 / -12021
5Straight Lines And Pair Of Straight Lines
Let tan\(\alpha\), tan\(\beta\) and tan\(\gamma\); \(\alpha\), \(\beta\), \(\gamma\) \(\ne\) \({{(2n - 1)\pi } \over 2}\), n\(\in\)N be the slopes of three line segments OA, OB and OC, respectively, where O is origin. If circumcentre of $$\...
INTEGER+4 / -12021
6Straight Lines And Pair Of Straight Lines
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 A1 and A2 be the areas of \(\Delta\)ABC and \(\Delta\)PQC respectively, such that A1 = 3A2, the...
MCQ+4 / -12021
7Straight Lines And Pair Of Straight Lines
Let C be the centroid of the triangle with
vertices (3, –1), (1, 3) and (2, 4). Let P be the
point of intersection of the lines x + 3y – 1 = 0
and 3x – y + 1 = 0. Then the line passing through
the points C and P also passes through the
poin...
vertices (3, –1), (1, 3) and (2, 4). Let P be the
point of intersection of the lines x + 3y – 1 = 0
and 3x – y + 1 = 0. Then the line passing through
the points C and P also passes through the
poin...
MCQ+4 / -12020
8Straight Lines And Pair Of Straight Lines
Let two points be A(1, –1) and B(0, 2). If a point
P(x', y') be such that the area of \(\Delta\)PAB = 5 sq.
units and it lies on the line, 3x + y – 4\(\lambda\) = 0,
then a value of \(\lambda\) is :
P(x', y') be such that the area of \(\Delta\)PAB = 5 sq.
units and it lies on the line, 3x + y – 4\(\lambda\) = 0,
then a value of \(\lambda\) is :
MCQ+4 / -12020
9Straight Lines And Pair Of Straight Lines
Let A(1, 0), B(6, 2) and C \(\left( {{3 \over 2},6} \right)\) 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, then the length of the line segment PQ, wher...
INTEGER+4 / -02020
10Straight Lines And Pair Of Straight Lines
The locus of the mid-points of the perpendiculars drawn from points on the line, x = 2y to the line
x = y is :
x = y is :
MCQ+4 / -12020
11Straight Lines And Pair Of Straight Lines
A ray of light coming from the point (2, \(2\sqrt 3\)) is incident at an angle 30o on the line x = 1 at the
point A. The ray gets reflected on the line x = 1 and meets x-axis at the point B. Then, the line AB
passes through the point :
point A. The ray gets reflected on the line x = 1 and meets x-axis at the point B. Then, the line AB
passes through the point :
MCQ+4 / -12020
12Straight Lines And Pair Of Straight Lines
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 this line is :
y intercepts as 3 and 1 respectively. Then the
image of the point (–1, –4) in this line is :
MCQ+4 / -12020
13Straight Lines And Pair Of Straight Lines
If the line, 2x - y + 3 = 0 is at a distance \({1 \over {\sqrt 5 }}\)
and \({2 \over {\sqrt 5 }}\) from the lines 4x - 2y + \(\alpha\) = 0 and 6x - 3y + \(\beta\) = 0, respectively, then the sum of all possible values of \(\alpha\) and $...
and \({2 \over {\sqrt 5 }}\) from the lines 4x - 2y + \(\alpha\) = 0 and 6x - 3y + \(\beta\) = 0, respectively, then the sum of all possible values of \(\alpha\) and $...
INTEGER+4 / -02020
14Straight Lines And Pair Of Straight Lines
Two vertical poles AB = 15 m and CD = 10 m are standing apart on a horizontal ground with points A
and C on the ground. If P is the point of intersection of BC and AD, then the height of P (in m)
above the line AC is :
and C on the ground. If P is the point of intersection of BC and AD, then the height of P (in m)
above the line AC is :
MCQ+4 / -12020
15Straight Lines And Pair Of Straight Lines
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 :
MCQ+4 / -12020
16Straight Lines And Pair Of Straight Lines
If a \(\Delta\)ABC has vertices A(–1, 7), B(–7, 1) and
C(5, –5), then its orthocentre has coordinates :
C(5, –5), then its orthocentre has coordinates :
MCQ+4 / -12020
17Straight Lines And Pair Of Straight Lines
The set of all possible values of
\(\theta\) in the interval
(0, \(\pi\)) for which the points (1, 2) and (sin
\(\theta\), cos \(\theta\)) lie on the same side of the line x + y =
1 is :
\(\theta\) in the interval
(0, \(\pi\)) for which the points (1, 2) and (sin
\(\theta\), cos \(\theta\)) lie on the same side of the line x + y =
1 is :
MCQ+4 / -12020
18Straight Lines And Pair Of Straight Lines
Consider the set of all lines px + qy + r = 0 such that 3p + 2q + 4r = 0. Which one of the following statements
is true?
is true?
MCQ+4 / -12019
19Straight Lines And Pair Of Straight Lines
Let the equations of two sides of a triangle be 3x \(-\) 2y + 6 = 0 and 4x + 5y \(-\) 20 = 0. If the orthocentre of this triangle is at (1, 1), then the equation of its third side is :
MCQ+4 / -12019
20Straight Lines And Pair Of Straight Lines
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 :
intersecting the line, x + y = 7 at a distance of
4 units from P, is :
MCQ+4 / -12019
21Straight Lines And Pair Of Straight Lines
If the two lines x + (a – 1) y = 1 and
2x + a2y = 1 (a\(\in\)R – {0, 1}) are perpendicular, then
the distance of their point of intersection from the
origin is :
2x + a2y = 1 (a\(\in\)R – {0, 1}) are perpendicular, then
the distance of their point of intersection from the
origin is :
MCQ+4 / -12019
22Straight Lines And Pair Of Straight Lines
A point on the straight line, 3x + 5y = 15 which is equidistant from the coordinate axes will lie only
in :
in :
MCQ+4 / -12019
23Straight Lines And Pair Of Straight Lines
Let O(0, 0) and A(0, 1) be two fixed points. Then
the locus of a point P such that the perimeter of
\(\Delta\)AOP is 4, is :
the locus of a point P such that the perimeter of
\(\Delta\)AOP is 4, is :
MCQ+4 / -12019
24Straight Lines And Pair Of Straight Lines
Suppose that the points (h,k), (1,2) and (–3,4) lie
on the line L1
. If a line L2
passing through the points
(h,k) and (4,3) is perpendicular to L1
, then
\(k \over h\)
equals :
on the line L1
. If a line L2
passing through the points
(h,k) and (4,3) is perpendicular to L1
, then
\(k \over h\)
equals :
MCQ+4 / -12019
25Straight Lines And Pair Of Straight Lines
If the system of linear equations
x – 2y + kz = 1
2x + y + z = 2
3x – y – kz = 3
has a solution (x,y,z), z \(\ne\) 0, then (x,y) lies on
the straight line whose equation is :
x – 2y + kz = 1
2x + y + z = 2
3x – y – kz = 3
has a solution (x,y,z), z \(\ne\) 0, then (x,y) lies on
the straight line whose equation is :
MCQ+4 / -12019
26Straight Lines And Pair Of Straight Lines
If the straight line, 2x – 3y + 17 = 0 is perpendicular to the line passing through the points (7, 17) and (15, \(\beta\)), then \(\beta\) equals :
MCQ+4 / -12019
27Straight Lines And Pair Of Straight Lines
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 :
MCQ+4 / -12019
28Straight Lines And Pair Of Straight Lines
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 60o with the line x + y = 0. Then an equation
of the line L is ...
the perpendicular from the origin to this line makes an angle of 60o with the line x + y = 0. Then an equation
of the line L is ...
MCQ+4 / -12019
29Straight Lines And Pair Of Straight Lines
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 :
equation of the diagonal AD is :
MCQ+4 / -12019
30Straight Lines And Pair Of Straight Lines
If the line 3x + 4y – 24 = 0 intersects the x-axis 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 :
MCQ+4 / -12019
31Straight Lines And Pair Of Straight Lines
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 \(\Delta\)PQR is a line :
MCQ+4 / -12019
32Straight Lines And Pair Of Straight Lines
If 5, 5r, 5r2 are the lengths of the sides of a triangle, then r cannot be equal to :
MCQ+4 / -12019
33Straight Lines And Pair Of Straight Lines
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 :
MCQ+4 / -12019
34Straight Lines And Pair Of Straight Lines
Two sides of a parallelogram are along the lines, x + y = 3 & x – y + 3 = 0. If its diagonals intersect at (2, 4), then one of its vertex is :
MCQ+4 / -12019
35Straight Lines And Pair Of Straight Lines
The region represented by| x – y | \(\le\) 2 and | x + y| \(\le\) 2 is bounded by a :
MCQ+4 / -12019
36Straight Lines And Pair Of Straight Lines
Lines are drawn parallel to the line 4x – 3y + 2 = 0, at a distance
\({3 \over 5}\)
from the origin. Then which one of the
following points lies on any of these lines ?
\({3 \over 5}\)
from the origin. Then which one of the
following points lies on any of these lines ?
MCQ+4 / -12019
37Straight Lines And Pair Of Straight Lines
In a triangle ABC, coordinates of A are (1, 2) and the equations of the medians through B and C are respectively, x + y = 5 and x = 4. Then area of \(\Delta\) ABC (in sq. units) is :
MCQ+4 / -12018
38Straight Lines And Pair Of Straight Lines
The sides of a rhombus ABCD are parallel to the lines, x \(-\) y + 2 = 0 and 7x \(-\) y + 3 = 0. If the diagonals of the rhombus intersect P(1, 2) and the vertex A (different from the origin) is on the y-axis, then the coordinate of A is :
MCQ+4 / -12018
39Straight Lines And Pair Of Straight Lines
The foot of the perpendicular drawn from the origin, on the line, 3x + y = \(\lambda\) (\(\lambda\) \(\ne\) 0) is P. If the line meets x-axis at A and y-axis at B, then the ratio BP : PA is :
MCQ+4 / -12018
40Straight Lines And Pair Of Straight Lines
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 R is :
the origin and the rectangle OPRQ is completed, then the locus of R is :
MCQ+4 / -12018
41Straight Lines And Pair Of Straight Lines
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 30o with the positive direction of the x-axis, then the sum of the x-coordinates of the vertices...
one of the sides passing through the origin makes an angle 30o with the positive direction of the x-axis, then the sum of the x-coordinates of the vertices...
MCQ+4 / -12017
42Straight Lines And Pair Of Straight Lines
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 orthocentre of this triangle is at the point :
MCQ+4 / -12017