Remesh’s Mathematics [XI MATHEMATICS QUESTION BANK]
CHAPTER 10 MARCH 2023
STRAIGHT LINES 4. i) Find the equation of a line passing through
1
the point (−4,3) with slope 2. (2)
MARCH 2024
ii) Write the equation of the line passing
1. Consider the line L1 : 3x − 4y + 12 = 0
through the points (1. −1) and (3,5) (2)
and a point A(2, −3).
iii) Find the angle between the lines obtained
i) Find the equation of the line passing
in (i) and (ii). (2)
through A and parallel to the given line
L1 . (2) IMPROVEMENT 2022
ii) Find the distance from the origin to the
5. A straight line which makes an angle 45 with
given line L1 . (1)
positive direction of x-axis, passes through the
2. The vertices of ∆PQR are
point (1, 2).
P(1,0), Q(5,4) and R(−1,4).
a) Write the slope of the line (1)
i) Find the equation of the line representing
b) Write equation of the straight line (2)
the side PQ. (2)
6. Given equation of a line is x – 2y + 3 = 0.
ii) Find the equation of the line through R
a) Find the x – intercept and slope of the
and perpendicular to the side PQ. (2)
above line (2)
IMPROVEMENT 2023 b) Find the distance of the point (1, 3) from the
above line. (2)
3. Consider the triangle given in following
figure:
MARCH 2022
7. Find the angle between the lines
𝑦 − √3𝑥 − 5 = 0 and √3𝑦 − 𝑥 + 6 = 0 (3)
8. i) Find the slope of the line 𝑥 − 7𝑦 + 5 = 0
(1)
ii) Find the equation of the line perpendicular to
the above line having 𝑥 intercept 3. (3)
IMPROVEMENT 2021
i) Find the slope of line joining the points
A and B. (1) 9. a) Find 𝑥 and 𝑦 intercept of the line
ii) Write the equation of line passing through 3𝑥 − 4𝑦 + 10 = 0 (2)
A and B. (1) b) Express the above line in intercept form.
iii) Find the equation of line through P and (1)
perpendicular to AB. (2)
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, Remesh’s Mathematics [XI MATHEMATICS QUESTION BANK]
10. a) Find the value of 𝑥 for which the points
(𝑥, −1), (2,1) and (4,5) are collinear. (2)
b) Find the equation of the line passing
through the point (−2,3) with slope −4.
(2)
MARCH 2021
11. Consider the line 2𝑥 + 3𝑦 − 6 = 0. Find its
a) Slope. (2) a) Find equation of a line passing through the
b) y-intercept. (1) midpoint of AB and perpendicular to AB.
(2)
12. Find the equation of the line perpendicular to
b) Find a point C on X axis which is
the line 𝑥 − 7𝑦 + 5 = 0 and passing through
equidistant from A and B. (2)
(2, −3).
c) Find area of Δ𝐴𝐵𝐶. (2)
IMPROVEMENT 2020
IMPROVEMENT 2019
13. Consider the circle 𝑥 2 + 𝑦 2 = 1 given in the
figure. Let OP make an angle 300 with the
15. a) The slope of the line through the Points
𝑥 axis.
(2,5) and (−3,6) is ………. (1)
b) Find the equation of the line passing
through the point (−3,5) and perpendicular
to the line through the points (2,5) and
(−3,6). (2)
c) If A,B,C are in arithmetic progression,
then the straight line Ax + By + C = 0
always passes through the point.
i) (1,-2) ii) (2,-1)
iii) (0,0) iv) (1,2) (1)
16. Consider the straight line 3x − 4 y − 16 = 0 .
i) Find the equation of the tangent line to the a) Find the slope of the line (1)
circle passing through the point P. (2) b) Slope of a line which is perpendicular to
ii) Find the 𝑥 intercept and 𝑦 intercept made the above line is ………. (1)
by the line. (2) c) Find the equation of the line passing
iii) Find the equation of the other tangent to the through (-1,3) are perpendicular to the
circle parallel to the first one. (2) above line. (1)
17. Find the co-ordinates of the foot of the
MARCH 2020 perpendicular from the point (-1,3) to this
line. (1)
14. Consider the following diagram:
MARCH 2019
18. The figure shows a unit circle and a line L
which makes 300 with the positive direction of
x axis.
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, Remesh’s Mathematics [XI MATHEMATICS QUESTION BANK]
b) Find the equation of the line perpendicular
to 2x + 3 y − 6 = 0 and passing through
(−1,1). (3)
c) Find the foot of the perpendicular from
(−1,1) to the line 2 x + 3 y − 6 = 0 . (2)
a) Write the equation of the line L. (2) Or
b) Write the coordinates of the points A
a) Slope of a line making an angle of 1200
and B (2)
c) Find the equation of the tangent line to with positive direction of X – axis is
the circle at A. (2) ……… (1)
19. Consider two lines:
L1 : 2 x + y = 4 −1 3
i) ii)
L2 :2 x − y = 2 2 2
1
a) Find the angle between L1 and L2 (2) iii) − 3 iv) −
b) Deleted
3
c) Deleted b) Find the x and y intercepts of the line
3x − 4 y + 10 = 0 . (2)
IMPROVEMENT 2018
c) Find the angle between the lines
20. a) Find the equation of the perpendicular
𝑦 = √3𝑥 + 5 and √3𝑦 + 𝑥 + 6 = 0 (3)
bisector of the line joining the points
( 0,0) and ( −3, 4). (3) MARCH 2017
b) Find the coordinates of the point on the
line y = 3x + 2 that is equidistant from 23. a) The slope of the line passing through the
( 0,0) and ( −3, 4) (1) points (3,−2) and (7,−2) is ………..
21. a) Reduce the equation x − y = 4 into normal i) −1 ii) 2
form. (3)
iii) 0 iv) 1 (1)
b) Write the distance of this line from
origin. (1) b) Reduce the equation 6x + 3y − 5 = 0 into
slope-intercept from and hence find its
IMPROVEMENT 2017 slope and y- intercept. (2)
d) Find a point on the x- axis which is
22. a) Slope of the line 2x + 3 y − 6 = 0 is ………
equidistant from the points (7,6)
(1) and (3,4). (2)
−2 −3
i) ii) IMPROVEMENT 2016
3 2
iii) 2 iv) 3 (1) 24. a) Which is the slope of the line
3
perpendicular to the line with slope − ?
2
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, Remesh’s Mathematics [XI MATHEMATICS QUESTION BANK]
−3 −2 c) Deleted
i) ii)
2 3
OR
3 2
iii) iv) (1) a) Slope of the line L : 2x + 3y + 5 = 0 is
2 3
b) Find the equation of the line intersecting ……….. (1)
the x-axis at a distance of 3 units to the left
2 2 3 3
i) − 3 ii) 3 iii) − 2 iv) 2
of origin with slop −2. (2)
b) Find the equation of the line 𝐿′ parallel
c) Assume that straight lines work as the plane
to L and passing through (2,2). (2)
mirror for a point, find the image of the
c) Find the distance of the lines L and 𝐿′
point (1,2) in the line x − 3 y + 4 = 0 . (3)
from the origin. Also find the distance
MARCH 2016 between the lines L and L . (3)
25. a) Which one of the following pair of straight MARCH 2015
lines are parallel?
i) x − 2 y − 4 = 0 ;2 x − 3 y − 4 = 0 27. a) Find the equation of the line passing
ii) x − 2 y − 4 = 0 ; x − 2 y − 5 = 0 through e points (3,−2) and (−1,4). (2)
iii) 2x − 3 y − 8 = 0 ;3x − 3 y − 8 = 0 b) Reduce the equation 3 x + y − 8 = 0 into
iv) 2 x − 3 y − 8 = 0;3x − 2 y − 8 = 0 (1) normal form. (2)
b) Equation of a straight line is c) If the angle between two lines is / 4 and
1
3x − 4 y + 10 = 0. Convert it into the slope of one of the lines is , find the slope
2
intercept form and write of the other line. (2)
the x- intercept and y – intercept. (2)
IMPROVEMENT 2014
c) Find the equation of the line perpendicular
28. a) Find the equation of the line passing
to the line x − 7 y + 5 = 0 and having
through the two points (1,−1) and (3,5).
x-intercept 3. (3) (2)
SEPTEMBER 2015 b) Find the angle between the lines
26. a) Slope of a line ' L1 ' making an angle 1350 y − 3 x − 5 = 0 and 3y − x + 6 = 0 (4)
with the positive direction of the x- axis MARCH 2014
is ………
i) 1 ii) −1 29. a) Find the slope of the line passing through
iii) 3 iv) − 3 (1) the point(3,−2) and (−1,4). (1)
b) Find the equation of the line ' L 2 ' b) Find the distance of the point (3,−5) from
perpendicular to ' L1 ' and passing through the line 3x−4y−26=0. (2)
the point (−2,3) (2)
c) Consider the equation of the line
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CHAPTER 10 MARCH 2023
STRAIGHT LINES 4. i) Find the equation of a line passing through
1
the point (−4,3) with slope 2. (2)
MARCH 2024
ii) Write the equation of the line passing
1. Consider the line L1 : 3x − 4y + 12 = 0
through the points (1. −1) and (3,5) (2)
and a point A(2, −3).
iii) Find the angle between the lines obtained
i) Find the equation of the line passing
in (i) and (ii). (2)
through A and parallel to the given line
L1 . (2) IMPROVEMENT 2022
ii) Find the distance from the origin to the
5. A straight line which makes an angle 45 with
given line L1 . (1)
positive direction of x-axis, passes through the
2. The vertices of ∆PQR are
point (1, 2).
P(1,0), Q(5,4) and R(−1,4).
a) Write the slope of the line (1)
i) Find the equation of the line representing
b) Write equation of the straight line (2)
the side PQ. (2)
6. Given equation of a line is x – 2y + 3 = 0.
ii) Find the equation of the line through R
a) Find the x – intercept and slope of the
and perpendicular to the side PQ. (2)
above line (2)
IMPROVEMENT 2023 b) Find the distance of the point (1, 3) from the
above line. (2)
3. Consider the triangle given in following
figure:
MARCH 2022
7. Find the angle between the lines
𝑦 − √3𝑥 − 5 = 0 and √3𝑦 − 𝑥 + 6 = 0 (3)
8. i) Find the slope of the line 𝑥 − 7𝑦 + 5 = 0
(1)
ii) Find the equation of the line perpendicular to
the above line having 𝑥 intercept 3. (3)
IMPROVEMENT 2021
i) Find the slope of line joining the points
A and B. (1) 9. a) Find 𝑥 and 𝑦 intercept of the line
ii) Write the equation of line passing through 3𝑥 − 4𝑦 + 10 = 0 (2)
A and B. (1) b) Express the above line in intercept form.
iii) Find the equation of line through P and (1)
perpendicular to AB. (2)
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10. a) Find the value of 𝑥 for which the points
(𝑥, −1), (2,1) and (4,5) are collinear. (2)
b) Find the equation of the line passing
through the point (−2,3) with slope −4.
(2)
MARCH 2021
11. Consider the line 2𝑥 + 3𝑦 − 6 = 0. Find its
a) Slope. (2) a) Find equation of a line passing through the
b) y-intercept. (1) midpoint of AB and perpendicular to AB.
(2)
12. Find the equation of the line perpendicular to
b) Find a point C on X axis which is
the line 𝑥 − 7𝑦 + 5 = 0 and passing through
equidistant from A and B. (2)
(2, −3).
c) Find area of Δ𝐴𝐵𝐶. (2)
IMPROVEMENT 2020
IMPROVEMENT 2019
13. Consider the circle 𝑥 2 + 𝑦 2 = 1 given in the
figure. Let OP make an angle 300 with the
15. a) The slope of the line through the Points
𝑥 axis.
(2,5) and (−3,6) is ………. (1)
b) Find the equation of the line passing
through the point (−3,5) and perpendicular
to the line through the points (2,5) and
(−3,6). (2)
c) If A,B,C are in arithmetic progression,
then the straight line Ax + By + C = 0
always passes through the point.
i) (1,-2) ii) (2,-1)
iii) (0,0) iv) (1,2) (1)
16. Consider the straight line 3x − 4 y − 16 = 0 .
i) Find the equation of the tangent line to the a) Find the slope of the line (1)
circle passing through the point P. (2) b) Slope of a line which is perpendicular to
ii) Find the 𝑥 intercept and 𝑦 intercept made the above line is ………. (1)
by the line. (2) c) Find the equation of the line passing
iii) Find the equation of the other tangent to the through (-1,3) are perpendicular to the
circle parallel to the first one. (2) above line. (1)
17. Find the co-ordinates of the foot of the
MARCH 2020 perpendicular from the point (-1,3) to this
line. (1)
14. Consider the following diagram:
MARCH 2019
18. The figure shows a unit circle and a line L
which makes 300 with the positive direction of
x axis.
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, Remesh’s Mathematics [XI MATHEMATICS QUESTION BANK]
b) Find the equation of the line perpendicular
to 2x + 3 y − 6 = 0 and passing through
(−1,1). (3)
c) Find the foot of the perpendicular from
(−1,1) to the line 2 x + 3 y − 6 = 0 . (2)
a) Write the equation of the line L. (2) Or
b) Write the coordinates of the points A
a) Slope of a line making an angle of 1200
and B (2)
c) Find the equation of the tangent line to with positive direction of X – axis is
the circle at A. (2) ……… (1)
19. Consider two lines:
L1 : 2 x + y = 4 −1 3
i) ii)
L2 :2 x − y = 2 2 2
1
a) Find the angle between L1 and L2 (2) iii) − 3 iv) −
b) Deleted
3
c) Deleted b) Find the x and y intercepts of the line
3x − 4 y + 10 = 0 . (2)
IMPROVEMENT 2018
c) Find the angle between the lines
20. a) Find the equation of the perpendicular
𝑦 = √3𝑥 + 5 and √3𝑦 + 𝑥 + 6 = 0 (3)
bisector of the line joining the points
( 0,0) and ( −3, 4). (3) MARCH 2017
b) Find the coordinates of the point on the
line y = 3x + 2 that is equidistant from 23. a) The slope of the line passing through the
( 0,0) and ( −3, 4) (1) points (3,−2) and (7,−2) is ………..
21. a) Reduce the equation x − y = 4 into normal i) −1 ii) 2
form. (3)
iii) 0 iv) 1 (1)
b) Write the distance of this line from
origin. (1) b) Reduce the equation 6x + 3y − 5 = 0 into
slope-intercept from and hence find its
IMPROVEMENT 2017 slope and y- intercept. (2)
d) Find a point on the x- axis which is
22. a) Slope of the line 2x + 3 y − 6 = 0 is ………
equidistant from the points (7,6)
(1) and (3,4). (2)
−2 −3
i) ii) IMPROVEMENT 2016
3 2
iii) 2 iv) 3 (1) 24. a) Which is the slope of the line
3
perpendicular to the line with slope − ?
2
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, Remesh’s Mathematics [XI MATHEMATICS QUESTION BANK]
−3 −2 c) Deleted
i) ii)
2 3
OR
3 2
iii) iv) (1) a) Slope of the line L : 2x + 3y + 5 = 0 is
2 3
b) Find the equation of the line intersecting ……….. (1)
the x-axis at a distance of 3 units to the left
2 2 3 3
i) − 3 ii) 3 iii) − 2 iv) 2
of origin with slop −2. (2)
b) Find the equation of the line 𝐿′ parallel
c) Assume that straight lines work as the plane
to L and passing through (2,2). (2)
mirror for a point, find the image of the
c) Find the distance of the lines L and 𝐿′
point (1,2) in the line x − 3 y + 4 = 0 . (3)
from the origin. Also find the distance
MARCH 2016 between the lines L and L . (3)
25. a) Which one of the following pair of straight MARCH 2015
lines are parallel?
i) x − 2 y − 4 = 0 ;2 x − 3 y − 4 = 0 27. a) Find the equation of the line passing
ii) x − 2 y − 4 = 0 ; x − 2 y − 5 = 0 through e points (3,−2) and (−1,4). (2)
iii) 2x − 3 y − 8 = 0 ;3x − 3 y − 8 = 0 b) Reduce the equation 3 x + y − 8 = 0 into
iv) 2 x − 3 y − 8 = 0;3x − 2 y − 8 = 0 (1) normal form. (2)
b) Equation of a straight line is c) If the angle between two lines is / 4 and
1
3x − 4 y + 10 = 0. Convert it into the slope of one of the lines is , find the slope
2
intercept form and write of the other line. (2)
the x- intercept and y – intercept. (2)
IMPROVEMENT 2014
c) Find the equation of the line perpendicular
28. a) Find the equation of the line passing
to the line x − 7 y + 5 = 0 and having
through the two points (1,−1) and (3,5).
x-intercept 3. (3) (2)
SEPTEMBER 2015 b) Find the angle between the lines
26. a) Slope of a line ' L1 ' making an angle 1350 y − 3 x − 5 = 0 and 3y − x + 6 = 0 (4)
with the positive direction of the x- axis MARCH 2014
is ………
i) 1 ii) −1 29. a) Find the slope of the line passing through
iii) 3 iv) − 3 (1) the point(3,−2) and (−1,4). (1)
b) Find the equation of the line ' L 2 ' b) Find the distance of the point (3,−5) from
perpendicular to ' L1 ' and passing through the line 3x−4y−26=0. (2)
the point (−2,3) (2)
c) Consider the equation of the line
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