Straight Lines Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. If (– 4, 5) is one vertex and 7x – y + 8 = 0 is one diagonal of a square,
then the equation of second diagonal is
(a) x  + 3y = 21
(b) 2x – 3y = 7
(c) x + 7y = 31
(d) 2x + 3y = 21
2. A line through A (– 5, – 4) meets the line x + 3y + 2 = 0,2x + y + 4 = 0
and x – y – 5 =  0 at B, C and D respectively. If  + = 
, then the equation of the line is
(a) 2x + 3y + 22 = 0
(b) 5x – 4y + 7 = 0
(c) 3x – 2y + 3 = 0
(d) None of these
3. The number of lines that are parallel to 2x + 6y + 7 =0 and have an
Page 2


PART-I (Single Correct MCQs)
1. If (– 4, 5) is one vertex and 7x – y + 8 = 0 is one diagonal of a square,
then the equation of second diagonal is
(a) x  + 3y = 21
(b) 2x – 3y = 7
(c) x + 7y = 31
(d) 2x + 3y = 21
2. A line through A (– 5, – 4) meets the line x + 3y + 2 = 0,2x + y + 4 = 0
and x – y – 5 =  0 at B, C and D respectively. If  + = 
, then the equation of the line is
(a) 2x + 3y + 22 = 0
(b) 5x – 4y + 7 = 0
(c) 3x – 2y + 3 = 0
(d) None of these
3. The number of lines that are parallel to 2x + 6y + 7 =0 and have an
intercept of length 10 between the coordinate axes is
(a) 1
(b) 2
(c) 4
(d) Infinitely many
4. For what value of ‘p’ , y
2
 + xy + px
2
 – x – 2y + p = 0 represent 2 straight
lines :
(a) 2
(b)
(c)
(d)
5. The point on the line x + y = 4 which lie at a unit distance from the line
4x + 3y = 10, are
(a) (3, 1), (– 7, 11)
(b) (3, 1), (7, 11)
(c) (–3, 1), (–7, 11)
(d) (1, 3), (–7, 11)
6. The straight line y = x – 2 rotates about a point where it cuts the x-axis
and becomes perpendicular to the straight line ax + by + c = 0. Then its
equation is
(a) ax + by + 2a = 0
(b) ax – by – 2a = 0
(c) bx + ay – 2b = 0
(d) ay – bx + 2b = 0
7. The slopes of the lines represented by
x
2
 + 2hxy + 2y
2
 = 0 are in the ratio 1 : 2, then h equals
(a)
(b)
Page 3


PART-I (Single Correct MCQs)
1. If (– 4, 5) is one vertex and 7x – y + 8 = 0 is one diagonal of a square,
then the equation of second diagonal is
(a) x  + 3y = 21
(b) 2x – 3y = 7
(c) x + 7y = 31
(d) 2x + 3y = 21
2. A line through A (– 5, – 4) meets the line x + 3y + 2 = 0,2x + y + 4 = 0
and x – y – 5 =  0 at B, C and D respectively. If  + = 
, then the equation of the line is
(a) 2x + 3y + 22 = 0
(b) 5x – 4y + 7 = 0
(c) 3x – 2y + 3 = 0
(d) None of these
3. The number of lines that are parallel to 2x + 6y + 7 =0 and have an
intercept of length 10 between the coordinate axes is
(a) 1
(b) 2
(c) 4
(d) Infinitely many
4. For what value of ‘p’ , y
2
 + xy + px
2
 – x – 2y + p = 0 represent 2 straight
lines :
(a) 2
(b)
(c)
(d)
5. The point on the line x + y = 4 which lie at a unit distance from the line
4x + 3y = 10, are
(a) (3, 1), (– 7, 11)
(b) (3, 1), (7, 11)
(c) (–3, 1), (–7, 11)
(d) (1, 3), (–7, 11)
6. The straight line y = x – 2 rotates about a point where it cuts the x-axis
and becomes perpendicular to the straight line ax + by + c = 0. Then its
equation is
(a) ax + by + 2a = 0
(b) ax – by – 2a = 0
(c) bx + ay – 2b = 0
(d) ay – bx + 2b = 0
7. The slopes of the lines represented by
x
2
 + 2hxy + 2y
2
 = 0 are in the ratio 1 : 2, then h equals
(a)
(b)
(c)
(d)
8. The distance of the line 2x + y = 3 from the point (–1, 3) in the
direction whose slope is 1 is
(a)
(b)
(c)
(d)
9. The equation of the straight line, the portion of which intercepted
between the coordinate axes being divided by the point (–5, 4) in the
ratio 1 : 2, is
(a) 8x + 5y = 60
(b) 8x – 5y = 60
(c) –8x + 5y = 60
(d) None of these
10. The reflection of the point (4, –13) in the line 5x + y + 6 = 0 , is
(a) (–1, –14)
(b) (3, 4)
(c) (1, 2)
(d) (–4, 13)
11. The combined equation of the pair of lines through the point (1, 0) and
parallel to the lines represented by   is
(a)
(b)
(c)
(d) None of these
Page 4


PART-I (Single Correct MCQs)
1. If (– 4, 5) is one vertex and 7x – y + 8 = 0 is one diagonal of a square,
then the equation of second diagonal is
(a) x  + 3y = 21
(b) 2x – 3y = 7
(c) x + 7y = 31
(d) 2x + 3y = 21
2. A line through A (– 5, – 4) meets the line x + 3y + 2 = 0,2x + y + 4 = 0
and x – y – 5 =  0 at B, C and D respectively. If  + = 
, then the equation of the line is
(a) 2x + 3y + 22 = 0
(b) 5x – 4y + 7 = 0
(c) 3x – 2y + 3 = 0
(d) None of these
3. The number of lines that are parallel to 2x + 6y + 7 =0 and have an
intercept of length 10 between the coordinate axes is
(a) 1
(b) 2
(c) 4
(d) Infinitely many
4. For what value of ‘p’ , y
2
 + xy + px
2
 – x – 2y + p = 0 represent 2 straight
lines :
(a) 2
(b)
(c)
(d)
5. The point on the line x + y = 4 which lie at a unit distance from the line
4x + 3y = 10, are
(a) (3, 1), (– 7, 11)
(b) (3, 1), (7, 11)
(c) (–3, 1), (–7, 11)
(d) (1, 3), (–7, 11)
6. The straight line y = x – 2 rotates about a point where it cuts the x-axis
and becomes perpendicular to the straight line ax + by + c = 0. Then its
equation is
(a) ax + by + 2a = 0
(b) ax – by – 2a = 0
(c) bx + ay – 2b = 0
(d) ay – bx + 2b = 0
7. The slopes of the lines represented by
x
2
 + 2hxy + 2y
2
 = 0 are in the ratio 1 : 2, then h equals
(a)
(b)
(c)
(d)
8. The distance of the line 2x + y = 3 from the point (–1, 3) in the
direction whose slope is 1 is
(a)
(b)
(c)
(d)
9. The equation of the straight line, the portion of which intercepted
between the coordinate axes being divided by the point (–5, 4) in the
ratio 1 : 2, is
(a) 8x + 5y = 60
(b) 8x – 5y = 60
(c) –8x + 5y = 60
(d) None of these
10. The reflection of the point (4, –13) in the line 5x + y + 6 = 0 , is
(a) (–1, –14)
(b) (3, 4)
(c) (1, 2)
(d) (–4, 13)
11. The combined equation of the pair of lines through the point (1, 0) and
parallel to the lines represented by   is
(a)
(b)
(c)
(d) None of these
12. P is a point on either of the two lines  at a distance of 5
units from their point of intersection. The coordinates of the foot of the
perpendicular from P on the bisector of the angle between them are
(a) or  depending on which the point P is taken
(b)
(c)
(d)
13. Equation of the hour hand at 4 O’ clock is
(a)
(b)
(c)
(d)
14. If the image of point P(2, 3) in a line L is Q(4, 5), then the image of
point R(0, 0) in the same line is:
(a) (2,2)
(b) (4, 5)
(c) (3, 4)
(d) (7, 7)
15. If one of the diagonals of a square is along the line x = 2y and one of its
vertices is (3, 0), then its sides through this vertex are given by the
equations
(a)
(b)
(c)
(d)
Page 5


PART-I (Single Correct MCQs)
1. If (– 4, 5) is one vertex and 7x – y + 8 = 0 is one diagonal of a square,
then the equation of second diagonal is
(a) x  + 3y = 21
(b) 2x – 3y = 7
(c) x + 7y = 31
(d) 2x + 3y = 21
2. A line through A (– 5, – 4) meets the line x + 3y + 2 = 0,2x + y + 4 = 0
and x – y – 5 =  0 at B, C and D respectively. If  + = 
, then the equation of the line is
(a) 2x + 3y + 22 = 0
(b) 5x – 4y + 7 = 0
(c) 3x – 2y + 3 = 0
(d) None of these
3. The number of lines that are parallel to 2x + 6y + 7 =0 and have an
intercept of length 10 between the coordinate axes is
(a) 1
(b) 2
(c) 4
(d) Infinitely many
4. For what value of ‘p’ , y
2
 + xy + px
2
 – x – 2y + p = 0 represent 2 straight
lines :
(a) 2
(b)
(c)
(d)
5. The point on the line x + y = 4 which lie at a unit distance from the line
4x + 3y = 10, are
(a) (3, 1), (– 7, 11)
(b) (3, 1), (7, 11)
(c) (–3, 1), (–7, 11)
(d) (1, 3), (–7, 11)
6. The straight line y = x – 2 rotates about a point where it cuts the x-axis
and becomes perpendicular to the straight line ax + by + c = 0. Then its
equation is
(a) ax + by + 2a = 0
(b) ax – by – 2a = 0
(c) bx + ay – 2b = 0
(d) ay – bx + 2b = 0
7. The slopes of the lines represented by
x
2
 + 2hxy + 2y
2
 = 0 are in the ratio 1 : 2, then h equals
(a)
(b)
(c)
(d)
8. The distance of the line 2x + y = 3 from the point (–1, 3) in the
direction whose slope is 1 is
(a)
(b)
(c)
(d)
9. The equation of the straight line, the portion of which intercepted
between the coordinate axes being divided by the point (–5, 4) in the
ratio 1 : 2, is
(a) 8x + 5y = 60
(b) 8x – 5y = 60
(c) –8x + 5y = 60
(d) None of these
10. The reflection of the point (4, –13) in the line 5x + y + 6 = 0 , is
(a) (–1, –14)
(b) (3, 4)
(c) (1, 2)
(d) (–4, 13)
11. The combined equation of the pair of lines through the point (1, 0) and
parallel to the lines represented by   is
(a)
(b)
(c)
(d) None of these
12. P is a point on either of the two lines  at a distance of 5
units from their point of intersection. The coordinates of the foot of the
perpendicular from P on the bisector of the angle between them are
(a) or  depending on which the point P is taken
(b)
(c)
(d)
13. Equation of the hour hand at 4 O’ clock is
(a)
(b)
(c)
(d)
14. If the image of point P(2, 3) in a line L is Q(4, 5), then the image of
point R(0, 0) in the same line is:
(a) (2,2)
(b) (4, 5)
(c) (3, 4)
(d) (7, 7)
15. If one of the diagonals of a square is along the line x = 2y and one of its
vertices is (3, 0), then its sides through this vertex are given by the
equations
(a)
(b)
(c)
(d)
16. The line parallel to the x- axis and passing through the intersection of
the lines ax + 2by + 3b = 0 and bx – 2ay – 3a = 0, where (a, b)  (0, 0)
is
(a) below the x-axis at a distance of  from it
(b) below the x-axis at a distance of  from it
(c) above the x-axis at a distance of  from it
(d) above the x-axis at a distance of  from it
17. A straight line L through the point (3, –2) is inclined at an angle 60° to the
line If L also intersects thex-axis, then the equation of L is
(a)
(b)
(c)
(d)
18. The equation of a straight line, which passes through the point (a, 0)
and whose perpendicular distance from the point (2a, 2a) is a, is
(a) 3x – 4y – 3a = 0
(b) x – a = 0
(c) both (a) and (b)
(d) Neither (a) nor (b)
19. The points (1,3) and (5,1) are two opposite vertices of a rectangle. The
other two vertices lie on the line y = 2x + c, then one of the remaining
vertices is
(a) (4,4)