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JEE Questions for Maths Straight Line And Pair Of Straight Lines Quiz 2 - MCQExams.com
JEE
Maths
Straight Line And Pair Of Straight Lines
Quiz 2
The area (in square unit) of the triangle formed by
x
+ y + 1 = 0 and the pair of straight lines
x
2
- 3
x
y + 2y
2
= 0 is
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0%
7/12
0%
5/12
0%
1/12
0%
1/6
The lines represents by a
x
2
+ 2h
x
y + by
2
are perpendicular to each other, if
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0%
h2 = a + b
0%
a + b = 0
0%
h2 = ab
0%
h = 0
A pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve
x
2
+ y = 4 with
x
+ y = a. The set containing the value of a is
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0%
{-2, 2}
0%
{-3, 3}
0%
{-4, 4}
0%
{-5, 5}
The angle between lines joining origin and intersection points of line 2
x
+ y = 1 and curve 3
x
2
+ 4y
x
- 4
x
+ 1 = 0
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0%
π/2
0%
π/3
0%
π/4
0%
π/6
The angle between the line joining the points (1, -2), (3,and the line
x
+ 2y - 7 = 0 is
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0%
π
0%
π/2
0%
π/3
0%
π/6
A line passing through origin and is perpendicular to two given lines 2
x
+ y + 6 = 0 and 4
x
+ 2y - 9 = 0. The ratio in which the origins divides the line, is
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0%
1 : 2
0%
2 : 1
0%
4 : 2
0%
4 : 3
If the bisectors of angles represented by a
x
2
+ 2h
x
y + by
2
+ by
2
= 0 and a\'
x
2
+ 2h\'
x
y + b\'y
2
= 0 are same, then
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0%
(a - b) h' = (a'- b' ) h
0%
(a - b) h = (a'- b' )h'
0%
(a + b ) h' = (a'- b' )h
0%
(a - b) h' = (a' + b' )h
The pairs of straight lines
x
2
- 3
x
y + 2y
2
+
x
- 2 = 0 from a
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0%
square but not rhombus
0%
rhombus
0%
parallelogram
0%
rectangle but no a square
If the lines k
x
- 2y - 1 = 0 and 6
x
- 4y - m = 0 are identical (coincident) lines, then the values of k and m are
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0%
k = 3, m = 2
0%
k = - 3, m = 2
0%
k = - 3, m = - 2
0%
k = 3, m = - 2
Let a and b be non - zero and real numbers. Then , the equations (a
x
2
+ by
2
+ c) (
x
2
- 5
x
y + 6y
2
) = 0 represents
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0%
four straight lines, when c = 0 and a, b are of the same sign
0%
two straight lines and a circle, when a = b and c is of sign opposite to that of a
0%
two straight lines and a hyperbola, when a and b are of the same sign and c is of sign opposite to that of a
0%
a circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that of a
The perpendicular bisector of the line segment joining P(1,and Q (k,has y-intercept - 4. Then, the possible value of k is
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0%
- 4
0%
1
0%
2
0%
- 2
A line passes through the point of intersection of the lines 3
x
+ y + 1 = 0 and 2
x
- y + 3 = 0 and makes equal intercepts with axes. Then, equation of the line is
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0%
5x + 5y - 3 = 0
0%
x + 5y - 3 = 0
0%
5x - y - 3 = 0
0%
5x + 5y + 3 = 0
The equations of perpendicular bisectors of sides AB and AC of a ∆ ABC are
x
- y + 5= 0 and
x
+ 2y = 0, respectively. If the coordinates of vertex A are (1, - 2), then equation of BC is
Report Question
0%
14x + 23y - 40 = 0
0%
14x - 23y - 40 = 0
0%
23x + 14y - 40 = 0
0%
23x - 14y + 40 = 0
The equation 12
x
2
+ 7
x
y+ ay
2
+13
x
- y + 3 = O represents a pair of perpendicular lines. Then, the value of a is
Report Question
0%
7/2
0%
- 19
0%
- 12
0%
12
If x
1
, x
2
, x
3
as well as y
1
, y
2
, y
3
, are in G.P. with the same common ratio, then the points (x
1
, y
1
), (x
2
, y
2
) and (x
3
, y
3
).
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0%
lie on a straight line
0%
lie on an ellipse
0%
lie on a circle
0%
are vertices of a triangle
If a line with y-intercept 2, is perpendicular to the line 3
x
- 2y = 6, then its
x
-intercept is
Report Question
0%
1
0%
2
0%
- 4
0%
4
0%
3
The line, which is parallel to X-axis and crosses the curve y = √
x
at an angle 45
o
, is
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0%
y = 1/4
0%
y = 1/2
0%
y = 1
0%
y = 4
The equation of the line bisecting perpendicularly the segment joining the points (- 4,and (8,is
Report Question
0%
6x + y - 19 = 0
0%
y = 7
0%
6x + 2y - 19 = 0
0%
x + 2y - 7 = 0
If the lines
x
+ 3y - 9 = 0, 4
x
+ by - 2 = 0 and 2
x
- y - 4 = 0 are concurrent, then b is equal to
Report Question
0%
- 5
0%
5
0%
1
0%
0
The equation of straight line equally inclined to the axes and equidistant from the points (1, -and (3,is a
x
+ by + c = 0, where
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0%
a = 1, b = - 1, c = 3
0%
a = 1, b = - 1, c = -3
0%
a = 1, b = 1, c = -3
0%
None of these
The value of λ
x
2
- 10
x
y + 12y
2
+ 5
x
- 16 - y - 3 =0 represents a pair of straight lines is
Report Question
0%
1
0%
- 1
0%
2
0%
- 2
The starlight lines 3
x
+ 4y - 5 = 0 and 4
x
= 3y + 15 interested at the point P. On these lines the points Q and R are chosen so that PQ = PR. The slopes of the lines QR passing through (1,are
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0%
-7, 1/7
0%
7, 1/7
0%
7, (-1/7)
0%
3, -(1/3)
The line passing through the point of intersection of
x
+ y = 2,
x
- y = 0 and is parallel to
x
+ 2y = 5 is
Report Question
0%
x + 2y = 4
0%
x + 2y = 2
0%
x + 2y = 4
0%
x + 2y = 3
The equation of the line passing through the point of intersection of the lines
x
- 3y + 2 = 0 and 2
x
+ 5y - 7 = 0 and perpendicular to the line 3
x
+ 2y+ 5 = 0, is
Report Question
0%
2x - 3y + 1 = 0
0%
6x - 9y + 11 = 0
0%
2x - 3y + 15 = 0
0%
3x - 2y + 1 = 0
If one of the lines given by 6
x
2
-
x
y + 4cy
2
= 0 is 3
x
+ 4y = 0 then C is equal to
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0%
1
0%
- 1
0%
3
0%
- 3
The equations of the lines through the point (3,which makes an angle of 45
o
with the line.
x
- 2y = 3 are
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0%
3x - y = 7 and x + 3y = 9
0%
x - 3y = 7 and 3x + y = 9
0%
x - y = 3 and x + y = 2
0%
2x + y = 7 and x - 2y = 9
0%
2x - y = 7 and x + 2y = 9
The equation of the pair of straight lines parallel to X - axis and touching the circle
x
2
+ y
2
- 6
x
- 4y - 12 = 0 is
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0%
y2 - 4y - 21 = 0
0%
y2 + 4y - 21 = 0
0%
y2 - 4y + 21 = 0
0%
y2 + 4y + 21 = 0
If the lines 3
x
+ 4y + 1 = 0, 5
x
+ λ y + 3 = 0 and 2
x
+ y - 1= 0 are concurrent, then λ is equal to
Report Question
0%
- 8
0%
8
0%
4
0%
- 4
The equation of the line which is such that the portion of line segment intercepted between the coordinate axes is bisected at (4, -3), is
Report Question
0%
3x + 4y = 24
0%
3x - 4y = 12
0%
3x - 4y = 24
0%
4x - 3y = 24
0%
4x - 3y = 12
Report Question
0%
0%
2)
0%
0%
If the lines
x
2
+ 2
x
y - 35y
2
- 4
x
+ 44y - 12 = 0 and 5
x
+ λy - 8 = 0 are concurrent, then the value of λ is
Report Question
0%
0
0%
1
0%
- 1
0%
2
If non - zero numbers a, b, c are in HP, then the straight line χ/a + y/b + 1/c = 0 always passes through a fixed point. That point is
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0%
(1, - 1/2)
0%
(1, -2)
0%
(-1, -2)
0%
(-1,
The point of concurrence of the line a
x
+ by + c = 0 and a, b, c satisfy the relation 3a + 2b + 4c = 0 is
Report Question
0%
(3/2, 1/4)
0%
(3/4, 1/4)
0%
(3/4, 1/2)
0%
(3/2, 1/2)
Report Question
0%
9 : 8
0%
8 : 9
0%
1 : 2
0%
2 : 1
If (sin θ, cos θ) and (3,lie on the same side of the line
x
+ y = 1, then θ lies between
Report Question
0%
(0, π/2)
0%
(0, π)
0%
(π/4, π/2)
0%
(0, π/4)
The equation of the line bisecting the join of (3, -and (5,and having its intercepts on the X-axis and the Y-axis in the ratio 2 : 1 is
Report Question
0%
x + y - 3 = 0
0%
2x - y = 9
0%
x + 2y = 2
0%
2x + y = 7
The equation of the line passing through the origin and the point of intersection of the lines
x
/a + y/b = 1 and
x
/b + y/a = 1 is
Report Question
0%
bx - ay = o
0%
x + y = 0
0%
ax - by = 0
0%
x - y = 0
0%
ax + by = 0
The three straight lines a
x
+ by = c, b
x
+ cy = a and c
x
+ ay = b are collinear, if
Report Question
0%
b + c = a
0%
c + a = b
0%
a + b + c = 0
0%
a + b = c
The values of λ, for which the equation
x
2
- y
2
-
x
+ λy - 2 = 0 represents a pair of straight lines, is
Report Question
0%
-3, 1
0%
-1, 1
0%
3, - 3
0%
3, 1
The equation of pair of lines joining origin to the points of intersection of
x
2
+ y
2
= 9 and
x
+ y = 3 is
Report Question
0%
(x2 + - x)2 = 9
0%
xy = 0
0%
(3 + y)2 + y2 = 9
0%
(x - y)2 = 9
The value of p for which the equation
x
2
+ p
x
y + y
- 5
x
- 7y + 6 = 0 represents a pair of straight lines, is
Report Question
0%
5/2
0%
5
0%
2
0%
2/5
A straight line through the point (2,intersects the lines √3
x
+ y = 0 and √3
x
- y = 0 at the points A and B. The equation of the line AB, so that ∆OAB is equilateral, is
Report Question
0%
x - 2 = 0
0%
y - 2 = 0
0%
x + y - 4 = 0
0%
None of these
If a
x
2
- y
2
+ 4
x
- y = 0 represents a pair of lines, then a is equal to
Report Question
0%
- 16
0%
16
0%
4
0%
- 4
The centroid of the triangle formed by the pair of straight lines 12
x
2
- 20
x
y + 7y
2
= 0 and the line 2
x
- 3y + 4 = 0 is
Report Question
0%
0%
2)
0%
0%
The straight line whose sum of the intercepts on the axes is equal to half of the product of the intercepts, passes through the point
Report Question
0%
(1, 1)
0%
(2, 2)
0%
(3, 3)
0%
(4, 4)
Report Question
0%
0%
2)
0%
0%
A straight line through P(1,is such that its intercept between the axes is bisected at P. Its equation is
Report Question
0%
x + 2y = 5
0%
x + y = - 1
0%
x + y = 3
0%
2x + y = 4
If the equations k
x
2
- 2
x
y - y
2
- 2
x
+ 2y = 0 represents a pair of lines, then k is equal to
Report Question
0%
2
0%
- 2
0%
- 5
0%
3
The equation of a line passing through (-2, -and perpendicular to line 3
x
- y + 5 = 0 is
Report Question
0%
3y + x - 8 = 0
0%
3x + y + 6 = 0
0%
x + 3y + 14 = 0
0%
None of the above
If the point (a, a) falls between the line |
x
+ y|= 4, then
Report Question
0%
|a|= 2
0%
|a|= 3
0%
|a| < 2
0%
|a| < 3
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