The equation of a straight line, which passes through the 2008 point (a cos 3 θ, a sin 3 θ) and perpendicular to x sec θ + y cosec θ = a, is

x cos θ -y sin θ = a cos 2 θ

x cos θ + y sin θ = a cos 2 θ

x cos θ + y sin θ - a cos 2 θ = 1

x cos θ -y sin θ + a cos 2 θ = -1

Joint equation of pair of lines through (3, -and parallel to x 2 - 4 x y + 3y 2 = 0 is

x2 +3y2 - 4xy - 14x + 24y + 45 = 0

x2 +3y2 + 4xy -14x + 24y + 45 = 0

x2 +3y2 + 4xy - 14x + 24y - 45 = 0

x2 +3y2 + 4xy - 14x - 24y - 45 = 0

reflection in the line through origin with slope tan (α/2)

clockwise rotation around origin through an angle α

anticlockwise rotation around origin through an angle α

reflection in the line through origin with slope tan α

JEE Questions for Maths Straight Line And Pair Of Straight Lines Quiz 1

The equation of line perpendicular to x = c is

0%
y = d
0%
x = d
0%
x = 0
0%
None of these

The lines represented by the equation x² - y² - x + 3y - 2 = 0

0%
x + y - 1 = 0, x - y + 2 = 0
0%
x - y - 2 = 0, x + y + 1 = 0
0%
x + y + 2 = 0, x - y - 1 = 0
0%
x - y + 1 = 0, x + y - 2 = 0

The lines 15x – 18y + 1 = 0, 12x + 10y – 3 = 0 and 6x + 66y – 11 = 0 are

0%
Parallel
0%
Perpendicular
0%
Concurrent
0%
None of these

If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is

0%
square
0%
circle
0%
straight line
0%
two intersecting lines

If the lines ax + 2y + 1 = 0, bx + 3y + 1 = 0 and cx + 4y + 1 = 0 are concurrent, then a,b,c are in

0%
A.P
0%
G.P
0%
H.P
0%
None of these

The lines 2x + y – 1 = 0, ax + 3y – 3 = 0 and 3x + 2y – 2 = 0 are concurrent for

0%
All a
0%
a = 4 only
0%
–1≤ a ≤ 3
0%
a > 0 only

If lines 4x + 3y = 1 ,y = x + 5 and 5y + bx = 3 are concurrent, then b equals

0%
1
0%
3
0%
6
0%
0

The bisector of the acute angle formed between the lines 4x - 3y + 7 = 0 and 3x - 4y +14 = 0 has the equation

0%
x + y + 3 = 0
0%
x + y - 3 = 0
0%
x - y + 3 = 0
0%
3x + y - 7 = 0

The points (–a, – b), (0, 0), (a, b) and (a², ab) are :

0%
Collinear
0%
Vertices of a parallelogram
0%
Vertices of a rectangle
0%
None of these

The point (4,undergoes the following three transformations successively

(i) Reflection about the line y = x.

(ii) Translation through a distance 2 units along the positive direction of x-axis.

(iii) Rotation through an angle p/4 about the origin in the counter clockwise direction.

Then the final position of the point is given by the coordinates.

0%
0%
2)
0%
0%

The straight lines x + y = 0, 3x + y – 4 = 0, x + 3y – 4 = 0 form a triangle which is

0%
isosceles
0%
equilateral
0%
right angled
0%
none of these

The points (2,and (5,are two opposite vertices of a rectangle. If other two vertices are points on the straight line y = 2x + k, then the value of k is

0%
4
0%
3
0%
-4
0%
-3
0%
1

A straight line perpendicular to the line 2x + y = 3 is passing through (1, 1). Its y -intercept is

0%
1
0%
2
0%
3
0%
0%

The ratio by which the line 2x + 5y - 7 = 0 divides the straight line joining the points (- 4,and (6, -is

0%
1 : 4
0%
1 : 2
0%
1 : 1
0%
2 : 3
0%
1 : 3

The straight lines x + y = 0, 5x + y = 4 and x + 5y = 4 form

0%
an isosceles triangle
0%
an equilateral triangle
0%
a scalene triangle
0%
a right angled triangle

Line L has intercepts a and b on the coordinate axes. When the axes are rotated through a given angle, keeping the origin fixed, the same line L has intercepts p and q, then

0%
a2 + b2 = p2 + q2
0%
2)
0%
a2 + p2 = b2 + q2
0%

Let A (2, -and B (- 2,be vertices of a ∆ABC. If the centroid of this triangle moves on the line 2x + 3y = 1, then the locus of the vertex C is the line

0%
3x - 2y = 3
0%
2x + 3y = 9
0%
2x - 3y = 7
0%
3x + 2y = 5

The point of intersection of lines represented by the equation 3x² + 8xy - 3y² + 29x - 3y + 18 = 0 is

0%
0%
2)
0%
(-3,-5)
0%
(3,5)

Maths-Straight Line and Pair of Straight Lines-51501.png

0%
ellipse
0%
parabola
0%
hyperbola
0%
none of these

The equations to a pair of opposite sides of parallelogram are x² – 5x + 6 = 0 and y² – 6y + 5 = 0, the equations to its diagonals are

0%
x + 4y = 13, y = 4x – 7
0%
4x + y = 13, 4y = x – 7
0%
4x + y = 13, y = 4x – 7
0%
y – 4x = 13, y + 4x = 7

The orthocentre of the triangle formed by the lines xy = 0 and x + y = 1 is

0%
0%
2)
0%
(0, 0)
0%

The straight line 3x + y = 9 divides the line segment joining the points (1,and (2,in the ratio

0%
3 : 4 externally
0%
3 : 4 internally
0%
4 : 5 internally
0%
5 : 6 externally

The equations y = ±√3x, y =1 are the sides of

0%
an equilateral triangle
0%
a right angled triangle
0%
an isosceles triangle
0%
a scalene triangle

The equation of a straight line, which passes through the 2008 point (a cos³ θ, a sin³θ) and perpendicular to x sec θ + y cosec θ = a, is

0%
0%
x cos θ -y sin θ = a cos 2 θ
0%
x cos θ + y sin θ = a cos 2 θ
0%
x cos θ + y sin θ - a cos 2 θ = 1
0%
x cos θ -y sin θ + a cos 2 θ = -1

If the line px - qy = r intersects the coordinate axes at (a,and (0, b), then the value of a + b is equal to

0%
0%
2)
0%
0%
0%

The equations of the lines through (1,and making angles of 45° with the line x + y = 0 are

0%
x - 1= 0, x - y = 0
0%
x - y = 0, y - l = 0
0%
x + y - 2 = 0, y - 1 = 0
0%
x - 1 = 0, y - 1 = 0

Let PQR be a right angled isosceles triangle, right angled at P (2, 1). If the equation of the line QR is 2x + y = 3, then the equation representing the pair of lines PQ and PR is

0%
3x2 – 3y2 + 8xy + 20x + 10y + 25 = 0
0%
3x2 – 3y2 + 8xy – 20x – 10y + 25 = 0
0%
3x2 – 3y2 + 8xy + 10x + 15y + 20 = 0
0%
3x2 – 3y2 – 8xy – 10x – 15y – 20 = 0

Joint equation of pair of lines through (3, -and parallel to x² - 4xy + 3y² = 0 is

0%
x2 +3y2 - 4xy - 14x + 24y + 45 = 0
0%
x2 +3y2 + 4xy -14x + 24y + 45 = 0
0%
x2 +3y2 + 4xy - 14x + 24y - 45 = 0
0%
x2 +3y2 + 4xy - 14x - 24y - 45 = 0

If the slope of one of the lines represented by ax²+2hxy+by² = 0 is the square of the other, then
Maths-Straight Line and Pair of Straight Lines-51513.png

Maths-Straight Line and Pair of Straight Lines-51513.png

0%
3
0%
4
0%
5
0%
6

If point P (a, b) lies on the straight line 3x + 2y = 13 and the point Q (b, a) lies on the straight line 4x - y = 5, then equation of the line PQ is

0%
x - y = 5
0%
x + y = 5
0%
x + y = -5
0%
x - y = -5

Let PS be the median of the triangle with vertices P(2, 2), Q(6, –and R(7, 3). The equation of the line passing through (1,–and parallel to PS is

0%
2x – 9y – 7 = 0
0%
2x – 9y – 11 = 0
0%
2x + 9y – 11 = 0
0%
2x + 9y + 7 = 0

If the lines ax + ky + 10 = 0, bx + (k + 1)y + 10 = 0 and cx + k (k + 2)y + 10 = 0 are concurrent, then

0%
a,b, c are in GP
0%
a ,b.e are in HP
0%
a ,b ,c are in AP
0%
(a + 1)2 = c
0%
a + b = c

A straight line through the point A(3,is such that its intercept between the axes is bisected at A. Its equation is

0%
3x - 4y + 7= 0
0%
4x + 3y = 24
0%
3x + 4y = 25
0%
x + y = 7

The number of integer values of m, for which the x-coordinate of the point of intersection of the lines 3x + 4y = 9 and y = mx + 1 is also an integer, is

0%
2
0%
0
0%
4
0%
1

Maths-Straight Line and Pair of Straight Lines-51514.png

0%
clockwise rotation around origin through an angle α
0%
anticlockwise rotation around origin through an angle α
0%
reflection in the line through origin with slope tan α
0%
reflection in the line through origin with slope tan (α/2)

A straight line through the point (1,meets the X-axis at A and Y-axis at B. The locus of the mid-point of AB is

0%
2xy + x + y = 0
0%
x + y - 2xy = 0
0%
x + y + 2 = 0
0%
x + y - 2 = 0

The equation of the pair of straight lines perpendicular to the pair 2x² + 3xy + 2y² + 10x + 5y = 0 and passing through the origin, is

0%
2x2 + 5xy + 2y2 = 0
0%
2x2 - 3xy + 2y2 = 0
0%
2x2 + 3xy + y2 = 0
0%
2x2 - 5xy + 2y2 = 0

The distance of the point (1,from the line x + y + 5 = 0 measured along the line parallel to 3x - y = 7 is equal to

0%
4√10
0%
40
0%
√40
0%
10√2
0%
2√20

The distance between the lines 5x - 12y + 65 = 0 and 5x - 12y - 39 = 0 is

0%
4
0%
16
0%
2
0%
8

Maths-Straight Line and Pair of Straight Lines-51515.png

0%
0%
2)
0%
0%

The distance between the parallel lines y = χ + a, y = χ + b is

0%
0%
|a - b|
0%
|a + b|
0%

If A (2, -and B(6,are two points, then the ratio in which the foot of the perpendicular from (4,to AB divides it, is

0%
8 : 15
0%
5 : 8
0%
-5 : 8
0%
-8 : 5

If 3 and 4 are intercepts of a line L ≡ 0, then the distance of L ≡ 0 from the origin is

0%
5 units
0%
12 units
0%
5/12 unit
0%
12/5 units

The number of intergral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices (0,0), (0,and (21,0), is

0%
133
0%
190
0%
233
0%
105

L is a variable line such that the algebraic sum of the distances of the points (1, 1), (2,and (0,from the line is equal to zero. The line L will always pass through

0%
(1, 1)
0%
(2, 1)
0%
(1, 2)
0%
(2, 2)

Orthocentre of triangle with vertices (0, 0), (3,and (4,is

0%
0%
(3, 12)
0%
0%
(3, 9)

The distance between the pair of parallel lines given by x² - 1005x + 2006 = 0 is

0%
1001
0%
1000
0%
1005
0%
2006

Let α be the distance between the lines - x + y = 2 and x - y = 2 and β be the distance between the lines 4x - 3y = 5 and 6y - 8x = 1, then

0%
20√2β = 11α
0%
20√2α = 11β
0%
11√2β = 20α
0%
None of the above

If line (tan² θ + cos² θ) x² - 2 tan θ xy + sin² θ . y² = 0 makes angles α and β with X - axis, then tan α - tan β is equal to

0%
2
0%
4
0%
tan θ
0%
2 tan θ

The line parallel to the X-axis and passing through the point of intersection of the line ax + 2by + 3b = 0 and bx - 2ay - 3a = 0, where (a, b) ≠ (0, 0), is

0%
above the X-axis at a distance of 3/2
0%
above the X-axis at a distance of 2/3
0%
below the X-axis at a distance of 2/3
0%
below the X-axis at a distance of 3/2
0%
below the X-axis at a distance of 3

JEE Questions for Maths Straight Line And Pair Of Straight Lines Quiz 1 - MCQExams.com

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Practice Maths Quiz Questions and Answers

JEE Questions for Maths Straight Line And Pair Of Straight Lines Quiz 1 - MCQExams.com

0:0:1

Practice Maths Quiz Questions and Answers

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