JEE Questions for Maths Straight Line And Pair Of Straight Lines Quiz 3 - MCQExams.com

The equation of the straight line perpendicular to 5x - 2y = 7 and passing through the point of intersection of the lines 2x + 3y = 1 and 3x + 4y = 6, is
  • 2x + 5y + 17 = 0
  • 2x + 5y - 17 = 0
  • 2x - 5y + 17 = 0
  • 2x - 5y = 17
If PM is the perpendicular from P(2,onto the line x + y = 3, then the coordinates of M are
  • (2, 1)
  • (-1, 4)
  • (1, 2)
  • (4, - 1)
The equation of line bisecting perpendicularly the segment joining the points (- 4,and (8, 8), is
  • y = 7
  • 6x + y - 19 = 0
  • x + 2y - 7 = 0
  • 6x + 2y - 19 = 0
If the slopes of one of the lines given by ax2 + 2hxy + by2 = 0 is 5 times the other, then
  • 5h2 = 9ab
  • 5h2 = ab
  • h2 = ab
  • 9h2 = 5ab
Two of the lines represented by the equation ay4 + bxy3 + cx2 y2 + dx3 y + ex4 = 0 will be perpendicular then
  • (b + d) (ad + be) + (e - a)2 (a + c + e) = 0
  • (b + d) (ad + be) + (e + a)2 (a + c + e) = 0
  • (b - d) (ad - be) + (e - a)2 (a + c + e) = 0
  • (b - d) (ad - be) + (e + a)2 (a + c + e) = 0
The points (1, 1), (- 5,and (13, λ) lie on the same straight line, if λ is equal to
  • 7
  • - 7
  • ± 7
  • 0
A straight line passes through the points (5,and (0, 3). The length of perpendicular from the point (4,on the line is
  • 15/√34
  • √17/2
  • 17/2

  • Maths-Straight Line and Pair of Straight Lines-51547.png
If p is the length of the perpendicular from the origin to the line, whose intercepts with the coordinate axes are 1/3 and 1/4 then the value of p is
  • 3/4
  • 1/12
  • 5
  • 12
  • 1/5
If p and q are respectively the perpendiculars from the origin upon the straight lines, whose equations are x sec θ + y, θ = a and x cosθ - y sin θ = a cos 2θ then 4p2 + q2 is equal to
  • 5a2
  • 4a2
  • 3a2
  • 2a2
  • a2
If any point P is at the equal distances from points A (a + b, a - b) and B (a - b, a + b), then locus of a point is
  • x - y = 0
  • ax + by = 0
  • bx + ay = 0
  • x + y = 0
For a > b > c > 0, if the distance between (1,and the point of intersection of the lines ax + by + c = 0 and bx + ay + c = 0 is less than 2√2. Then,
  • a + b - c > 0
  • a - b + c < 0
  • a - b + c > 0
  • a + b - c < 0
The equation of the perpendicular bisector of the line segment joining A (- 2,and B (6, -is
  • x - y = - 1
  • x - y = 3
  • x + y = 3
  • x + y = 1
  • x + y = - 1
The equation of second degree x2 + 2√2xy + 2 y2 + 4x + 4√2y + 1 = 0 represents a pair of straight lines. The distance between them is
  • 2√3
  • 2√5
  • 2
  • 02010
The line L given by x/5 + y/b = 1 passes through the point (13, 32). The line k is parallel to L and has the equation x/c + y/3 = 1. Then, the distance between L and K is
  • 23/√15
  • √17
  • 17/√15
  • 23/√17
The equation of one of the lines parallel to 4x - 3y = 5 and at a unit distance from the point (-1, -is
  • 3x + 4y - 3 = 0
  • 3x + 4y + 3 = 0
  • 4x - 3y + 3 = 0
  • 4x - 3y - 3 = 0
  • 4x - 3y - 4 = 0
A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at points P and Q respectively. Then the point O divides the segemnt PQ in the ratio
  • 1 : 2
  • 3 : 4
  • 2 : 1
  • 4 : 3
A line through the point A (2,which makes an angle of 30° with the positive direction of X-axis is rotated about A in clockwise direction through an angle of 15°. Then, the equation of the straight line in the new position is
  • (2 - √x + y + 4 + 2 √3 = 0
  • (2 - √3)x - y - 4 + 2 √ = 0
  • (2 - √3)x + y + 4 + 2 √3 = 0
  • (2 - √3)x + y + 4 + 2 √3 = 0
The number of points on the line x + y = 4, which are unit distance apart from the line 2x + 2y = 5, is
  • 0
  • 1
  • 2
  • ∞
The coordinates of the foot of perpendicular from (a,on the line y = mx + a/m are

  • Maths-Straight Line and Pair of Straight Lines-51553.png
  • 2)
    Maths-Straight Line and Pair of Straight Lines-51554.png

  • Maths-Straight Line and Pair of Straight Lines-51555.png

  • Maths-Straight Line and Pair of Straight Lines-51556.png
The distance between the pair of lines represented by the equations x2 - 6xy + 9y2 + 3x - 9y - 4 = 0 is
  • 15/√10
  • 1/2

  • Maths-Straight Line and Pair of Straight Lines-51557.png
  • 1/√10
The coordinates of the foot of the perpendicular drawn from the point (3, - 4). Then, the equations of the line is
  • (9/5, 17/5)
  • (1, 5)
  • (-5, 1)
  • (1, - 5)
If the foot of the perpendicular from the origin to a straight line is at the point (3, -4 ). Then, the equation of the line is
  • 3x - 4y = 25
  • 3x - 4y + 25 = 0
  • 4x + 3y - 25 = 0
  • 4x + 3y + 25 = 0
The distance between the lines 3x + 4y = 9 and 6x + 8y = 15 is
  • 3/2
  • 3/10
  • 6
  • None of these
The distance between the pair of parallel lines x2 + 2xy + y2 - 8ax - 8ay - 9a2 = 0 is
  • 2√5 a
  • √10 a
  • 10a
  • 5√2 a
If the equation of base of an equilateral triangle is 2x - y = 1 and the vertex (-1, 2), then the length of the side of the triangle is

  • Maths-Straight Line and Pair of Straight Lines-51558.png
  • 2/√15

  • Maths-Straight Line and Pair of Straight Lines-51559.png

  • Maths-Straight Line and Pair of Straight Lines-51560.png
  • √5
The length of perpendicular from the point (a cos α, a sin α) upon the straight line y = x tan α + c (where, c >is
  • c
  • c sin2 α
  • c cos α
  • c sec2 α
The product of the perpendicular distances from the origin on the pair of straight lines 12x2 + 25xy + 12y2 + 10x + 11y + 2 = 0 is
  • 1/25
  • 2/25
  • 3/25
  • 4/25
The slopes of the lines, which make an angle 45o with the line 3x - y = -5 are
  • 1, - 1
  • 1/2, - 1
  • 1, 1/2
  • 2, - 1/2
  • -2, 1/2
The locus of the orthocentre of the triangle formed by the lines (1 + p)x - py + p(1 + p) = 0, (1 + p)x - qy + q (1 + q) = 0 and y = 0, where p ≠ q, is
  • a hyperbola
  • a parabola
  • an ellipse
  • a straight line
The lines p(p2 + 1)x - y + q = 0 and (p2 + 1)2x + (p2 + 1)y + 2q = -0 are perpendicular to a common line for
  • exactly one value of p
  • exactly two values of p
  • more than two values of p
  • no value of p
All chords of the curve 3x2 - y2 - 2x + 4y = 0 which subtend a right angle at the origin, pass through the fixed point
  • (1, 2)
  • (1, - 2)
  • (-1, 2)
  • (-1, -2)
If the line px2 - qxy - y2 = 0 makes the angles α and β with X - axis, then the value of tan (α + β) is

  • Maths-Straight Line and Pair of Straight Lines-51561.png
  • 2)
    Maths-Straight Line and Pair of Straight Lines-51562.png

  • Maths-Straight Line and Pair of Straight Lines-51563.png

  • Maths-Straight Line and Pair of Straight Lines-51564.png
If θ is the angle between the lines ax2 + 2bxy + by2 = 0, then angle between x2 + 2xy sec θ + y2 = 0 is
  • θ
  • 2θ
  • θ/2
  • 3θ
If the lines y = 3x + 1 and 2y = x + 3 are equally inclined to the line y = mx + 4, (1/2 < m < 3), then the values of m is

  • Maths-Straight Line and Pair of Straight Lines-51566.png
  • 2)
    Maths-Straight Line and Pair of Straight Lines-51567.png

  • Maths-Straight Line and Pair of Straight Lines-51568.png

  • Maths-Straight Line and Pair of Straight Lines-51569.png
The pair of lines joining origin to the points of intersection of the two curves ax2 + 2hxy + by2 + 2gx = 0 and a\' x2 2h\' xy + b\' y2 + 2g\' x = 0 will be at right angles, if
  • (a' + b' ) g' = (a + b) g
  • (a + b ) g' = (a' + b') g
  • h2 - ab = h'2 - a'b'
  • a + b + h2 = a' + b' + h'2
A line passes through point (2,and perpendicular to the line 3x + y = 3. Then, y - intercept is
  • 2
  • 5/3
  • 4/3
  • 3/4
The lines (a + 2b)x + (a - 3b)y = a - b for different values of a and b pass through the fixed point, whose coordinates are
  • (2/5, 2/5)
  • (3/5, 3/5)
  • (1/5, 1/5)
  • (3/5, 2/5)
  • ((2/5, 3/
A line passes through the point of intersection of the lines 100x + 50y - 1 = 0 and 75x + 25y + 3 = 0 and makes equal intercept on the axes. Its equation is
  • 25x + 25y - 1 = 0
  • 5x - 5y + 3 = 0
  • 25x + 25y - 4 = 0
  • 25x - 25y + 6 = 0
  • 5x - 5y + 7 = 0
The acute angle between the lines joining the origin to the points of intersection of the line √3x + y = 2 and the circle x2 + y2 = 4 is
  • π/2
  • π/3
  • π/4
  • π/6
  • π/12
The angle between the straight lines x - y √3 = 5 and √3x + y = 7 is
  • 90o
  • 60o
  • 75o
  • 30o
The angle between the pair of straight lines formed by joining the points of intersection of x2 + y2 = 4 and y = 3x + c to the origin is a right angle. Then, C2 is equal to
  • 20
  • 13
  • 1/5
  • 5
The angle between the pair of lines (x2 + y2) sin2 α = (x cos θ - y sin θ)2 is
  • θ
  • 2θ
  • α
  • 2α
If (a, a2) falls inside the angle made by the lines y = x/2, x > 0 and y = 3x, x > 0, then a belongs to
  • (3, ∞)
  • (1/2, 3)
  • (-3, - (1/2))
  • (0, 1/2)
The angle between the lines represented by the equation 2x2 + 3xy - 5y2 = 0, is
  • π/3
  • π/2
  • tan-1 |12/5|
  • tan-1 |7/3|
The angle between the lines √3x - y - 2 = 0 and x - √3y + 1 = 0 is
  • 90o
  • 60o
  • 45o
  • 15o
  • 30o
The angle between the lines in x2 - xy - 6y2 - 7x + 31y - 18 = 0 is
  • 60o
  • 45o
  • 30o
  • 90o
The angle between the pair of straight lines y2 sin2 θ - xy sin2 θ + x2 (cos2 θ -= 0 is
  • π/3
  • π/4
  • π/6
  • π/2
  • π
Let P = (- 1, 0), 0 = (0,and Q = (3, 3√be three points. Then, the equation of the bisector of the ∠POQ is
  • y = √3x
  • √3y = x
  • y = - √3x
  • √3y = -x
If two pairs of lines x2 - 2mxy - y2 = 0 and x2 - 2nxy - y2 = 0 are such that one of them represents the bisector of the angles between the other, then
  • mn = 1
  • m + n = mn
  • mn = - 1
  • m - n = mn

Maths-Straight Line and Pair of Straight Lines-51571.png
  • Statement I is correct, Statement II is correct; Statement II is not a correct explanation for Statement I
  • Statement I is correct, Statement II is incorrect
  • Statement I is incorrect, Statement II is correct
  • Statement I is correct, Statement II is correct; Statement II is a correct explanation for Statement I
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