JEE Questions for Maths Straight Line And Pair Of Straight Lines Quiz 6 - MCQExams.com

If the ratio of gradients of the lines represented by ax2 + 2hxy + by2 = 0 is 1 : 3, then the value of the ratio h2 : ab is
  • 1/3
  • 3/4
  • 4/3
  • 1
If the sum of slopes of the pair of lines represented by 4x2 + 2hxy – 7y2 = 0 is equal to the product of the slopes, then the value of h is
  • –6
  • –2
  • –4
  • 4
The gradient of one of the lines of ax2 + 2hxy + by2 = 0 is twice that of the other then
  • h2 = ab
  • h = a + b
  • 8h2 = 9ab
  • 9h2 = 8ab
If λx2 – 5xy + 6y2 + x – 3y = 0 represents a pair of straight lines, then their point of intersection is
  • (–1, –3)
  • (1, 3)
  • (3, 1)
  • (–3, –1)
Angle between the lines represented by the equation x2 + 2xy sec θ + y2 = 0, is
  • θ
  • 2θ

  • Maths-Straight Line and Pair of Straight Lines-51701.png
  • None of these

Maths-Straight Line and Pair of Straight Lines-51703.png

  • Maths-Straight Line and Pair of Straight Lines-51704.png
  • 2)
    Maths-Straight Line and Pair of Straight Lines-51705.png

  • Maths-Straight Line and Pair of Straight Lines-51706.png
  • None of these
The angle between the lines represented by the equation ax2 + xy + by2 = 0 will be 45o, if
  • a = 1, b = 6
  • a = 1, b = –6
  • a = 6, b = 1
  • None of these
The lines represented by the equation 9x2 + 24xy + 16y2 + 21x + 28y + 6 = 0 are
  • Parallel
  • Coincident
  • Perpendicular
  • None of these
Acute angle between the lines represented by (x2 + y2)√3 = 4xy is

  • Maths-Straight Line and Pair of Straight Lines-51710.png
  • 2)
    Maths-Straight Line and Pair of Straight Lines-51711.png

  • Maths-Straight Line and Pair of Straight Lines-51712.png
  • None of these
If the angle between the lines represented by the equation y2 + kxy – x2 tan2 A = 0 be 2A, then k =
  • 0
  • 1
  • 2
  • tan A
The angle between the lines xy = 0 is
  • 45o
  • 60o
  • 90o
  • 180o
The angle between the lines represented by the equation λx2 + (1 – λ)2 xy – λy2 = 0 is
  • 30o
  • 45o
  • 60o
  • 90o
If the sum of the slopes of the lines represented by the equation x2 – 2xy tan A – y 2 = 0 be 4, then ∠A =
  • 0o
  • 45o
  • 60o
  • tan–1(–2)
If the equation 12x2 + 7xy – py2 – 18x + qy + 6 = 0 represents a pair of perpendicular straight lines, then
  • p = 12, q = 1
  • p = 1, q = 12
  • p = –1, q = 12
  • p = 1, q = –12
The angle between the pair of straight lines x2 – y2 – 2y – 1 = 0, is
  • 90o
  • 60o
  • 75o
  • 36o
The equation 12x2 + 7xy + ay2 + 13x – y + 3 = 0 represents a pair of perpendicular lines.Then the value of \'a\' is
  • 7/2
  • –19
  • –12
  • 12
Pair of straight lines perpendicular to each other represented by
  • 2x2 = 2y (2x + y)
  • x2 + y2 + 3 = 0
  • 2x2 = y(2x + y)
  • x2 = 2 (x – y)
The angle between the lines x2 – xy – 6y2 – 7x + 31y – 18 = 0 is
  • 45o
  • 60o
  • 90o
  • 30o
Condition that the two lines represented by the equation ax2 + 2hxy + by2 = 0 to be perpendicular is
  • ab = –1
  • a = –b
  • a = b
  • ab = 1
If in general quadratic equation f(x,y) = 0, ∆ = 0 and a + b = 0, then the equation represents
  • Two parallel straight lines
  • Two perpendicular straight lines
  • Two lines passing through origin
  • None of these
The angle between the lines represented by the equation x2 – 2pxy + y2 = 0, is
  • sec–1p
  • cos–1p
  • tan–1p
  • None of these

Maths-Straight Line and Pair of Straight Lines-51720.png

  • Maths-Straight Line and Pair of Straight Lines-51721.png
  • 2)
    Maths-Straight Line and Pair of Straight Lines-51722.png

  • Maths-Straight Line and Pair of Straight Lines-51723.png
  • None of these
The angle between the lines given by x2 – y2 = 0 is
  • 15o
  • 45o
  • 75o
  • 90o
Slope of a line which cuts intercepts of equal lengths on the axes is
  • –1
  • 0
  • 2
  • √3
If the coordinates of the points A and B be (3,and (7,then the length of the portion of the line AB intercepted between the axes is

  • Maths-Straight Line and Pair of Straight Lines-51725.png
  • 2)
    Maths-Straight Line and Pair of Straight Lines-51726.png

  • Maths-Straight Line and Pair of Straight Lines-51727.png
  • None of these
If the transversal y = mrx ; r = 1,2,3 cut off equal intercepts on the transversal x + y = 1, then 1+ m1, 1 +m2, 1 + m3 are in
  • A.P
  • G.P
  • H.P
  • None of these
The gradient of the line joining the points on the curve y = x2 + 2x whose abscissa are 1 and 3, is
  • 6
  • 5
  • 4
  • 3
If P = (1, 0), Q = (–1,and R = (2,are three given points, then locus of the point S satisfying the relation SQ2 + SR2 = 2SP2, is
  • a straight line parallel to x-axis
  • a circle passing through the origin
  • a circle with the centre at the origin
  • a straigth line parallel to y-axis.
The equation of the straight lline which passes through the point (1,-and cuts off equal intercepts from axes, is
  • x + y = 1
  • x – y = 1
  • x + y + 1 = 0
  • x – y – 2 = 0
The equation of the line whose slope is 3 and which cuts off an intercept 3 from the positive x-axis is
  • y = 3x – 9
  • y = 3x + 3
  • y = 3x + 9
  • None of these
The equation of the straight line passing through the point (3,and perpendicular to the line y = x is
  • x – y = 5
  • x + y = 5
  • x + y = 1
  • x – y = 1
The point (–4,is the vertex of a square and one of its diagonals is (7x – y += 0.The equation of the other diagonal is
  • 7x – y + 23 = 0
  • 7y + x = 30
  • 7y + x = 31
  • x – 7y = 30
The equations of the lines which pass through the point (3, –and are inclined at 60o to the line √3x + y = 1 are

  • Maths-Straight Line and Pair of Straight Lines-51736.png
  • 2)
    Maths-Straight Line and Pair of Straight Lines-51737.png

  • Maths-Straight Line and Pair of Straight Lines-51738.png
  • None of the above
The equation of the line joining the origin to the point (–4,is
  • 5x + 4y = 0
  • 3x + 4y = 2
  • 5x – 4y = 0
  • 4x – 5y = 0
Equation of the line passing through (1,and parallel to the line y = 3x – 1is
  • y + 2 = x + 1
  • y + 2 = 3(x + 1)
  • y – 2 = 3(x – 1)
  • y – 2 = x – 1
The line passing through the point of intersection of x + y = 2, x – y = 0 and is parallel to x + 2y = 5 is
  • x + 2y = 1
  • x + 2y = 2
  • x + 2y = 4
  • x + 2y = 3
The equation of a line through the intersection of lines x = 0 and y = 0 and through the point (2,2), is
  • y = x – 1
  • y = –x
  • y = x
  • y = –x + 2
Equation of a line through the origin and perpendicular to, the line joining (a,and (–a,is
  • y = 0
  • n = 0
  • a = –a
  • y = –a
For specifying a straight line how many geometrical parameters should be known ?
  • 1
  • 2
  • 4
  • 3
If l,m,n are in arithmetic progression, then the straight line lx + my + n = 0 will pass through the point
  • (–1, 2)
  • (1, –2)
  • (1, 2)
  • (2, 1)
The equation of the line passing through (4,–and makes an angle 45o with positive x-axis, is
  • x – y – 10 = 0
  • x – 2y – 16 = 0
  • x – 3y – 22 = 0
  • None of these
Equation of the hour hand at 4\'O clock is

  • Maths-Straight Line and Pair of Straight Lines-51748.png
  • 2)
    Maths-Straight Line and Pair of Straight Lines-51749.png

  • Maths-Straight Line and Pair of Straight Lines-51750.png

  • Maths-Straight Line and Pair of Straight Lines-51751.png
The straight line passes through the point of intersection of the straight lines x + 2y – 10 = 0 and 2x + y + 5 = 0, is
  • 5x – 4y = 0
  • 5x + 4y = 0
  • 4x – 5y = 0
  • 4x + 5y = 0
The lines represented by ax2 + 2hxy + by2 = 0 are perpendicular to each other if
  • h2 = a + b
  • a + b = 0
  • h2 = ab
  • h = 0
Let ABCD be a parallelogram and let E be the mid point of side AB. If EC is perpendicular to ED, then
  • ED = EC
  • EB = BC
  • EA = ED
  • EC + ED = 2BC
Line passing through (1,and (2,is
  • 3x – y + 1 = 0
  • 3x + y + 1 = 0
  • y – 3x + 1 = 0
  • 3x + y – 1 = 0
The number of lines that are parallel to 2x + 6y + 7 = 0 and have an intercept of length 10 between the coordinate axes is
  • 1
  • 2
  • 4
  • Infinitely many
The 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 the equation of line PQ is
  • x – y = 5
  • x + y = 5
  • x + y = –5
  • x – y = –5
The line joining the points (–1,and (4, –will pass through the point (p,q) if
  • p – q = 1
  • p + q = 1
  • p – q = 2
  • p + q = 2
A straight line through the point A(3,is such that its intercept between the axes is bisected at A. Its equation is
  • x + y = 7
  • 3x – 4y + 7 = 0
  • 4x + 3y = 24
  • 3x + 4y = 25
0:0:1


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