JEE Questions for Maths Straight Line And Pair Of Straight Lines Quiz 5 - MCQExams.com

The equation of the line joining the point (3,to the point of intersection of the lines 4x + y – 1 = 0 and 7x – 3y – 35 = 0 is equidistant from the points (0,and (8,34)
  • True
  • False
  • Nothing can be said
  • None of these
A variable line passes through a fixed point P. The algebraic sum of the perpendicular drawn from (2,0), (0,and (1,on the line is zero, then the coordinates of the P are
  • (1, –1)
  • (1, 1)
  • (2, 1)
  • (2, 2)
The diagonals of a parallelogram PQRS are along the lines x + 3y = 4 and 6x – 2y = 7.Then PQRS must be a
  • Rectangle
  • Square
  • Cyclic quadrilateral
  • Rhombus
The area enclosed within the curve |x| + |y| = 1 is
  • √2
  • 1
  • √3
  • 2
The locus of point P which divides the line joining (1,and (2 cos θ, 2 sin θ) internally in the ratio 2 : 3 for all θ, is a
  • Straight line
  • Circle
  • Pair of straight lines
  • Parabola
All points lying inside the triangle formed by the points (1,3), (5,and (–1,satisfy
  • 3x + 2y ≥ 0
  • 2x + y – 13 ≥ 0
  • 2x – 3y – 12 ≤ 0
  • – 2x + y ≥ 0
  • Both (and (3)
The intercept of a line between the co-ordinates axes is divided by point (–5,in the ratio 1 : 2. The equation of the line will be
  • 5x – 8y + 60 = 0
  • 8x – 5y + 60 = 0
  • 2x – 5y + 30 = 0
  • None of these
The lines ax + by + c = 0, where 3a + 2b + 4c = 0 are concurrent at the point
  • (1/2, 3/4)
  • (1, 3)
  • (3, 1)
  • (3/4, 1/2)
The number of integral points (integral point means both the co-ordinates should be integer) exactly in the interior of the triangle with vertices (0, 0), (0,and (21,is
  • 133
  • 190
  • 233
  • 105
Two vertices of a triangle are (5, –and (–2, 3). If orthocentre is the origin then co-ordinates of the third vertex are
  • (7, 4)
  • (–4, 7)
  • (4, –7)
  • (–4, –7)
If C is the reflection of A(2,x in x-axis and B is the reflection of C in y-axis , then |AB| is
  • 20
  • 2)
    Maths-Straight Line and Pair of Straight Lines-51646.png

  • Maths-Straight Line and Pair of Straight Lines-51647.png
  • 4
The perpendicular bisector of the line segment joining P(1,and Q(k,has y-intercept -4. Then a possible value of k is
  • 2
  • –2
  • –4
  • 1

Maths-Straight Line and Pair of Straight Lines-51650.png
  • Circle
  • Pair of straight lines
  • Parabola
  • Ellipse

Maths-Straight Line and Pair of Straight Lines-51652.png

  • Maths-Straight Line and Pair of Straight Lines-51653.png
  • 2)
    Maths-Straight Line and Pair of Straight Lines-51654.png

  • Maths-Straight Line and Pair of Straight Lines-51655.png

  • Maths-Straight Line and Pair of Straight Lines-51656.png
If the pair of straight lines xy – x – y + 1 = 0 and the line ax + 2y – 3 = 0 are concurrent , then a =
  • –1
  • 0
  • 3
  • 1
The area of the triangle formed by the line 4x2 – 9xy – 9y2 = 0 and x = 2 is
  • 2
  • 3

  • Maths-Straight Line and Pair of Straight Lines-51659.png

  • Maths-Straight Line and Pair of Straight Lines-51660.png
If the pair of straight lines given by Ax2 + 2Hxy + By2 = 0, (H2 > AB) forms an equilateral triangle with line ax + by + c = 0, then (A + 3B) (3A + B) is
  • H2
  • –H2
  • 2H2
  • 4H2
If the bisectors of the lines x2 – 2pxy – y2 = 0 be x2 – 2qxy – y2 = 0, then
  • pq + 1 = 0
  • pq – 1 = 0
  • p + q = 0
  • p – q = 0
The pair of lines represented by 3ax2 + 5xy + (a2 – 2)y2 = 0 are perpendicular to each other for
  • Two values of a
  • 2)
    Maths-Straight Line and Pair of Straight Lines-51664.png
  • For one value of a
  • For no value of a
The equation x2 – 3xy + λy2 + 3x – 5y + 2 = 0 when λ is a real number, represents a pair of straight lines. If θ is the angle between the lines, then cosec2 θ is equal to
  • 3
  • 9
  • 10
  • 100
The circumcentre of the triangle formed by the lines xy + 2x + 2y + 4 = 0 and x + y + 2 = 0
  • (0,0)
  • (– 2, – 2)
  • (– 1, – 1)
  • (– 1, – 2)
The area bounded by the angle bisectors of the lines x2 – y2 + 2y = 1 and the line x + y = 3, is
  • 2
  • 3
  • 4
  • 6
The lines joining the points of intersection of curve 5x2 + 12xy – 8y2 + 8x – 4y + 12 = 0 and the line x – y = 2 to the origin, makes the angles with the axis
  • 30o and 45o
  • 45o and 60o
  • Equal
  • parallel to axis
If one of the lines of my2 + (1 – m2) xy – mx2 = 0 is a bisector of the angle between the lines xy = 0, then m is

  • Maths-Straight Line and Pair of Straight Lines-51670.png
  • 2)
    Maths-Straight Line and Pair of Straight Lines-51671.png
  • 1
  • 2
The equation of the bisectors of the angle between the lines represented by the equation x2 – y2 = 0 is
  • x = 0
  • y = 0
  • xy = 0
  • None of these
The combined equation of bisectors of angles between co-ordinates axis, is
  • x2 + y2 = 0
  • x2 – y2 = 0
  • xy = 0
  • x + y = 0
The combined equation of the bisectors of the angle between the lines represented by (x2 + y2)√3 = 4xy is
  • x2 – y2 = 0
  • xy = 0
  • x2 + y2 = 2xy

  • Maths-Straight Line and Pair of Straight Lines-51675.png
The equation of the bisectors of the angles between the lines represented by x2 + 2xy cot θ + y2 = 0 , is
  • x2 – y2 = 0
  • x2 – y2 = xy
  • (x2 – ycot θ = 2xy
  • None of these
One bisector of the angle between the lines given by a(x – 1)2 + 2h(x – 1)y + by2 = 0 is 2x + y – 2 = 0.The other bisector is
  • x – 2y + 1 = 0
  • 2x + y – 1 = 0
  • x + 2y – 1 = 0
  • x – 2y – 1 = 0
The point of intersection of the lines represented by the equation 2x2 + 3y2 + 7xy + 8x + 14y + 8 = 0 is
  • (0, 2)
  • (1, 2)
  • (–2, 0)
  • (–2, 1)
The point of intersection of the lines represented by equation 2(x + 2)2 + 3(x +(y ––2(y – 2)2 = 0 is
  • (2, 2)
  • (–2, –2)
  • (–2, 2)
  • (2, –2)
The equation (x + y)2 – (x2 + y2) = 0 represents
  • A circle
  • Two lines
  • Two parallel lines
  • Two mutually perpendicular lines
Two lines represented by equation x2 + xy + y2 = 0 are
  • Coincident
  • Parallel
  • Mutually perpendicular
  • Imaginary
If the equation hxy + gx + fy + c = 0 represents a pair of straight lines, then
  • fh = cg
  • fg = ch
  • h2 = gf
  • fgh = c
The values of h for which the equation 3x2 + 2hxy – 3y2 – 40x + 30y – 75 = 0 represents a pair of straight lines, are
  • 4, 4
  • 4, 6
  • 4, –4
  • 0, 4
The equation (x – 5)2 + (x – 5)(y ––2(y – 6)2 = 0 represents
  • A circle
  • Two straight lines passing through origin
  • Two straight lines passing through the point (5, 6)
  • None of these
A second degree homogeneous equation in x and y always represents
  • A pair of straight lines
  • A circle
  • A conic section
  • None of the above
If 4ab = 3h2, then the ratio of slopes of the lines represented by the equation ax2 + 2hxy + by2 = 0 will be

  • Maths-Straight Line and Pair of Straight Lines-51685.png
  • 2)
    Maths-Straight Line and Pair of Straight Lines-51686.png
  • 2 : 1
  • 1 : 3
The lines a2 x2 + bcy2 = a(b + c)xy will be coincident, if
  • a = 0 or b = c
  • a = b or a = c
  • c = 0 or a = b
  • a = b + c
The equation xy + a2 = a(x + y) represents
  • A parabola
  • A pair of straight lines
  • An ellipse
  • Two parallel straight lines
The equation 2y2 – xy – x2 + 6x – 8 = 0 represents
  • A pair of straight lines
  • A circle
  • An ellipse
  • A parabola
One of the lines represented by the equation x2 + 6xy = 0 is
  • Parallel to x-axis
  • Parallel to y-axis
  • x-axis
  • y-axis
The equation 4x2 – 24xy + 11y2 = 0 represents
  • Two parallel lines
  • Two perpendicular lines
  • Two lines through the origin
  • A circle
If the equation ax2 + by2 + cx + cy = 0, represents a pair of straight lines, then
  • a(b + c) = 0
  • b(c + a) = 0
  • c(a + b) = 0
  • a + b + c = 0
If the sum of the slopes of the lines given by x2 – 2cxy – 7y2 = 0 is four times their product, then c has the value
  • –2
  • –1
  • 2
  • 1
The equation y2 – x2 + 2x – 1 = 0 represents
  • A pair of straight lines
  • A circle
  • A parabola
  • An ellipse
The equation x2 + ky2 + 4xy = 0 represents two coincident lines, if k =
  • 0
  • 1
  • 4
  • 16
If one of the lines given by 6x2 – xy + 4cy2 = 0 is 3x + 4y = 0, then c equals
  • –3
  • –1
  • 3
  • 1
If the point (2, –lies on kx2 – 3y2 + 2x + y – 2 = 0 then then k is equal to
  • 1/7
  • 16
  • 7
  • 12
Difference of slopes of the lines represented by equation x2 (sec2 θ – sin2 θ) – 2xy tanθ + y2 sin2 θ = 0 is
  • 4
  • 3
  • 2
  • None of these
0:0:1


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