PAIR OF STRAIGHT LINE-02- (ASSIGNMENT)

1. The values of h for which the equation represents a pair of straight lines, are (a) 4, 4 (b) 4, 6 (c) 4, –4 (d) 0, 4 2. Which of the following second degree equation represents a pair of straight lines (a) (b) (c) (d) 3. The equation represents (a) A pair of straight lines (b) A circle (c) An ellipse (d) A parabola 4. One of the lines represented by the equation is (a) Parallel to x-axis (b) Parallel to y-axis (c) x-axis (d) y-axis 5. The equation represents a (a) Circle (b) Pair of parallel straight lines (c) Pair of perpendicular straight lines (d) Pair of non-perpendicular intersecting straight lines 6. The equation represents (a) A pair of straight lines (b) A circle (c) A parabola (d) An ellipse 7. If the equation represents two straight lines, then the value of will be [Rajasthan PET 1989] (a) 3 (b) 2 (c) 8 (d) – 8 8. The joint equation of the straight lines and is (a) (b) (c) (d) 9. The value of for which the equation may represent a pair of straight lines is (a) 2 (b) 3 (c) 4 (d) 1 10. will represent a pair of straight lines, when = (a) 2 (b) 4 (c) 6 (d) 8 11. If represents a pair of straight line, then L is (a) 1 (b) 2 (c) 3 (d) –1 12. Separate equations of lines, for a pair of lines, whose equation is are (a) and (b) and (c) and (d) and 13. If the equation represents a pair of lines, then k is equal to (a) 4 (b) 2 (c) 1 (d) – 4 14. If equation represents a pair of lines, then k is equal to (a) 9 (b) 1 (c) 0 (d) – 9 15. Equation represents (a) Pair of straight lines (b) Ellipse (c) Hyperbola (d) None of these 16. For what value of 'p' , represents two straight lines (a) 2 (b) (c) (d) 17. If represents a pair of straight lines, then k = (a) –15 (b) 6 (c) –10 (d) –4 18. If the equation represents a pair of lines, then (a) (b) (c) (d) 19. The equation represents a pair of straight lines, then k is (a) (b) (c) (d) 20. The equation represents a pair of lines. The value of k is (a) (b) (c) (d) 21. The equation represents (a) Two parallel lines (b) Two perpendicular lines (c) Two lines through the origin (d) A circle 22. The value of k so that the equation represents a pair of straight lines, is [Kurukshetra CEE 2002] (a) 4 (b) 6 (c) 0 (d) 8 23. The equation to the pair of straight lines through the origin which are perpendicular to the lines is (a) (b) (c) (d) 24. The equation represents (a) A parabola (b) A pair of straight lines (c) An ellipse (d) Two parallel straight lines 25. If the equation represents a pair of straight lines, then (a) < 0 (b) = 0 (c) > 0 (d) None of these 26. The equation of pair of straight lines perpendicular to the pair is (a) (b) (c) (d) 27. If the equation represents two lines and then (a) and (b) and (c) and (d) and 28. Difference of slopes of the lines represented by equation is (a) 4 (b) 3 (c) 2 (d) None of these 29. If the ratio of gradients of the lines represented by is 1 : 3, then the value of the ratio is (a) (b) (c) (d) 1 30. If the sum of slopes of the pair of lines represented by is equal to the product of the slopes, then the value of h is (a) –6 (b) –2 (c) –4 (d) 4 31. The gradient of one of the lines of is twice that of the other, then (a) (b) (c) (d) 32. If the slope of one line of the pair of lines represented by is 3 times the slope of the other line, then a is (a) 1 (b) 2 (c) 3 (d) 4 33. If the slope of one of the lines given by is 5 times the other, then (a) (b) (c) (d) 34. The value of k such that may represent a pair of straight lines, is (a) 3 (b) 4 (c) 6 (d) 8 35. If denotes a pair of straight lines, then k = (a) 2 (b) (c) (d) 36. The equation represents a pair of real and distinct lines if (a) (b) (c) (d) 37. Lines represented by are (a) Coincident (b) Parallel but not coincident (c) Not parallel (d) Perpendicular 38. If represents a pair of straight lines, then k = (a) 3 (b) 4 (c) –3 (d) None of these 39. Equation of pair of straight lines drawn through (1, 1) and perpendicular to the pair of lines is (a) (b) (c) (d) None of these 40. If the lines represented by the equation make angles and with x-axis, then (a) 0 (b) (c) (d) 41. If one of the lines given by is , then c equals (a) –3 (b) –1 (c) 3 (d) 1 42. If represents a pair of lines, then a = (a) –16 (b) 16 (c) 4 (d) – 4 43. The value of , for which the equation represent a pair of straight lines, are (a) 3, –3 (b) –3, 1 (c) 3, 1 (d) –1, 1 44. The equation represents a (a) Circle (b) Pair of straight lines (c) Parabola (d) Ellipse 45. The locus of the point satisfying the relation is a [Orissa JEE 2002] (a) Straight line (b) Pair of straight lines (c) Circle (d) Ellipse 46. If the equation represents a pair of perpendicular straight lines, then [Kurukshetra CEE 2002] (a) (b) (c) (d) 47. The equation of the pair of straight lines parallel to x-axis and touching the circle is (a) (b) (c) (d) 48. Two pairs of straight lines have the equations and . One line will be common among them if (a) (b) (c) (d) 49. If and then curve is (a) A line represented by u (b) A different line (c) Not a line (d) None of these 50. If one of the line represented by the equation is coincident with one of the line represented by , then (a) (b) (c) (d) None of these 51. The angle between the lines represented by the equation is given by (a) (b) (c) (d) 52. The angle between the pair of straight lines , is [MNR 1991; UPSEAT 2000] (a) (b) (c) (d) 53. If the angle is acute, then the acute angle between is (a) (b) (c) (d) 54. The angle between the pair of lines is (a) (b) (c) (d) 55. The equation when is a real number, represents a pair of straight lines. If is the angle between the lines, then = (a) 3 (b) 9 (c) 10 (d) 100 56. The equation represents a pair of perpendicular lines. Then the value of 'a' is (a) (b) –19 (c) –12 (d) 12 57. The angle between the lines is (a) (b) (c) (d) 58. If the angle between the two lines represented by is , then (a) (b) 1 (c) (d) 7 59. Pair of straight lines perpendicular to each other represented by (a) (b) (c) (d) 60. The angle between the pair of straight lines , is (a) (b) (c) (d) 61. The angle between the pair of straight lines , is (a) (b) (c) (d) None of these 62. The angle between the pair of lines given by equation , is (a) (b) (c) (d) 0 63. Acute angle between the lines represented by is [MP PET 1992] (a) (b) (c) (d) None of these 64. The angle between the lines given by is (a) (b) (c) (d) 65. The angle between the lines is (a) (b) (c) (d) 66. The angle between the lines represented by the equation are (a) (b) (c) (d) 67. Condition that the two lines represented by the equation to be perpendicular is (a) (b) (c) (d) 68. The straight lines represented by the equation are (a) Coincident (b) Perpendicular (c) Parallel (d) Inclined at an angle of 69. The nature of straight lines represented by the equation is (a) Real and coincident (b) Real and different (c) Imaginary and different (d) None of these 70. The equation represents two coincident lines, if = (a) 0 (b) 1 (c) 4 (d) 16 71. The straight lines joining the origin to the points of intersection of the line and curve include an angle (a) (b) (c) (d) 72. If the acute angles between the pairs of lines and be and respectively, then (a) (b) (c) (d) None of these 73. The point of lines represented by and perpendicular to each other for (a) Two values of a (b) For all values of a (c) For one value of a (d) For no values of a 74. The figure formed by the lines and , is (a) A right angled triangle (b) An isosceles triangle (c) An equilateral triangle (d) None of these 75. The equation of the pair of straight lines, each of which makes an angle with the line is (a) (b) (c) (d) 76. The combined equation of the lines is and that of the lines is . If the angle between and be then the angle between and will be (a) (b) (c) (d) 77. If and are the angles which the lines make with the axis of x, then is equal to (a) (b) (c) 2 (d) 1 78. The combined equation of bisectors of angles between coordinate axes, is (a) (b) (c) (d) 79. The equation of the bisectors of the angle between the lines represented by the equation , is (a) (b) (c) (d) None of these 80. If be one of the bisectors of the angle between the lines then (a) (b) (c) (d) 81. The combined equation of the bisectors of the angle between the lines represented by is (a) (b) (c) (d) 82. One bisector of the angle between the lines given by is . The other bisector is (a) (b) (c) (d) 83. If the equation has the one line as the bisector of angle between the coordinate axes, then (a) (b) (c) (d) 84. If the bisectors of the angles between the pairs of lines given by the equation and be coincident, then (a) a (b) b (c) h (d) Any real number 85. If the bisectors of the angles of the lines represented by and are same, then the angle made by the lines represented by first with the second, is (a) (b) (c) (d) 86. If pairs of straight lines and be such that each pair bisects the angle between the other pair, then (a) 1 (b) –1 (c) 0 (d) 87. If the lines represented by are rotated about the origin through an angle , one in clockwise direction and other in anti –clockwise direction , then the equation of the bisectors of the angle between the lines in the new position is (a) (b) (c) (d) None of these 88. If then a bisector of the angle between the lines represented by the equation is (a) (b) (c) (d) 89. If the pair of lines intersect on the y-axis, then (a) (b) (c) (d) None of these 90. The point of intersection of the lines represented by equation is (a) (b) (c) (d) 91. The equations to a pair of opposite sides of a parallelogram are and . The equations to its diagonals are (a) and (b) and (c) and (d) and 92. The circumcentre of the triangle formed by the lines and is (a) (b) (c) (d) 93. If the equations of opposite sides of a parallelogram are and then the equation of its one diagonal is (a) (b) (c) (d) 94. The limiting position of the point of intersection of the straight lines and as is (a) (b) (c) (d) None of these 95. If two sides of a triangle are represented by and the centroid is (1, 0), then the equation of third side is (a) (b) (c) (d) 96. If the lines represents the adjacent sides of a parallelogram, then the equation of second diagonal if one is , will be (a) (b) (c) (d) None of these 97. The lines joining the origin to the points of intersection of the line and the curve , are (a) Parallel to each other (b) Perpendicular to each other (c) Inclined at to each other (d) None of these 98. The distance between the parallel lines is (a) (b) (c) (d) 99. The equation represents a pair of straight lines. The distance between them is (a) (b) (c) (d) None of these 100. The equation of second degree represents a pair of straight lines. The distance between them is (a) 4 (b) (c) 2 (d) 101. If the straight lines joining origin to the points of intersections of the line with the curve are perpendicular to each other, then the value of m should be (a) 0 (b) 1/2 (c) 1 (d) – 1 102. The lines joining the points of intersection of the curve and the line to the origin are perpendicular, then (a) (b) (c) (d) 103. The equation of pair of lines joining origin to the points of intersection of and is (a) (b) (c) (d) 104. The acute angle formed between the lines joining the origin to the points of intersection of the curves and , is (a) (b) (c) (d) 105. The lines joining the origin to the points of intersection of the line and the circle will be mutually perpendicular, if (a) (b) (c) (d) 106. The angle between lines joining the origin to the points of intersection of the line and the curve is (a) (b) (c) (d) 107. The pair of lines joining the origin to the points of intersection of the curves and will be at right angles to one another if (a) (b) (c) (d) None of these 108. The square of distance between the point of intersection of the lines represented by the equation and origin, is (a) (b) (c) (d) None of these 109. If the portion of the line falling inside the circle subtends an angle of at the origin, then (a) (b) (c) (d) None of these 110. The product of perpendiculars drawn from the origin to the lines represented by the equation will be [Bihar CEE 1994] (a) (b) (c) (d) 111. A curve with equation of the form has zero gradient at the point (0,1) and also touches the x-axis at the point (–1,0). Then the values of x for which the curve has negative gradients are (a) (b) (c) (d) 112. Two of the lines represented by the equation will be perpendicular, then (a) (b) (c) (d) 113. Let PQR be a right angled isosceles triangle, right angled at . If the equation of the line QR is , then the equation representing the pair of lines PQ and PR is (a) (b) (c) (d) 114. The area (in square units) of the quadrilateral formed by the two pairs of lines and is (a) (b) (c) (d) 115. Two lines represented by the equation are rotated about the point (1, 0), the line making the bigger angle with the positive direction of the x-axis being turned by in the clockwise sense and the other line being turned by in the anticlockwise sense. The combined equation of the pair of lines in their new positions is (a) (b) (c) (d) None of these 116. The combined equation of three sides of a triangle is If is an interior point and (b, 1) is an exterior point of the triangle, then (a) (b) (c) (d) 117. The diagonals of a square are along the pair of lines whose equation is . If (2, 1) is a vertex of the square, then another vertex consecutive to it can be (a) (b) (c) (d) 118. The equation represent three straight lines passing through the origin, the slopes of which form an (a) A.P. (b) G.P. (c) H.P. (d) None of these 119. If denote the length of the perpendiculars from the point on the lines given by then (a) (b) (c) (d) 120. The equation of the locus of feet of perpendicular drawn from the origin to the line passing through a fixed point (a, b) is (a) (b) (c) (d) None of these