R.C.C.-02- ASSIGNMENT

1. The distance between the points and is (a) 13 (b) 12 (c) 11 (d) 10 2. In a plane, the co-ordinates ( )of a point are equivalent (a) (b) (c) (d) 3. The system of coordinates known as the cartesian system of coordinates was first introduced by (a) Euclid (b) Euler (c) Descarte (d) Bhasker 4. Which of the following polar coordinates are associated to the same point I : II : III : IV : V : VI : (a) I, III and IV (b) II, IV and VI (c) II, IV, V and VI (d) IV and VI 5. If the distance between the points (a, 2) and (3, 4) be 8, then a = (a) (b) (c) (d) 6. The distance between the points and is (a) (b) (c) (d) 7. The distance of the point from origin is (a) (b) (c) (d) 8. The distance between the points and is (a) (b) (c) (d) 9. The point on y-axis equidistant from the points (3, 2) and (–1, 3) is (a) (0, –3) (b) (c) (d) (0, 3) 10. The point P is equidistant from A(1, 3), B(– 3, 5) and C(5, –1). Then PA = (a) 5 (b) (c) 25 (d) 11. The point whose abscissa is equal to its ordinate and which is equidistant from the points (1, 0) and (0, 3) is (a) (1, 1) (b) (2, 2) (c) (3, 3) (d) (4, 4) 12. Mid-point of the sides AB and AC of a are (3, 5) and (–3, –3) respectively, then the length of the side BC is (a) 10 (b) 20 (c) 15 (d) 30 13. The distance of the middle point of the line joining the points and from the origin (a) (b) (c) (d) a 14. A point on the line at a distance of 2 units from the origin is (a) (b) (c) (d) 15. If the points (1, 1), (–1, –1) and are vertices of an equilateral triangle then the value of k will be (a) 1 (b) –1 (c) (d) 16. If O be the origin and if the coordinates of any two points and be and respectively, then (a) (b) (c) (d) 17. If the line segment joining the points and B(c, d) subtends an angle at the origin, then is equal to (a) (b) (c) (d) None of these 18. The vertices of a triangle ABC are (0, 0), (2, –1) and (9, 2) respectively, then (a) (b) (c) (d) 19. If are vertices of any triangle, then the length of median passes through C will be (a) (b) (c) (d) 20. If a vertex of an equilateral triangle is on origin and second vertex is (4, 0), then its third vertex is (a) (b) (c) (d) 21. The locus of the point P equidistant from the points and is , then the value of c is (a) (b) (c) (d) 22. Let be squares such that for each , the length of a side of equals the length of a diagonal of . If the length of a side of is 10 cm, then for which of the following values of n is the area of less than 1 sq. cm. (a) 7 (b) 8 (c) 9 (d) 10 23. The three points (– 2, 2), (8, – 2) and (– 4, – 3) are the vertices of (a) An isosceles triangle (b) An equilateral triangle (c) A right angled triangle (d) None of these 24. The points and are the vertices of a (a) Parallelogram (b) Rectangle (c) Rhombus (d) None of these 25. Two opposite vertices of a rectangle are (1,3) and (5,1). If the other two vertices of the rectangle lie on the line then (a) 1 (b) – 1 (c) 2 (d) None of these 26. Three vertices of a parallelogram are (1, 3) (2, 0) and (5, 1). Then its fourth vertex is (a) (3, 3) (b) (4, 4) (c) (4, 0) (d) (0, – 4) 27. The quadrilateral formed by the vertices (– 1, 1), (0, – 3), (5, 2) and (4, 6) will be (a) Square (b) Parallelogram (c) Rectangle (d) Rhombus 28. The triangle formed by the lines and is (a) Equilateral (b) Isosceles (c) Right angled (d) None of these 29. The following points and are the vertices of (a) An acute angled triangle (b) An right angled triangle (c) An isosceles triangle (d) None of these 30. The triangle joining the points is (a) Equilateral triangle (b) Right-angled triangle (c) Isosceles triangle (d) Scalene triangle 31. The points (1, 3) and (5, 1) are the opposite vertices of a rectangle. The other two vertices lie on the line then the value of c will be (a) 4 (b) – 4 (c) 2 (d) – 2 32. If the three vertices of a rectangle taken in order are the points (2, –2), (8, 4) and (5, 7). The coordinates of fourth vertex are (a) (1, 1) (b) (1, –1) (c) (–1, 1) (d) None of these 33. If vertices of a quadrilateral are and then quadrilateral ABCD is a (a) Parallelogram (b) Rectangle (c) Square (d) Rhombus 34. The coordinates of the third vertex of an equilateral triangle whose two vertices are at (3, 4) and (–2, 3) are (a) (1, 1) or (1, –1) (b) or (c) or (d) None of these 35. The quadrilateral joining the points (1, –2); (3, 0); (1, 2) and (–1, 0) is (a) Parallelogram (b) Rectangle (c) Square (d) Rhombus 36. If , then the two triangle with vertices and must be (a) Similar (b) Congruent (c) Never congruent (d) None of these 37. All points lying inside the triangle formed by the points (1, 3), (5, 0) and (–1, 2) satisfy (a) (b) (c) (d) All of these 38. The common property of points lying on x-axis, is (a) (b) (c) (d) 39. Vertices of a figure are (– 2, 2); (– 2, – 1); (3, –1); (3, 2), it is a (a) Square (b) Rhombus (c) Rectangle (d) Parallelogram 40. If ABCD is a quadrilateral, if the mid point of consecutive sides AB, BC, CD and DA are combined by straight lines, then the quadrilateral PQRS is always (a) Square (b) Parallelogram (c) Rectangle (d) Rhombus 41. Three vertices of a parallelogram taken in order are and . The fourth vertex is (a) (1, 4) (b) (4, 1) (c) (1, 1) (d) (4, 4) 42. If and are the vertices of a parallelogram PQRS, then (a) (b) (c) (d) 43. The sides of a triangle are and where , then the triangle is (a) Right angled (b) Obtuse angled (c) Equilateral (d) None of these 44. If the vertices of triangle have integral coordinates then the triangle is (a) Equilateral (b) Never equilateral (c) Isosceles (d) None of these 45. The opposite angular points of a square are (3, 4) and (1, –1). Then the coordinates of other two vertices are (a) (b) (c) (d) None of these 46. The quadrilateral formed by the lines is (a) Square (b) Rectangle (c) Rhombus (d) Parallelogram 47. Point divides the line joining the points (3, – 5) and (– 7, 2) in the ratio of (a) 1 : 3 internally (b) 3 : 1 internally (c) 1 : 3 externally (d) 3 : 1 externally 48. In what ratio does the y-axis divide the join of (–3, –4) and (1, –2) (a) 1 : 3 (b) 2 : 3 (c) 3 : 1 (d) None of these 49. The points which trisect the line segment joining the points (0, 0) and (9, 12) are (a) (3, 4), (6, 8) (b) (4, 3), (6, 8) (c) (4, 3), (8, 6) (d) (3, 4), (8, 6) 50. If the point dividing internally the line segment joining the points and in the ratio 2 : 1 be (4, 6) then (a) (b) (c) (d) 51. If A and B are the points and (2, 1). Then the co-ordinates of point C on AB produced such that AC = 2BC are (a) (2, 4) (b) (3, 7) (c) (7, –2) (d) 52. The line segment joining the points (1, 2) and (– 2, 1) is divided by the line in the ratio (a) 3 : 4 (b) 4 : 3 (c) 9 : 4 (d) 4 : 9 53. If the points are the middle points of line segments respectively and particles of masses are placed respectively on these points. If G is the mass-centre of so placed infinite particles and , then p is (a) 0 (b) (c) (d) 54. If coordinates of the points A and B are (2, 4) and (4, 2) respectively and point M is such that A-M-B also AB = 3AM, then the coordinates of M are (a) (b) (c) (d) 55. The mid-points of sides of a triangle are (2, 1), (–1, –3) and (4, 5). Then the coordinates of its vertices are (a) (7, 9), (– 3, – 7), (1, 1) (b) (– 3, – 7), (1, 1), (2, 3) (c) (1, 1), (2, 3), (– 5, 8) (d) None of these 56. The coordinates of the points A, B, C are , and D divides the line AB in the ratio . If P divides the line DC in the ratio then the coordinates of P are (a) (b) (c) (d) None of these 57. If the coordinates of the vertices of a triangle be and , then the centroid of the triangle (a) Lies at the origin (b) Cannot lie on x-axis (c) Cannot lie on y-axis (d) None of these 58. If and are the vertices of a triangle, then its centroid will be (a) (– 3, 3) (b) (3, 3) (c) (3, 1) (d) (1, 3) 59. Two vertices of a triangle are (5, 4) and (– 2, 4). If its centroid is (5, 6) then the third vertex has the coordinates (a) (12, 10) (b) (10, 12) (c) (–10, 12) (d) (12, –10) 60. The centroid of a triangle, whose vertices are (2, 1), (5, 2) and (3, 4) is (a) (b) (c) (d) 61. If the middle points of the sides of a triangle be (–2, 3), (4, –3) and (4, 5), then the centroid of the triangle is (a) (5/3, 2) (b) (5/6, 1) (c) (2, 5/3) (d) (1, 5/6) 62. If and are the vertices of a triangle, then the excentre with respect to B is (a) (b) (c) (d) None of these 63. If two vertices of an equilateral triangle have integral co-ordinates then the third vertex will have (a) Integral co-ordinates (b) Co-ordinates which are rational (c) At least one co-ordinate irrational (d) Co-ordinates which are irrational 64. If the orthocentre and centroid of triangle are (–3, 5), (3, 3), then the circumcentre is (a) (6, 2) (b) (0, 8) (c) (6, –2) (d) (0, 4) 65. The centroid and a vertex of an equilateral triangle are (1, 1) and (1, 2) respectively. Another vertex of the triangle can be (a) (b) (c) (d) None of these 66. The incentre of triangle formed by lines , and is (a) (b) (1, 1) (c) (d) 67. Orthocentre of triangle with vertices (0, 0), (3, 4), (4, 0) is (a) (b) (3, 12) (c) (d) (3, 9) 68. Orthocentre of the triangle whose vertices are (0, 0)), (2, – 1) and (1, 3) is (a) (b) (c) (– 4, – 1) (d) (4, 1) 69. The orthocentre of the triangle formed by the lines , and is (a) (1, 2) (b) (1, –2) (c) (–1, – 2) (d) (–1, 2) 70. Coordinates of the orthocentre of the triangle whose sides are , and , will be (a) (0, 0) (b) (3, 0) (c) (0, 4) (d) (3, 4) 71. The orthocentre of the triangle formed by (0, 0), (8, 0), (4, 6) is (a) (b) (3, 4) (c) (4, 3) (d) (–3, 4) 72. If the line cuts the x-axis in A and y-axis in B, then incentre of (where O is the origin) is (a) (1, 2) (b) (2, 2) (c) (12, 12) (d) (2, 12) 73. The distance between the orthocentre and circumcentre of the triangle with vertices (0, 0) , (0, a) and (b, 0) is (a) (b) (c) (d) 74. The incentre of the triangle formed by (0, 0); (5, 12); (16, 12) is (a) (9, 7) (b) (7, 9) (c) (–9, 7) (d) (–7, 9) 75. If two vertices of a triangles are (6, 4); (2, 6) and its centroid is (4, 6), then the third vertex is (a) (4, 8) (b) (8, 4) (c) (6, 4) (d) None of these 76. If the vertices of a triangle be (a, 1); (b, 3) and (4, c), then the centroid of the triangle will lie on x-axis if (a) (b) (c) (d) 77. The vertices of a triangle are (0, 0), (3, 0) and (0, 4). Its orthocentre is at (a) (0, 0) (b) (c) (d) None of these 78. The equations of the sides of a triangle are and then the coordinates of the circumcentre are (a) (2, 1) (b) (1, 2) (c) (2, –2) (d) (1, – 2) 79. The mid points of the sides of a triangle are (5, 0); (5, 12) and (0, 12). The orthocentre of this triangle is (a) (0, 0) (b) (10, 0) (c) (0, 24) (d) 80. The orthocentre of the triangle with vertices and is (a) (b) (c) (d) 81. If the coordinates of the vertices of a triangle are rational numbers then which of the following points of the triangle will always have rational coordinates (a) Centroid (b) Incentre (c) Circumcentre (d) Orthocentre 82. In the , the coordinates of B are (0, 0), and the middle point of BC has the coordinates (2, 0). The centroid of the triangle is (a) (b) (c) (d) None of these 83. The vertices of triangle are (6, 0), (0, 6) and (6, 6). The distance between its circumcentre and centroid is (a) (b) 2 (c) (d) 1 84. Two vertices of a triangle are (5, –1) and (–2, 3). If orthocentre is the origin then co-ordinates of the third vertex are (a) (7, 4) (b) (–4, 7) (c) (4, –7) (d) (– 4, – 7) 85. The orthocentre of the triangle formed by the lines and lies in quadrant (a) First (b) Second (c) Third (d) Fourth 86. Two vertices of a triangle are (4, –3) and (–2, 5). If the orthocentre of the triangle is at (1, 2) , then the third vertex is (a) (– 33, –26) (b) (33, 26) (c) (26, 33) (d) None of these 87. The equations to the sides of a triangle are , and . The line passes through (a) The incentre (b) The centroid (c) The circumcentre (d) The orthocentre of the triangle 88. The vertices of a triangle are , , , then the coordinates of its orthocentre are (a) (b) (c) (d) None of these 89. The equations of the three sides of a triangle are and . The coordinates of the circumcentre of the triangle are (a) (4, 0) (b) (2, –1 ) (c) (0, 4) (d) None of these 90. The area of the triangle with vertices at (–4, 1), (1, 2), (4, – 3) is (a) 14 (b) 16 (c) 15 (d) None of these 91. If the coordinates of the points A, B, C be (4, 4) (3, –2) and (3, – 16) respectively, then the area of the triangle ABC is (a) 27 (b) 15 (c) 18 (d) 7 92. If the vertices of a triangle are (5, 2), (2/3, 2) and (–4, 3), then the area of the triangle is (a) (b) (c) 43 (d) 93. The area of a triangle whose vertices are (1, –1), (–1, 1) and (–1, –1) is given by (a) 2 (b) (c) 1 (d) 3 94. The vertices of a triangle ABC are , and . If its area be 70 units then number of integral values of is (a) 1 (b) 2 (c) 4 (d) 0 95. The area of the pentagon whose vertices are (1, 2), (–3, 2), (4, 5), (–3, 3) and (–3, 0) is (a) 15/2 unit2 (b) 30 unit2 (c) 45 unit2 (d) None of these 96. If and are four points. If the ratio of area of and is 1 : 2, then the value of x will be [IIT 1959] (a) (b) (c) 3 (d) None of these 97. The point A divides the join of the points (– 5, 1) and (3, 5) in the ratio k : 1 and the coordinates of the points B and C are (1, 5) and (7, – 2) respectively. If the area of the triangle ABC be 2 units, then k = (a) 6, 7 (b) 31/9, 9 (c) 7, 31/9 (d) 7, 9 98. The area of a triangle is 5. If two of its vertices are (2, 1), (3, –2) and the third vertex lies on the line then the third vertex is (a) (b) (c) (d) 99. The area of the triangle formed by the lines and is (a) 8 sq. units (b) 12 sq. units (c) 14 sq. units (d) None of these 100. Area of the triangle with vertices (a, b), and where are in G.P. with common ratio ‘r’ and are in G.P. with common ratio ‘s’ is (a) (b) (c) (d) 101. If the area of the triangle whose vertices are and is , then the area of triangle whose vertices are and is (a) (b) (c) (d) None of these 102. are the vertices of a triangle and if through P and R lines parallel to opposite sides are drawn to intersect in S, then the area of PQRS is (a) 6 (b) 4 (c) 8 (d) 12 103. An equilateral triangle has each side equal to a. If the coordinates of its vertices are , then the square of the determinant equals (a) (b) (c) (d) None of these 104. Area of a units and its vertices A and B are (–5, 0) and (3, 0) respectively. If its vertex C lies on the line , then C is (a) (3, 5) (b) (– 3, – 5) (c) (– 5, 7) (d) None of these 105. Point P divides the line segment joining and internally in the ratio . If and area of then equals (a) 23 (b) 31/9 (c) 29/5 (d) None of these 106. Three points and are collinear if p = (a) – 1 (b) 1 (c) 2 (d) 0 107. If the points (a, 0), (0, b) and (1, 1) are collinear, then (a) (b) (c) (d) 108. If the points (a, b), and are collinear, then (a) (b) (c) (d) 109. If the points and be collinear, then the possible values of k are (a) (b) (c) (d) 110. If the points (–5, 1), (p, 5) and (10, 7) are collinear, then the value of p will be (a) 5 (b) 3 (c) 4 (d) 7 111. If the points are collinear, then the value of a is (a) (b) (c) (d) 112. If the points (5, 5), (10, K) and (–5, 1) are collinear, then K = (a) 3 (b) 5 (c) 7 (d) 9 113. The points are (a) Vertices of an equilateral triangle (b) Vertices of a right angled triangle (c) Vertices of an isosceles triangle (d) Collinear 114. The points and are (a) Vertices of an equilateral triangle (b) Vertices of an isosceles triangle (c) Vertices of a right angled isosceles triangle (d) Collinear 115. The points (a, b), (c, d) and are (a) Vertices of an equilateral triangle (b) Vertices of an isosceles triangle (c) Vertices of a right angled triangle (d) Collinear 116. A, B, C are the points (a, p), (b, q) and (c, r) respectively such that a, b, c are in A.P. and p, q, r in G.P. If the points are collinear, then (a) (b) (c) (d) 117. A, B, C are three collinear points such that AB = 2.5 and the co-ordinates of A and C are respectively (3, 4) and (11, 10), then the co-ordinates of the point B are (a) (b) (c) (d) 118. The points and are collinear (a) For all values of (b) 2 is A.M. of x, y (c) 2 is G.M. of x, y (d) 2 is H.M. of x, y 119. If and are distinct, the points and are collinear if (a) (b) (c) (d) 120. The points and are (a) Collinear (b) Vertices of a rectangle (c) Vertices of a parallelogram (d) None of these 121. The new coordinates of a point (4, 5), when the origin is shifted to the point (1, –2) are (a) (5, 3) (b) (3, 5) (c) (3, 7) (d) None of these 122. The co-ordinate axes are rotated through an angle . If the co-ordinates of a point P in the new system are known to be then the co-ordinates of P in the original system are (a) (b) (c) (d) 123. If the axes be rotated through an angle of in the clockwise direction, the point (4, 2) in the new system was formally (a) (b) (c) (d) None of these 124. Without changing the direction of coordinate axes origin is transferred to (h, k), so that the linear (one degree) terms in the equation are eliminated. Then the point (h, k) is (a) (3, 2) (b) (– 3, 2) (c) (2, – 3) (d) None of these 125. The point (4, 1) undergoes the following two successive transformations (i) reflection about the line (ii) rotation through a distance 2 units along the positive x-axis Then the final coordinates of the point are (a) (4, 3) (b) (3, 4) (c) (1, 4) (d) (7/2, 7/2) 126. Two points A and B have coordinates (1, 0) and (–1, 0) respectively and Q is a point which satisfies the relation AQ – BQ = . The locus of Q is (a) (b) (c) (d) 127. A point moves such that the sum of its distances from two fixed points (ae, 0) and (–ae, 0) is always 2a. Then equation of its locus is (a) (b) (c) (d) None of these 128. The locus of a point whose distance from the point is always ‘a’, will be (where (a) (b) (c) (d) None of these 129. The coordinates of the points A and B are and respectively. If a point P moves so that when k is a constant, then the equation to the locus of the point P is (a) (b) (c) (d) 130. If the distance of any point P from the points and are equal, then the locus of P is (a) (b) (c) (d) 131. The locus of a point whose difference of distance from points (3, 0) and (–3, 0) is 4, is (a) (b) (c) (d) 132. If A and B are two fixed points in a plane and = constant, then the locus of P is [MNR 1991; 1995] (a) Hyperbola (b) Circle (c) Parabola (d) Ellipse 133. If A and B are two points in a plane, so that PA + PB = constant, then the locus of P is (a) Hyperbola (b) Circle (c) Parabola (d) Ellipse 134. The equation of the locus of all points equidistant from the point (4, 2) and the x-axis, is (a) (b) (c) (d) None of these 135. The locus of a point which moves so that it is always equidistant from the points and is (a) A circle (b) Perpendicular bisector of the line segment AB (c) A line parallel to x-axis (d) None of these 136. The locus of a point which moves so that its distance from x-axis is double of its distance from y-axis is (a) (b) (c) (d) 137. O is the origin and A is the point (3, 4). If a point P moves so that the line segment OP is always parallel to the line segment OA, then the equation to the locus of P is (a) (b) (c) (d) 138. If A and B are two fixed points in a plane and P is another variable point such that constant, then the locus of the point P is (a) Hyperbola (b) Circle (c) Parabola (d) Ellipse 139. If sum of distances of a point from the origin and line is 4, then its locus is (a) (b) (c) (d) 140. The coordinates of the points A and B are and , . If a point P moves so that , then the equation to the locus of P is (a) (b) (c) (d) 141. The equation of the locus of a point whose distance from (a, 0) is equal to its distance from y-axis, is (a) (b) (c) (d) 142. The locus of the point of intersection of lines and is ( is a variable) (a) (b) (c) (d) None of these 143. Two points A and B move on the x- axis and the y-axis respectively such that the distance between the two points is always the same. The locus of the middle point of AB is (a) A straight line (b) A circle (c) A parabola (d) An ellipse 144. The locus of P such that area of units, where and is (a) (b) (c) (d) 145. Locus of centroid of the triangle whose vertices are and (1, 0), where t is a parameter is (a) (b) (c) (d) 146. If A is (2, 5), B is (4, –11) and C lies on then the locus of the centroid of the is a straight line parallel to the straight line (a) (b) (c) (d) 147. Two fixed points are and . If , then the locus of point C of triangle ABC will be (a) (b) (c) (d) 148. If and are two fixed points, then the locus of the point on which the line AB subtends the right angle, is (a) (b) (c) (d) 149. The coordinates of the points O, A and B are (0, 0), (0, 4) and (6, 0) respectively. If a point P moves such that the area of is always twice the area of , then the equation to both parts of the locus of P is (a) (b) (c) (d) None of these 150. A stick of length l rests against the floor and a wall of a room. If the stick begins to slide on the floor, then the locus of its middle point is (a) A straight line (b) Circle (c) Parabola (d) Ellipse 151. Given the points and . Then the equation of the locus of the point such that , is (a) (b) (c) (d) 152. If and are three given points, then the locus of a point S satisfying the relation is (a) A straight line parallel to x-axis (b) A circle through origin (c) A circle with centre at the origin (d) A straight line parallel to y-axis 153. The locus of a point which moves in such a way that its distance from (0, 0) is three times its distance from the x-axis, as given by (a) (b) (c) (d) 154. and are two fixed points of triangle The vertex C moves in such a way that , where is a constant. Then the locus of the point C is (a) (b) (c) (d) None of these 155. A line of fixed length moves so that its ends are always on two fixed perpendicular lines. The locus of the point which divides this line into portions of lengths a and b is (a) A circle (b) An ellipse (c) A hyperbola (d) None of these