JEE Main & Advanced Mathematics Rectangular Cartesian Coordinates Question Bank

done Critical Thinking Total Questions - 15

• question_answer1)
  Point of intersection of the diagonals of square is at origin and coordinate axis are drawn along the diagonals. If the side is of length a, then one which is not the vertex of square is
  A)
  \[(a\sqrt{2},0)\] done clear
  B)
  \[\left( 0,\frac{a}{\sqrt{2}} \right)\] done clear
  C)
  \[\left( \frac{a}{\sqrt{2}},0 \right)\] done clear
  D)
  \[\left( -\frac{a}{\sqrt{2}},0 \right)\] done clear
  View Solution play_arrow

• question_answer2)
  ABC is an isosceles triangle. If the coordinates of the base are B (1,3) and C (- 2, 7), the coordinates of vertex A can be [Orrissa JEE 2002; Pb. CET 2002]
  A)
  (1, 6) done clear
  B)
  \[\left( -\frac{1}{2},\,5 \right)\] done clear
  C)
  \[\left( \frac{5}{6},\,6 \right)\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer3)
  If \[A(a{{t}^{2}},\,2at),\ B(a/{{t}^{2}},\,-2a/t)\] and \[C(a,\,0)\], then 2a is equal to      [RPET 2000]
  A)
  A.M. of CA and CB done clear
  B)
  G.M. of CA and CB done clear
  C)
  H.M. of CA and CB done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer4)
  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 = 3 AM, then the coordinates of M are
  A)
  \[\left( \frac{8}{3},\,\frac{10}{3} \right)\] done clear
  B)
  \[\left( \frac{10}{3},\frac{14}{4} \right)\] done clear
  C)
  \[\left( \frac{10}{3},\frac{6}{3} \right)\] done clear
  D)
  \[\left( \frac{13}{4},\frac{10}{4} \right)\] done clear
  View Solution play_arrow

• question_answer5)
  The point of trisection of the line joining the points (0, 3) and (6, -3) are 
  A)
  \[(2,\,0)\]and\[(4,\,-1)\] done clear
  B)
  \[(2,\,-1)\]and \[(4,1)\] done clear
  C)
  \[(3,1)\]and\[(4,-1)\] done clear
  D)
  \[(2,1)\]and\[(4,-1)\] done clear
  View Solution play_arrow

• question_answer6)
  The following points A (2a, 4a), B(2a, 6a) and C \[(2a+\sqrt{3}a,\,5a)\], \[(a>0)\] are the vertices of
  A)
  An acute angled triangle done clear
  B)
  A right angled triangle done clear
  C)
  An isosceles triangle done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer7)
  If the coordinates of the vertices of a triangle be (1,a), (2,b) and \[({{c}^{2}},3)\], then the centroid of the triangle
  A)
  Lies at the origin done clear
  B)
  Cannot lie on x-axis done clear
  C)
  Cannot lie on y-axis done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer8)
  If the vertices of a triangle be (0,0), (6,0) and (6,8), then its incentre will be
  A)
  (2, 1) done clear
  B)
  (1,2) done clear
  C)
  (4, 2) done clear
  D)
  (2,4) done clear
  View Solution play_arrow

• question_answer9)
  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) done clear
  B)
  (5/6, 1) done clear
  C)
  (2, 5/3) done clear
  D)
  (1, 5/6) done clear
  View Solution play_arrow

• question_answer10)
  If the vertices P, Q, R of a triangle PQR are rational points, which of the following points of the triangle PQR is (are) always rational point(s) [IIT 1998]
  A)
  Centroid done clear
  B)
  Incentre done clear
  C)
  Circumcentre done clear
  D)
  Orthocentre (A rational point is a point both of whose coordinates are rational numbers) done clear
  View Solution play_arrow

• question_answer11)
  The centroid of a triangle is (2, 7) and two of its vertices are (4, 8) and (-2, 6). The third vertex is [Kerala (Engg.)  2002]
  A)
  (0, 0) done clear
  B)
  (4, 7) done clear
  C)
  (7, 4) done clear
  D)
  (7, 7) done clear
  View Solution play_arrow

• question_answer12)
  The points \[(1,\text{ }1)\], \[(0,{{\sec }^{2}}\theta ),\,(\text{cose}{{\text{c}}^{2}}\theta ,\text{ }0)\] are collinear for  [Roorkee 1963]
  A)
  \[\theta =\frac{n\pi }{2}\] done clear
  B)
  \[\theta \ne \frac{n\pi }{2}\] done clear
  C)
  \[\theta =n\pi \] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer13)
  The ends of a rod of length l move on two mutually perpendicular lines. The locus of the point on the rod which divides it in the ratio 1 : 2 is [IIT 1987; RPET 1997]
  A)
  \[36{{x}^{2}}+9{{y}^{2}}=4{{l}^{2}}\] done clear
  B)
  \[36{{x}^{2}}+9{{y}^{2}}={{l}^{2}}\] done clear
  C)
  \[9{{x}^{2}}+36{{y}^{2}}=4{{l}^{2}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer14)
  Two fixed points are \[A(a,0)\]and\[B(-a,0)\]. If\[\angle A-\angle B=\theta \], then the locus of point C of triangle ABC will be      [Roorkee 1982]
  A)
  \[{{x}^{2}}+{{y}^{2}}+2xy\tan \theta ={{a}^{2}}\] done clear
  B)
  \[{{x}^{2}}-{{y}^{2}}+2xy\tan \theta ={{a}^{2}}\] done clear
  C)
  \[{{x}^{2}}+{{y}^{2}}+2xy\cot \theta ={{a}^{2}}\] done clear
  D)
  \[{{x}^{2}}-{{y}^{2}}+2xy\cot \theta ={{a}^{2}}\] done clear
  View Solution play_arrow

• question_answer15)
  Let \[A(2,-3)\]and \[B(-2,1)\]be vertices of a triangle ABC. If the centroid of this triangle moves on the line \[2x+3y=1\], then the locus of the vertex C is the line [AIEEE 2004]
  A)
  \[3x-2y=3\] done clear
  B)
  \[2x-3y=7\] done clear
  C)
  \[3x+2y=5\] done clear
  D)
  \[2x+3y=9\] done clear
  View Solution play_arrow