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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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