1
IIT-JEE 2008 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
A straight line through the vertex p of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then :
A
$${1 \over {PS}} + {1 \over {ST}} < {2 \over {\sqrt {QS \times SR} }}$$
B
$${1 \over {PS}} + {1 \over {ST}} > {2 \over {\sqrt {QS \times SR} }}$$
C
$${1 \over {PS}} + {1 \over {ST}} < {4 \over {QR}}$$
D
$${1 \over {PS}} + {1 \over {ST}} > {4 \over {QR}}$$
2
IIT-JEE 1999
MCQ (More than One Correct Answer)
+3
-0.75
Let $${L_1}$$ be a straight line passing through the origin and $${L_2}$$ be the straight line $$x + y = 1$$. If the intercepts made by the circle $${x^2} + {y^2} - x + 3y = 0$$ on $${L_1}$$ and $${L_2}$$ are equal, then which of the following equations can represent $${L_1}$$?
A
$$x + y = 0$$
B
$$x -y = 0$$
C
$$x + 7y = 0$$
D
$$x - 7y = 0$$
3
IIT-JEE 1998
MCQ (More than One Correct Answer)
+2
-0.5
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)?
A
centroid ( A rational point is a point both of whose co-ordinates are rational numbers.)
B
incentre. ( A rational point is a point both of whose co-ordinates are rational numbers.)
C
circumcentre ( A rational point is a point both of whose co-ordinates are rational numbers.)
D
orthocentre ( A rational point is a point both of whose co-ordinates are rational numbers.)
4
IIT-JEE 1986
MCQ (More than One Correct Answer)
+2
-0.5
All points lying inside the triangle formed by the points $$\left( {1,\,3} \right),\,\left( {5,\,0} \right)$$ and $$\left( { - 1,\,2} \right)$$ satisfy
A
$$3x + 2y \ge 0$$
B
$$2x + y - 13 \ge 0$$
C
$$2x - 3y - 12 \le 0$$
D
$$- 2x + y \ge 0$$
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