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1

### IIT-JEE 1999

MCQ (More than One Correct Answer)
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
$$x - 7y = 0$$
2

### IIT-JEE 1998

MCQ (More than One Correct Answer)
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.)
3

### IIT-JEE 1986

MCQ (More than One Correct Answer)
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
$$- 2x + y \ge 0$$
4

### IIT-JEE 1985

MCQ (More than One Correct Answer)
Three lines $$px + qy + r = 0$$, $$qx + ry + p = 0$$ and $$rx + py + q = 0$$ are concurrent if
A
$$p + q + r = 0$$
B
$${p^2} + {q^2} + {r^2} = qr + rp + pq$$
C
$${p^3} + {q^3} + {r^3} = 3pqr$$
D
none of these.

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