1
IIT-JEE 1985
Fill in the Blanks
+2
-0
The orthocentre of the triangle formed by the lines $$x + y = 1,\,2x + 3y = 6$$ and $$4x - y + 4 = 0$$ lies in quadrant number .............
2
IIT-JEE 1985
MCQ (More than One Correct Answer)
+2
-0.5
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.
3
IIT-JEE 1985
Subjective
+3
-0
One of the diameters of the circle circumscribing the rectangle $$ABCD$$ is $$4y = x + 7$$. If $$A$$ and $$B$$ are the points $$(-3, 4)$$ and $$(5, 4)$$ respectively, then find the area of rectangle.
4
IIT-JEE 1985
Subjective
+5
-0
Two sides of rhombus $$ABCD$$ are parallel to the lines $$y = x + 2$$ and $$y = 7x + 3$$. If the diagonals of the rhombus intersect at the point $$(1, 2)$$ and the vertex $$A$$ is on the $$y$$-axis, find possible co-ordinates of $$A$$.
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