The number of integral values of m so that the abscissa of point of intersection of lines 3x + 4y = 9 and y = mx + 1 is also an integer, is :

The equation of one of the straight lines which passes through the point (1, 3) and makes an angles $${\tan ^{ - 1}}\left( {\sqrt 2 } \right)$$ with the straight line, y + 1 = 3$${\sqrt 2 }$$ x is :

In a triangle PQR, the co-ordinates of the points P and Q are ($$-$$2, 4) and (4, $$-$$2) respectively. If the equation of the perpendicular bisector of PR is 2x $$-$$ y + 2 = 0, then the centre of the circumcircle of the $$\Delta$$PQR is :

Let A($$-$$1, 1), B(3, 4) and C(2, 0) be given three points.
A line y = mx, m > 0, intersects lines AC and BC at point P and Q respectively. Let A₁ and A₂ be the areas of $$\Delta$$ABC and $$\Delta$$PQC respectively, such that A₁ = 3A₂, then the value of m is equal to :