If the two lines x + (a – 1) y = 1 and 2x + a²y = 1 (a$$ \in $$R – {0, 1}) are perpendicular, then the distance of their point of intersection from the origin is :

Slope of a line passing through P(2, 3) and intersecting the line, x + y = 7 at a distance of 4 units from P, is :

If the system of linear equations

x – 2y + kz = 1
2x + y + z = 2
3x – y – kz = 3

has a solution (x,y,z), z $$ \ne $$ 0, then (x,y) lies on the straight line whose equation is :

Suppose that the points (h,k), (1,2) and (–3,4) lie on the line L₁ . If a line L₂ passing through the points (h,k) and (4,3) is perpendicular to L₁ , then $$k \over h$$ equals :