The number of integral values of m for which the quadratic expression, (1 + 2m)x² – 2(1 + 3m)x + 4(1 + m), x $$ \in $$ R, is always positive, is :

If a straight line passing through the point P(–3, 4) is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is :

Let S and S' be the foci of an ellipse and B be any one of the extremities of its minor axis. If $$\Delta $$S'BS is a right angled triangle with right angle at B and area ($$\Delta $$S'BS) = 8 sq. units, then the length of a latus rectum of the ellipse is :

The set of all values of $$\lambda $$ for which the system of linear equations
x – 2y – 2z = $$\lambda $$x
x + 2y + z = $$\lambda $$y
– x – y = $$\lambda $$z
has a non-trivial solutions :