If (27)⁹⁹⁹ is divided by 7, then the remainder is :

The number of real values of $$\lambda $$ for which the system of linear equations

2x + 4y $$-$$ $$\lambda $$z = 0

4x + $$\lambda $$y + 2z = 0

$$\lambda $$x + 2y + 2z = 0

has infinitely many solutions, is :

If the sum of the first n terms of the series $$\,\sqrt 3 + \sqrt {75} + \sqrt {243} + \sqrt {507} + ......$$ is $$435\sqrt 3 ,$$ then n equals :

The tangent at the point (2, $$-$$2) to the curve, x²y² $$-$$ 2x = 4(1 $$-$$ y) does not pass through the point :