If the vertices of a hyperbola be at (–2, 0) and (2, 0) and one of its foci be at (–3, 0), then which one of the following points does not lie on this hyperbola?

Let  S_k = $${{1 + 2 + 3 + .... + k} \over k}.$$ If   $$S_1^2 + S_2^2 + .....\, + S_{10}^2 = {5 \over {12}}$$A,  then A is equal to :

If a variable line, 3x + 4y – $$\lambda $$ = 0 is such that the two circles x² + y² – 2x – 2y + 1 = 0 and x² + y² – 18x – 2y + 78 = 0 are on its opposite sides, then the set of all values of $$\lambda $$ is the interval :

Let y = y(x) be the solution of the differential equation, x$${{dy} \over {dx}}$$ + y = x log_e x, (x > 1). If 2y(2) = log_e 4 $$-$$ 1, then y(e) is equal to :