If R = {(x, y) : x, y $$ \in $$ Z, x² + 3y² $$ \le $$ 8} is a relation on the set of integers Z, then the domain of R^–1 is :

Let $$\alpha $$ and $$\beta $$ be the roots of the equation
5x² + 6x – 2 = 0. If S_n = $$\alpha $$ⁿ + $$\beta $$ⁿ, n = 1, 2, 3...., then :

The sum of the first three terms of a G.P. is S and their product is 27. Then all such S lie in :

A line parallel to the straight line 2x – y = 0 is tangent to the hyperbola
$${{{x^2}} \over 4} - {{{y^2}} \over 2} = 1$$ at the point $$\left( {{x_1},{y_1}} \right)$$. Then $$x_1^2 + 5y_1^2$$ is equal to :