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 :

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 X = {x $$ \in $$ N : 1 $$ \le $$ x $$ \le $$ 17} and
Y = {ax + b: x $$ \in $$ X and a, b $$ \in $$ R, a > 0}. If mean
and variance of elements of Y are 17 and 216
respectively then a + b is equal to :

Let y = y(x) be the solution of the differential equation,
$${{2 + \sin x} \over {y + 1}}.{{dy} \over {dx}} = - \cos x$$, y > 0,y(0) = 1.
If y($$\pi $$) = a and $${{dy} \over {dx}}$$ at x = $$\pi $$ is b, then the ordered pair (a, b) is equal to :