Reaction of [Co(H₂O)₆]²⁺ with excess ammonia and in the presence of oxygen results into a diamagnetic product. Number of electrons present in t_2g-orbitals of the product is ___________.

The moles of methane required to produce 81 g of water after complete combustion is _____________ $$\times$$ 10^$$-$$2 mol. [nearest integer]

Let f : R $$\to$$ R be defined as f (x) = x $$-$$ 1 and g : R $$-$$ {1, $$-$$1} $$\to$$ R be defined as $$g(x) = {{{x^2}} \over {{x^2} - 1}}$$.

Then the function fog is :

If the system of equations

$$\alpha$$x + y + z = 5, x + 2y + 3z = 4, x + 3y + 5z = $$\beta$$

has infinitely many solutions, then the ordered pair ($$\alpha$$, $$\beta$$) is equal to :