Let e₁ and e₂ be the eccentricities of the ellipse,
$${{{x^2}} \over {25}} + {{{y^2}} \over {{b^2}}} = 1$$(b < 5) and the hyperbola,
$${{{x^2}} \over {16}} - {{{y^2}} \over {{b^2}}} = 1$$ respectively satisfying e₁e₂ = 1. If $$\alpha $$
and $$\beta $$ are the distances between the foci of the
ellipse and the foci of the hyperbola
respectively, then the ordered pair ($$\alpha $$, $$\beta $$) is equal to :

The set of all real values of $$\lambda $$ for which the quadratic equations,
($$\lambda $$² + 1)x² – 4$$\lambda $$x + 2 = 0 always have exactly one root in the interval (0, 1) is :

If the sum of the series

20 + 19$${3 \over 5}$$ + 19$${1 \over 5}$$ + 18$${4 \over 5}$$ + ...

upto nth term is 488 and the n^th term is negative, then :

If the term independent of x in the expansion of
$${\left( {{3 \over 2}{x^2} - {1 \over {3x}}} \right)^9}$$ is k, then 18 k is equal to :