The number of values of $$\alpha$$ for which the system of equations :
x + y + z = $$\alpha$$
$$\alpha$$x + 2$$\alpha$$y + 3z = $$-$$1
x + 3$$\alpha$$y + 5z = 4
is inconsistent, is
If the sum of the squares of the reciprocals of the roots $$\alpha$$ and $$\beta$$ of
the equation 3x2 + $$\lambda$$x $$-$$ 1 = 0 is 15, then 6($$\alpha$$3 + $$\beta$$3)2 is equal to :
The set of all values of k for which
$${({\tan ^{ - 1}}x)^3} + {({\cot ^{ - 1}}x)^3} = k{\pi ^3},\,x \in R$$, is the interval :
Let S = {$$\sqrt{n}$$ : 1 $$\le$$ n $$\le$$ 50 and n is odd}.
Let a $$\in$$ S and $$A = \left[ {\matrix{ 1 & 0 & a \cr { - 1} & 1 & 0 \cr { - a} & 0 & 1 \cr } } \right]$$.
If $$\sum\limits_{a\, \in \,S}^{} {\det (adj\,A) = 100\lambda } $$, then $$\lambda$$ is equal to :