Let the system of linear equations
$$x + 2y + z = 2$$,
$$\alpha x + 3y - z = \alpha $$,
$$ - \alpha x + y + 2z = - \alpha $$
be inconsistent. Then $$\alpha$$ is equal to :
$$x = \sum\limits_{n = 0}^\infty {{a^n},y = \sum\limits_{n = 0}^\infty {{b^n},z = \sum\limits_{n = 0}^\infty {{c^n}} } } $$, where a, b, c are in A.P. and |a| < 1, |b| < 1, |c| < 1, abc $$\ne$$ 0, then :
Let $${{dy} \over {dx}} = {{ax - by + a} \over {bx + cy + a}}$$, where a, b, c are constants, represent a circle passing through the point (2, 5). Then the shortest distance of the point (11, 6) from this circle is :
Let a be an integer such that $$\mathop {\lim }\limits_{x \to 7} {{18 - [1 - x]} \over {[x - 3a]}}$$ exists, where [t] is greatest integer $$\le$$ t. Then a is equal to :