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 :

The number of distinct real roots of x⁴ $$-$$ 4x + 1 = 0 is :

The lengths of the sides of a triangle are 10 + x², 10 + x² and 20 $$-$$ 2x². If for x = k, the area of the triangle is maximum, then 3k² is equal to :