Let [t] denote the greatest integer $$ \le $$ t and $$\mathop {\lim }\limits_{x \to 0} x\left[ {{4 \over x}} \right] = A$$.
Then the function, f(x) = [x²]sin($$\pi $$x) is discontinuous, when x is equal to :

The following system of linear equations
7x + 6y – 2z = 0
3x + 4y + 2z = 0
x – 2y – 6z = 0, has

If the curves, x² – 6x + y² + 8 = 0 and
x² – 8y + y² + 16 – k = 0, (k > 0) touch each other at a point, then the largest value of k is ______.

Let $$\overrightarrow a $$, $$\overrightarrow b $$ and $$\overrightarrow c $$ be three vectors such that $$\left| {\overrightarrow a } \right| = \sqrt 3 $$, $$\left| {\overrightarrow b } \right| = 5,\overrightarrow b .\overrightarrow c = 10$$ and the angle between $$\overrightarrow b $$ and $$\overrightarrow c $$ is $${\pi \over 3}$$. If $${\overrightarrow a }$$ is perpendicular to the vector $$\overrightarrow b \times \overrightarrow c $$ , then $$\left| {\overrightarrow a \times \left( {\overrightarrow b \times \overrightarrow c } \right)} \right|$$ is equal to _____.