Let S be the set of all integer solutions, (x, y, z), of the system of equations
x – 2y + 5z = 0
–2x + 4y + z = 0
–7x + 14y + 9z = 0
such that 15 $$ \le $$ x² + y² + z² $$ \le $$ 150. Then, the number of elements in the set S is equal to ______ .

Let x_i (1 $$ \le $$ i $$ \le $$ 10) be ten observations of a random variable X. If
$$\sum\limits_{i = 1}^{10} {\left( {{x_i} - p} \right)} = 3$$ and $$\sum\limits_{i = 1}^{10} {{{\left( {{x_i} - p} \right)}^2}} = 9$$
where 0 $$ \ne $$ p $$ \in $$ R, then the standard deviation of these observations is :

If the surface area of a cube is increasing at a rate of 3.6 cm²/sec, retaining its shape; then the rate of change of its volume (in cm³/sec), when the length of a side of the cube is 10 cm, is :

Let the latus ractum of the parabola y² = 4x be the common chord to the circles C₁ and C₂ each of them having radius 2$$\sqrt 5 $$. Then, the distance between the centres of the circles C₁ and C₂ is :