If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x and y be 10 and 25 respectively, then x.y is equal to _______.

If the system of linear equations,
x + y + z = 6
x + 2y + 3z = 10
3x + 2y + $$\lambda $$z = $$\mu $$
has more than two solutions, then $$\mu $$ - $$\lambda $$² is equal to ______.

If the foot of the perpendicular drawn from the point (1, 0, 3) on a line passing through ($$\alpha $$, 7, 1) is $$\left( {{5 \over 3},{7 \over 3},{{17} \over 3}} \right)$$, then $$\alpha $$ is equal to______.

Let ƒ(x) be a polynomial of degree 5 such that x = ±1 are its critical points.

If $$\mathop {\lim }\limits_{x \to 0} \left( {2 + {{f\left( x \right)} \over {{x^3}}}} \right) = 4$$, then which one of the following is not true?