Let $$\lambda \ne 0$$ be in R. If $$\alpha $$ and $$\beta $$ are the roots of the
equation, x² - x + 2$$\lambda $$ = 0 and $$\alpha $$ and $$\gamma $$ are the roots of
the equation, $$3{x^2} - 10x + 27\lambda = 0$$, then $${{\beta \gamma } \over \lambda }$$ is equal to:

If the system of equations
x+y+z=2
2x+4y–z=6
3x+2y+$$\lambda $$z=$$\mu $$
has infinitely many solutions, then

If the variance of the following frequency distribution :

Class         : 10–20 20–30 30–40

Frequency :    2          x          2

is 50, then x is equal to____

Let {x} and [x] denote the fractional part of x and
the greatest integer $$ \le $$ x respectively of a real
number x. If $$\int_0^n {\left\{ x \right\}dx} ,\int_0^n {\left[ x \right]dx} $$ and 10(n² – n),
$$\left( {n \in N,n > 1} \right)$$ are three consecutive terms of a G.P., then n is equal to_____.