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_____.

Let a₁, a₂, ..., an be a given A.P. whose
common difference is an integer and
S_n = a₁ + a₂ + .... + a_n. If a₁ = 1, a_n = 300 and 15 $$ \le $$ n $$ \le $$ 50, then
the ordered pair (S_n-4, a_n–4) is equal to:

If a and b are real numbers such that
$${\left( {2 + \alpha } \right)^4} = a + b\alpha $$
where $$\alpha = {{ - 1 + i\sqrt 3 } \over 2}$$ then a + b is equal to :

Let $$\mathop \cup \limits_{i = 1}^{50} {X_i} = \mathop \cup \limits_{i = 1}^n {Y_i} = T$$ where each X_i contains 10 elements and each Y_i contains 5 elements. If each element of the set T is an element of exactly 20 of sets X_i’s and exactly 6 of sets Y_i’s, then n is equal to :