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 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____

If the perpendicular bisector of the line segment joining the points P(1 ,4) and Q(k, 3) has y-intercept equal to –4, then a value of k is :

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 :