What is the unit digit in the expansion of (57242)^{9×7×5×3×1}?

If ABC and DEF are both 3-digit numbers such that A, B, C, D, E and F are distinct non-zero digits such that ABC + DEF = 1111, then what is the value of A + B + C + D + E + F ?

D is a 3-digit number such that the ratio of the number to the sum of its digits is least. What is the difference between the digit at the hundred's place and the digit at the unit's place of D?

Three of the five positive integers p, q, r, s, t are even and two of them are odd (not necessarily in order). Consider the following :

1. p + q + r - s - t is definitely even.

2. 2p + q + 2r - 2s + t is definitely odd.

Which of the above statements is/are correct?