Let 1, ω, $\omega ^ 2$ be three cube roots of unity. If x = a + b $y=a\omega +b\omega ^{2}, z=a\omega ^{2}+b\omega$ then what is $ x ^ 2 + y ^ 2 + z ^ 2$ equal to?

How many 4-digit numbers that are divisible by 4 can be formed using the digits 1, 2, 3 and 4 (repetition of digits is not allowed)?

If a, b, c are the sides of a triangle ABC and p is the perimeter of the triangle, then what is equal to? det $\left|\begin{matrix}p+c&a&b\\ c&p+a&b\\ c&a&p+b\end{matrix}\right|$