Four fair six-sided dice are rolled. The probability that the sum of the results being 22 is X/1296. The value of X is__________

Which one of the following propositional logic formulas is TRUE when exactly two of $$p, q,$$ and $$r$$ are TRUE?

Let S denote the set of all functions $$f:\,{\{ 0,\,1\} ^4}\, \to \,\{ 0,\,1\} $$. Denote by N the number of functions from S to the set {0, 1}. The value of $${\log _2}$$ $${\log _2}$$ N is___________________

The value of the dot product of the eigenvectors corresponding to any pair of different eigen values of a 4-by-4 symmetric positive definite matrix is ____________.