Let $$f(x) = {x^3} + 15{x^2} - 33x - 36$$ be a real-valued function. Which of the following statements is/are TRUE?

Let A be the adjacency matrix of the graph with vertices {1, 2, 3, 4, 5}.

Let $$\lambda_1,\lambda_2,\lambda_3,\lambda_4$$, and $$\lambda_5$$ be the five eigenvalues of A. Note that these eigenvalues need not be distinct.

The value of $$\lambda_1+\lambda_2+\lambda_3+\lambda_4+\lambda_5=$$ ______________

The value of the definite integral

$$\int\limits_{ - 3}^3 {\int\limits_{ - 2}^2 {\int\limits_{ - 1}^1 {(4{x^2}y - {z^3})dz\,dy\,dx} } } $$

is ___________. (Rounded off to the nearest integer)

Let $$U = \{ 1,2,....,n\} $$, where n is a large positive integer greater than 1000. Let k be a positive integer less than n. Let A, B be subsets of U with $$|A| = |B| = k$$ and $$A \cap B = \phi $$. We say that a permutation of U separates A from B if one of the following is true.

- All members of A appear in the permutation before any of the members of B.

- All members of B appear in the permutation before any of the members of A.

How many permutations of U separate A from B?