Engineering Mathematics

The value of the definite integral \int_{-3}^{3} \int_{-2}^{2} \int_{-1}^{1} (4x^2y-z^3)dzdydx is _____. (Rounded off to the nearest integer)

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 = _____

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

Let A=\begin{bmatrix} 1 & 2 & 3 &4 \\ 4& 1& 2 &3 \\ 3& 4 & 1 &2 \\ 2 &3 &4 &1 \end{bmatrix} and B=\begin{bmatrix} 3& 4 & 1 &2 \\ 4& 1& 2 &3 \\ 1 & 2 & 3 &4 \\ 2 &3 &4 &1 \end{bmatrix}
Let det(A) and det(B) denote the determinants of the matrices A and B, respectively.
Which one of the options given below is TRUE?

Which of the following is/are the eigenvector(s) for the matrix given below?
\begin{pmatrix} -9 &-6 &-2 &-4 \\ -8& -6 & -3 & -1 \\ 20 & 15 & 8 & 5 \\ 32& 21& 7&12 \end{pmatrix}
MSQ