# Engineering Mathematics

 Question 1
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)
 A 0 B 1 C 2 D 3
GATE CSE 2023      Calculus
Question 1 Explanation:
 Question 2
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 $\lambda _1+\lambda _2+\lambda _3+ \lambda _4+ \lambda _5 =$ _____
 A 1 B 2 C 3 D 4
GATE CSE 2023      Linear Algebra
Question 2 Explanation:

 Question 3
Let $f(x)=x^3+15x^2-33x-36$ be a real-valued function.
Which of the following statements is/are TRUE?
 A $f(x)$ does not have a local maximum. B $f(x)$ has a local maximum. C $f(x)$ does not have a local minimum. D $f(x)$ has a local minimum.
GATE CSE 2023      Calculus
Question 3 Explanation:
 Question 4
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?
 A det(A) = det(B) B det(B) = - det(A) C det(A)=0 D det(AB) = det(A) + det(B)
GATE CSE 2023      Linear Algebra
Question 4 Explanation:
 Question 5
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
 A $\begin{pmatrix} -1\\ 1\\ 0\\ 1 \end{pmatrix}$ B $\begin{pmatrix} 1\\ 0\\ -1\\ 0 \end{pmatrix}$ C $\begin{pmatrix} -1\\ 0\\ 2\\ 2 \end{pmatrix}$ D $\begin{pmatrix} 0\\ 1\\ -3\\ 0 \end{pmatrix}$
GATE CSE 2022      Linear Algebra
Question 5 Explanation:

There are 5 questions to complete.

### 3 thoughts on “Engineering Mathematics”

1. Update Q184 as A instead of C

• 2. 