List of top Computer Science and IT Engineering Questions on Engineering Mathematics asked in GATE CS

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

Let $\lambda_1, \lambda_2, \lambda_3, \lambda_4, \lambda_5$ be the eigenvalues of $A$ (not necessarily distinct). Find: \[ \lambda_1 + \lambda_2 + \lambda_3 + \lambda_4 + \lambda_5 \;=\; \_\_\_\_\_\_ . \]

The Lucas sequence $L_n$ is defined by the recurrence relation: \[ L_n = L_{n-1} + L_{n-2}, \text{for } n \geq 3, \] with $L_1 = 1$ and $L_2 = 3$. Which one of the options given is TRUE?

Suppose two hosts are connected by a point-to-point link and they are configured to use Stop-and-Wait protocol for reliable data transfer. Identify in which one of the following scenarios, the utilization of the link is the lowest.

Let \[ A = \begin{bmatrix} 1 & 2 & 3 & 4 \\ 4 & 1 & 2 & 3 \\ 3 & 4 & 1 & 2 \\ 2 & 3 & 4 & 1 \end{bmatrix}, \quad B = \begin{bmatrix} 3 & 4 & 1 & 2 \\ 4 & 1 & 2 & 3 \\ 1 & 2 & 3 & 4 \\ 2 & 3 & 4 & 1 \end{bmatrix} \] 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?

The output of a 2-input multiplexer is connected back to one of its inputs as shown in the figure. Match the functional equivalence of this circuit to one of the following options.

Which of the following statements is/are CORRECT?

Geetha has a conjecture about integers, of the form \[ \forall x \big(P(x) \Rightarrow \exists y \, Q(x,y)\big) \] where $P$ is a statement about integers and $Q$ is a statement about pairs of integers. Which of the following option(s) would imply Geetha's conjecture?

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

Let $f$ and $g$ be functions of natural numbers given by $f(n)=n$ and $g(n)=n^2$. Which of the following statements is/are TRUE?

The value of the definite integral $\displaystyle \int_{-3}^{3}\int_{-2}^{2}\int_{-1}^{1}\big(4x^{2}y - z^{3}\big)\,dz\,dy\,dx$ is ________. (Rounded off to the nearest integer)

A particular number is written as $132$ in radix-$4$ representation. The same number in radix-$5$ representation is ________

The integer value printed by the ANSI-C program given below is ________.


int funcp(){
    static int x = 1;
    x++;
    return x;
}

int main(){
    int x,y;
    x = funcp();
    y = funcp() + x;
    printf("%d\n", (x+y));
    return 0;
}

Consider the following program:

int main() {
    f1();
    f2(2);
    f3();
    return(0);
}

int f1() {
    f1();
    return(1);
}

int f2(int X) {
    f3();
    if (X==1)
        return f1();
    else
        return (X * f2(X-1));
}

int f3() {
    return(5);
}

Which one of the following options represents the activation tree corresponding to the main function?

Let $f:A\to B$ be an onto (surjective) function, where $A$ and $B$ are nonempty sets. Define an equivalence relation $\sim$ on $A$ by $a_1\sim a_2$ iff $f(a_1)=f(a_2)$. Let $\mathcal{E=\{[x]:x\in A\}$ be the set of all equivalence classes under $\sim$. Define $F:\mathcal{E}\to B$ by $F([x])=f(x)$ for all classes $[x]\in\mathcal{E}$. Which of the following statements is/are TRUE?}

Let $X$ be a set and $2^{X}$ denote the power set of $X$. Define a binary operation $\,\Delta\,$ on $2^{X}$ by $A \Delta B = (A-B)\cup(B-A)$ (symmetric difference). Let $H=(2^{X},\Delta)$. Which of the following statements about $H$ is/are correct?

Consider a random experiment where two fair coins are tossed. Let $A$ be the event that denotes HEAD on both throws, $B$ the event that denotes HEAD on the first throw, and $C$ the event that denotes HEAD on the second throw. Which of the following statements is/are TRUE?

Let $U = \{1,2,\ldots,n\}$ with $n > 1000$. Let $k < n$ be a positive integer. Let $A,B \subseteq U$ with $|A| = |B| = k$ and $A \cap B = \varnothing$. A permutation of $U$ separates $A$ from $B$ if either all members of $A$ appear before any member of $B$, or all members of $B$ appear before any member of $A$.

How many permutations of $U$ separate $A$ from $B$?

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

Let $\lambda_1, \lambda_2, \lambda_3, \lambda_4, \lambda_5$ be the eigenvalues of $A$ (not necessarily distinct). Find: \[ \lambda_1 + \lambda_2 + \lambda_3 + \lambda_4 + \lambda_5 \;=\; \_\_\_\_\_\_ . \]

The value of the definite integral $\displaystyle \int_{-3}^{3}\int_{-2}^{2}\int_{-1}^{1}\big(4x^{2}y - z^{3}\big)\,dz\,dy\,dx$ is ________. (Rounded off to the nearest integer)

A particular number is written as $132$ in radix-$4$ representation. The same number in radix-$5$ representation is ________

The integer value printed by the ANSI-C program given below is ________.


int funcp(){
    static int x = 1;
    x++;
    return x;
}

int main(){
    int x,y;
    x = funcp();
    y = funcp() + x;
    printf("%d\n", (x+y));
    return 0;
}