Recent questions tagged gatecse2025-set1

Consider the given function $f(x)$.$$f(x)=\left\{\begin{array}{ll} a x+b & \text { for } x<1 \\x^{3}+x^{2}+1 & \text { for } x \geq 1\end{array}\right.$$If the function i...

A box contains $5$ coins: $4$ regular coins and $1$ fake coin. When a regular coin is tossed, the probability $P($ head $)=0.5$ and for a fake coin, $P($ head $)=1$. You ...

The pseudocode of a function $\text{fun ()}$ is given below: fun(int A[0,....,n-1]) { for i=0 to n-2 for j=0 to n-i-2 if (A[j]>A[j+1]) then swap A[j] and A[j+1] }Let $A[0...

 #include <stdio.h void foo(int *p, int x) { *p=x; } int main(){ int *z; int a = 20, b = 25; z = &a; foo(z,b); printf("%d",a); return 0; }The output of the given $\text{C...

The height of any rooted tree is defined as the maximum number of edges in the path from the root node to any leaf node.Suppose a Min-Heap $\text{T}$ stores $32$ keys. Th...

Consider a memory system with $1 \mathrm{M}$ bytes of main memory and $16 \mathrm{~K}$ bytes of cache memory. Assume that the processor generates $20$-bit memory address,...

A processor has $64$ general-purpose registers and $50$ distinct instruction types. An instruction is encoded in $32$-bits. What is the maximum number of bits that can be...

A computer has two processors, $M_{1}$ and $M_{2}$. Four processes $P_{1}, P_{2}, P_{3}, P_{4}$ with CPU bursts of $20,16,25$, and $10$ milliseconds, respectively, arrive...

Consider two relations describing teams and players in a sports league:teams(tid, tname): tid, tname are team-id and team-name, respectivelyplayers(pid,pname,tid): pid, p...

A packet with the destination $\text{IP}$ address $145.36 .109 .70$ arrives at a router whose routing table is shown. Which interface will the packet be forwarded to?$$\b...

Let $A$ be a $2 \times 2$ matrix as given.$$ A=\left[\begin{array}{rr} 1 & 1 \\ 1 & -1 \end{array}\right]$$What are the eigenvalues of the matrix $A^{13}$ ?$1,-1$$2 \sqrt...

Consider the following four variable Boolean function in sum-of-product form$$ F\left(b_{3}, b_{2}, b_{1}, b_{0}\right)=\sum(0,2,4,8,10,11,12)$$where the value of the fun...

Let $G(V, E)$ be an undirected and unweighted graph with $100$ vertices. Let $d(u, v)$ denote the number of edges in a shortest path between vertices $u$ and $v$ in $V$. ...

Consider the following two languages over the alphabet $\{a, b\}$:$$\begin{array}{l} L_{1}=\left\{\alpha \beta \alpha \mid \alpha \in\{a, b\}^{+} \text {AND } \beta \in\{...

Consider the following two languages over the alphabet $\{a, b, c\}$, where $m$ and $n$ are natural numbers.$$\begin{aligned} L_{1} & =\left\{a^{m} b^{m} c^{m+n} \mid m, ...

Which of the following statement(s) is/are TRUE while computing $\operatorname{First}$ and $\operatorname{Follow}$ during top down parsing by a compiler?For a production ...

Consider a relational schema team $\text{(name,city,owner)}$, with functional dependencies $\{\text{name} \rightarrow \text{city}, \text{name} \rightarrow \text{owner} \}...

Which of the following predicate logic formulae/formula is/are CORRECT representation(s) of the statement: "Everyone has exactly one mother"?The meanings of the predicate...

$A=\{0,1,2,3, \ldots\}$ is the set of non-negative integers. Let $F$ be the set of functions from $A$ to itself. For any two functions, $f_{1}, f_{2} \in \mathrm{~F}$, we...

Consider the following deterministic finite automaton (DFA) defined over the alphabet, $\Sigma=\{a, b\}$. Identify which of the following language(s) is/are accepted by t...

A disk of size $512 \text{ M}$ bytes is divided into blocks of $64 \text{ K}$ bytes. A file is stored in the disk using linked allocation. In linked allocation, each data...

A computer has a memory hierarchy consisting of two-level cache $\text{(L1}$ and $\text{L2)}$ and a main memory. If the processor needs to access data from memory, it fir...

In optimal page replacement algorithm, information about all future page references is available to the operating system (OS). A modification of the optimal page replacem...

Consider the following database tables of a sports league.player (pid, pname, age) team(tid, tname, city, cid) coach (cid, cname) members (pid,tid)An instance of the tabl...

Suppose a $5$-bit message is transmitted from a source to a destination through a noisy channel. The probability that a bit of the message gets flipped during transmissio...

Suppose a message of size $15000$ bytes is transmitted from a source to a destination using IPv4 protocol via two routers as shown in the figure. Each router has a define...

Consider a probability distribution given by the density function $P(x)$.$$P(x)=\left\{\begin{aligned}C x^{2}, & \text { for } 1 \leq x \leq 4 \\0, & \text { for } x\lt1 ...

Consider a finite state machine (FSM) with one input $X$ and one output $f$, represented by the given state transition table. The minimum number of states required to rea...

Consider the given sequential circuit designed using D-Flip-flops. The circuit is initialized with some value (initial state). The number of distinct states the circuit w...