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Recent questions tagged numerical-answers

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Gate 2023
Consider the language L over the alphabet {0, 1}, given below: L = {w ∈ {0, 1}* | w does not contain three or more consecutive 1’s}. The minimum number of states in a Deterministic Finite-State Automaton (DFA) for L is ______ .

ic3rror asked in Theory of Computation Feb 16

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GATE CSE 2023 | Question: 20
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 $\lambda_{1}+\lambda_{2}+\lambda_{3}+\lambda_{4}+\lambda_{5}=$____________

admin asked in Linear Algebra Feb 15

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GATE CSE 2023 | Question: 21
The value of the definite integral \[ \int_{-3}^{3} \int_{-2}^{2} \int_{-1}^{1}\left(4 x^{2} y-z^{3}\right) \mathrm{d} z \mathrm{~d} y \mathrm{~d} x \] is _________. (Rounded off to the nearest integer)

admin asked in Calculus Feb 15

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GATE CSE 2023 | Question: 22
A particular number is written as $132$ in radix-$4$ representation. The same number in radix-$5$ representation is _____________.

admin asked in Digital Logic Feb 15

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GATE CSE 2023 | Question: 23
Consider a $3$-stage pipelined processor having a delay of $10 \mathrm{~ns}$ (nanoseconds), $20 \mathrm{~ns}$, and $14 \mathrm{~ns},$ for the first, second, and the third stages, respectively. Assume that there is no other ... instruction is fetched every cycle. The total execution time for executing $100$ instructions on this processor is _____________ $\mathrm{ns}.$

admin asked in CO and Architecture Feb 15

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GATE CSE 2023 | Question: 24
A keyboard connected to a computer is used at a rate of $1$ keystroke per second. The computer system polls the keyboard every $10 \mathrm{~ms}$ (milli seconds) to check for a keystroke and consumes $100\; \mu \mathrm{s}$ (micro seconds) for ... interrupt and processing a keystroke. The ratio $\dfrac{T_{1}}{T_{2}}$ is _____________. (Rounded off to one decimal place)

admin asked in CO and Architecture Feb 15

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GATE CSE 2023 | Question: 25
The integer value printed by the $\textsf{ANSI-C}$ program given below is _______________ #include<stdio.h> 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; }

admin asked in Programming Feb 15

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GATE CSE 2023 | Question: 46
Let $U=\{1,2,3\}$. Let $2^{U}$ denote the powerset of $U$. Consider an undirected graph $G$ whose vertex set is $2^{U}$. For any $A, B \in 2^{U},(A, B)$ is an edge in $G$ if and only if (i) $A \neq B$, and (ii) ... $A$ is denoted by $\mathcal{B}(A)$. If $\emptyset$ denotes the empty set, then the cardinality of $\mathcal{B}(\emptyset)$ is ______________.

admin asked in Algorithms Feb 15

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GATE CSE 2023 | Question: 47
Consider the following two-dimensional array $\text{D}$ in the $\text{C}$ programming language, which is stored in row-major order: int D[128][128]; Demand paging is used for allocating memory and each physical page frame holds $512$ elements of the ... j++) D[j][i] *= 10; The number of page faults generated during the execution of this code snippet is _______________.

admin asked in Operating System Feb 15

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GATE CSE 2023 | Question: 48
Consider a computer system with $57$-bit virtual addressing using multi-level tree-structured page tables with $\mathrm{L}$ levels for virtual to physical address translation. The page size is $4 \mathrm{~KB}(1 \mathrm{~KB}=1024 \mathrm{~B})$ and a page table entry at any of the levels occupies $8$ bytes. The value of $\mathrm{L}$ is ______________.

admin asked in Operating System Feb 15

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GATE CSE 2023 | Question: 49
Consider a sequence $a$ of elements $a_{0}=1, a_{1}=5, a_{2}=7, a_{3}=8, a_{4}=9$, and $a_{5}=2$. The following operations are performed on a stack $S$ and a queue $Q,$ both of which are initially empty. $\textsf{push}$ the ... $S$. $\textsf{pop}$ an element from $S$. The top element of $S$ after executing the above operations is ______________.

admin asked in DS Feb 15

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GATE CSE 2023 | Question: 50
Consider the syntax directed translation given by the following grammar and semantic rules. Here $N, I, F$ and $B$ are non-terminals. $N$ is the starting non-terminal, and $\#, \mathbf{0}$ and $\mathbf{1}$ are lexical tokens ... \] The value computed by the translation scheme for the input string $10\#011$ is ____________. (Rounded off to three decimal places)

admin asked in Compiler Design Feb 15

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GATE CSE 2023 | Question: 51
Consider the following table named $\text{Student}$ in a relational database. The primary key of this table is $\text{rollNum}.$ $\text{Student}$ ... database. SELECT * FROM Student WHERE gender = 'F' AND marks > 65; The number of rows returned by the query is ___________.

admin asked in Databases Feb 15

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GATE CSE 2023 | Question: 52
Consider a database of fixed-length records, stored as an ordered file. The database has $25,000$ records, with each record being $100$ bytes, of which the primary key occupies $15$ bytes. The data file is block-aligned in that each data ... required to identify the block in the data file that may contain a record with the key, in the worst case, is _____________.

admin asked in Databases Feb 15

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GATE CSE 2023 | Question: 53
Consider the language $L$ over the alphabet $\{0,1\}$, given below: \[ L=\left\{w \in\{0,1\}^{*} \mid w \text { does not contain three or more consecutive } 1 \text { 's }\right\} . \] The minimum number of states in a Deterministic Finite-State Automaton $\text{(DFA)}$ for $L$ is ____________.

admin asked in Theory of Computation Feb 15

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GATE CSE 2023 | Question: 54
An $8$-way set associative cache of size $64 \mathrm{~KB} \;(1 \mathrm{~KB}=1024\; \text{bytes})$ is used in a system with $32$-bit address. The address is sub-divided into $\text{TAG, INDEX},$ and $\text{BLOCK OFFSET.}$ The number of bits in the $\text{TAG}$ is ___________.

admin asked in CO and Architecture Feb 15

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GATE CSE 2023 | Question: 55
The forwarding table of a router is shown below. ... to a destination address $200.150 .68 .118$ arrives at the router. It will be forwarded to the interface with $\text{ID}$ __________.

admin asked in Computer Networks Feb 15

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