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8
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2
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151
GATE CSE 2023 | Question: 18
Let $\qquad f(x)=x^{3}+15 x^{2}-33 x-36$ be a real-valued function. Which of the following statements is/are $\text{TRUE}?$ $f(x)$ does not have a local maximum. $f(x)$ has a local maximum. $f(x)$ does not have a local minimum. $f(x)$ has a local minimum.
Let $$\qquad f(x)=x^{3}+15 x^{2}-33 x-36$$be a real-valued function.Which of the following statements is/are $\text{TRUE}?$$f(x)$ does not have a local maximum.$f(x)$ has...
admin
5.1k
views
admin
asked
Feb 15, 2023
Calculus
gatecse-2023
calculus
maxima-minima
multiple-selects
1-mark
+
–
9
votes
4
answers
152
GATE CSE 2023 | Question: 19
Let $f$ and $g$ be functions of natural numbers given by $f(n)=n$ and $g(n)=n^{2}.$ Which of the following statements is/are $\text{TRUE}?$ $f \in O(g)$ $f \in \Omega(g)$ $f \in o(g)$ $f \in \Theta(g)$
Let $f$ and $g$ be functions of natural numbers given by $f(n)=n$ and $g(n)=n^{2}.$ Which of the following statements is/are $\text{TRUE}?$$f \in O(g)$$f \in \Omega(g)$$f...
admin
9.4k
views
admin
asked
Feb 15, 2023
Algorithms
gatecse-2023
algorithms
asymptotic-notation
multiple-selects
1-mark
+
–
9
votes
4
answers
153
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 $\lambda_{1}+\lambda_{2}+\lambda_{3}+\lambda_{4}+\lambda_{5}=$____________
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 eigenva...
admin
12.7k
views
admin
asked
Feb 15, 2023
Linear Algebra
gatecse-2023
linear-algebra
eigen-value
numerical-answers
1-mark
+
–
5
votes
2
answers
154
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)
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 _________. (Rounde...
admin
8.5k
views
admin
asked
Feb 15, 2023
Calculus
gatecse-2023
calculus
definite-integral
numerical-answers
1-mark
+
–
6
votes
2
answers
155
GATE CSE 2023 | Question: 22
A particular number is written as $132$ in radix-$4$ representation. The same number in radix-$5$ representation is _____________.
A particular number is written as $132$ in radix-$4$ representation. The same number in radix-$5$ representation is _____________.
admin
12.1k
views
admin
asked
Feb 15, 2023
Digital Logic
gatecse-2023
digital-logic
number-representation
numerical-answers
1-mark
+
–
9
votes
4
answers
156
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 _____________ $\mathrm{ns}.$
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...
admin
9.1k
views
admin
asked
Feb 15, 2023
CO and Architecture
gatecse-2023
co-and-architecture
pipelining
numerical-answers
1-mark
+
–
11
votes
2
answers
157
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)
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 ...
admin
7.8k
views
admin
asked
Feb 15, 2023
CO and Architecture
gatecse-2023
co-and-architecture
interrupts
numerical-answers
1-mark
+
–
18
votes
4
answers
158
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; }
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 ...
admin
10.6k
views
admin
asked
Feb 15, 2023
Programming in C
gatecse-2023
programming
programming-in-c
output
numerical-answers
1-mark
+
–
8
votes
1
answer
159
GATE CSE 2023 | Question: 26
Consider the following program: int main() { f1 (); f2(2); f3(); return (0); } int 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?
Consider the following program:int main() { f1 (); f2(2); f3(); return (0); } int f1 () { return(1); } int f2 (int X) { f3(); if (X==1); return f1 (); else return (X * f2...
admin
7.8k
views
admin
asked
Feb 15, 2023
Compiler Design
gatecse-2023
compiler-design
runtime-environment
2-marks
+
–
12
votes
4
answers
160
GATE CSE 2023 | Question: 27
Consider the control flow graph shown. Which one of the following choices correctly lists the set of live variables at the exit point of each basic block? $\text{B1: { }, B2: {a}, B3: {a}, B4: {a}}$ $\text{B1: {i, j}, B2: {a}, B3: {a}, B4: {i}}$ $\text{B1: {a, i, j}, B2: {a, i, j}, B3: {a, i}, B4: {a}}$ $\text{B1: {a, i, j}, B2: {a, j}, B3: {a, j}, B4: {a, i, j}}$
Consider the control flow graph shown.Which one of the following choices correctly lists the set of live variables at the exit point of each basic block?$\text{B1: { }, B...
admin
11.6k
views
admin
asked
Feb 15, 2023
Compiler Design
gatecse-2023
compiler-design
live-variable-analysis
2-marks
+
–
17
votes
2
answers
161
GATE CSE 2023 | Question: 28
Consider the two functions $\textsf{incr}$ and $\textsf{decr}$ shown below. incr(){ decr(){ wait(s); wait(s); X = X+1; X = X-1; signal(s); signal(s); } } There are $5$ threads each invoking $\textsf{incr}$ once, and $3$ threads each ... of the following choices corresponds to the minimum possible values of $\text{V1, V2},$ respectively? $15,7$ $7,7$ $12,7$ $12,8$
Consider the two functions $\textsf{incr}$ and $\textsf{decr}$ shown below. incr(){ decr(){ wait(s); wait(s); X = X+1; X = X-1; signal(s); signal(s); } }There are $5$ thr...
admin
11.8k
views
admin
asked
Feb 15, 2023
Operating System
gatecse-2023
operating-system
semaphore
2-marks
+
–
14
votes
5
answers
162
GATE CSE 2023 | Question: 29
Consider the context-free grammar $G$ below \[ \begin{array}{l} S \rightarrow a S b \mid X \\ X \rightarrow a X \mid X b \mid a \mid b, \end{array} \] where $S$ and $X$ are non-terminals, and $a$ and $b$ are terminal symbols. The starting non- ... $G$ is $a^{\ast} b^{\ast}(a+b)$ The language generated by $G$ is not a regular language
Consider the context-free grammar $G$ below\[\begin{array}{l}S \rightarrow a S b \mid X \\X \rightarrow a X \mid X b \mid a \mid b,\end{array}\]where $S$ and $X$ are non-...
admin
8.5k
views
admin
asked
Feb 15, 2023
Theory of Computation
gatecse-2023
theory-of-computation
context-free-grammar
2-marks
+
–
12
votes
5
answers
163
GATE CSE 2023 | Question: 30
Consider the pushdown automaton $\text{(PDA)}\;P$ below, which runs on the input alphabet $\{a, b\}$, has stack alphabet $\{\perp, A\}$, and has three states $\{s, p, q\}$, with $s$ being the start state. A transition from state $u$ to state $v$ ... $\left.0 \leq n\right\}$ $\left\{a^{m} \mid 0 \leq m\right\} \cup\left\{b^{n} \mid 0 \leq n\right\}$
Consider the pushdown automaton $\text{(PDA)}\;P$ below, which runs on the input alphabet $\{a, b\}$, has stack alphabet $\{\perp, A\}$, and has three states $\{s, p, q\}...
admin
6.8k
views
admin
asked
Feb 15, 2023
Theory of Computation
gatecse-2023
theory-of-computation
pushdown-automata
2-marks
+
–
8
votes
1
answer
164
GATE CSE 2023 | Question: 31
Consider the given $\text{C}$-code and its corresponding assembly code, with a few operands $\text{U1-U4}$ being unknown. Some useful information as well as the semantics of each unique assembly instruction is annotated as inline comments in the code. The memory is byte-addressable. Which one of ... $(3,4,4, \text{L01)}$ $(8,1,1, \text{L02)}$ $(3,1,1, \text{L01)}$
Consider the given $\text{C}$-code and its corresponding assembly code, with a few operands $\text{U1-U4}$ being unknown. Some useful information as well as the semantics...
admin
6.9k
views
admin
asked
Feb 15, 2023
CO and Architecture
gatecse-2023
co-and-architecture
assembly-code
2-marks
+
–
11
votes
2
answers
165
GATE CSE 2023 | Question: 32
A $4$ kilobyte $\text{(KB)}$ byte-addressable memory is realized using four $1 \mathrm{~KB}$ memory blocks. Two input address lines $\text{(IA4 and IA3)}$ are connected to the chip select $\text{(CS)}$ port of these memory blocks through a decoder as shown in the figure. The ... options is $\text{CORRECT}?$ $(0,1,2,3)$ $(0,1024,2048,3072)$ $(0,8,16,24)$ $(0,0,0,0)$
A $4$ kilobyte $\text{(KB)}$ byte-addressable memory is realized using four $1 \mathrm{~KB}$ memory blocks. Two input address lines $\text{(IA4 and IA3)}$ are connected t...
admin
6.1k
views
admin
asked
Feb 15, 2023
CO and Architecture
gatecse-2023
co-and-architecture
memory-interfacing
2-marks
+
–
6
votes
1
answer
166
GATE CSE 2023 | Question: 33
Consider a sequential digital circuit consisting of $\mathrm{T}$ flip-flops and $\mathrm{D}$ flip-flops as shown in the figure. $\text{CLKIN}$ is the clock input to the circuit. At the beginning, $\text{Q1, Q2}$ and $\text{Q3}$ have values $0,1$ and $1,$ respectively. ... $\text{NEVER}$ be obtained with this digital circuit? $(0,0,1)$ $(1,0,0)$ $(1,0,1)$ $(1,1,1)$
Consider a sequential digital circuit consisting of $\mathrm{T}$ flip-flops and $\mathrm{D}$ flip-flops as shown in the figure. $\text{CLKIN}$ is the clock input to the c...
admin
8.7k
views
admin
asked
Feb 15, 2023
Digital Logic
gatecse-2023
digital-logic
sequential-circuit
flip-flop
2-marks
+
–
19
votes
3
answers
167
GATE CSE 2023 | Question: 34
A Boolean digital circuit is composed using two $4$-input multiplexers $\text{(M1 and M2)}$ and one $2$-input multiplexer $\text{(M3)}$ as shown in the figure. $\text{X0-X7}$ are the inputs of the multiplexers $\text{M1 and M2}$ and could be connected to either $0$ or $1.$ The select lines of the ... $(1,1,0,0,1,1,0,1)$ $(1,1,0,1,1,1,0,0)$ $(0,0,1,1,0,1,1,1)$
A Boolean digital circuit is composed using two $4$-input multiplexers $\text{(M1 and M2)}$ and one $2$-input multiplexer $\text{(M3)}$ as shown in the figure. $\text{X0-...
admin
9.2k
views
admin
asked
Feb 15, 2023
Digital Logic
gatecse-2023
digital-logic
combinational-circuit
multiplexer
2-marks
+
–
10
votes
2
answers
168
GATE CSE 2023 | Question: 35
Consider the $\textsf{IEEE-754}$ single precision floating point numbers $\text{P} = \textsf{0xC1800000}$ and $\text{Q} = \textsf{0x3F5C2EF4}.$ ... $\textsf{IEEE-754}$ single precision format? $\textsf{0x404C2EF4}$ $\textsf{0x405C2EF4}$ $\textsf{0xC15C2EF4}$ $\textsf{0xC14C2EF4}$
Consider the $\textsf{IEEE-754}$ single precision floating point numbers $\text{P} = \textsf{0xC1800000}$ and $\text{Q} = \textsf{0x3F5C2EF4}.$Which one of the following ...
admin
10.3k
views
admin
asked
Feb 15, 2023
CO and Architecture
gatecse-2023
co-and-architecture
ieee-representation
2-marks
+
–
7
votes
3
answers
169
GATE CSE 2023 | Question: 36
Let $A$ be a priority queue for maintaining a set of elements. Suppose $A$ is implemented using a max-heap data structure. The operation $\text{EXTRACT-MAX} (A)$ extracts and deletes the maximum element from $A$. The operation $\operatorname{INSERT}(A, key )$ inserts a new ... $O(1)$ whereas $\operatorname{INSERT}(A, k e y)$ runs in $O(\log (n))$.
Let $A$ be a priority queue for maintaining a set of elements. Suppose $A$ is implemented using a max-heap data structure. The operation $\text{EXTRACT-MAX} (A)$ extracts...
admin
6.1k
views
admin
asked
Feb 15, 2023
DS
gatecse-2023
data-structures
priority-queue
time-complexity
heap
2-marks
+
–
8
votes
2
answers
170
GATE CSE 2023 | Question: 37
Consider the $\text{C}$ function $\text{foo}$ and the binary tree shown. typedef struct node { int val; struct node *left, *right; } node; int foo(node *p) { int retval; if (p == NULL) return 0; else { retval = p->val + foo(p->left) + foo(p->right); printf("%d ", ... $3 \;5\; 8\; 10\; 11\; 13$ $3 \;8 \;16 \;13\; 24\; 50$ $3\; 16\; 8\; 50\; 24\; 13$
Consider the $\text{C}$ function $\text{foo}$ and the binary tree shown.typedef struct node { int val; struct node *left, *right; } node; int foo(node *p) { int retval; i...
admin
6.6k
views
admin
asked
Feb 15, 2023
DS
gatecse-2023
data-structures
binary-tree
2-marks
+
–
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