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Recent questions tagged numerical-answers

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Questions with numerical answers and no options. No negative marks for these questions.

Recent questions tagged numerical-answers

1 vote
2 answers
1
GATE CSE 2021 Set 2 | Question: 16
Consider a complete binary tree with $7$ nodes. Let $A$ denote the set of first $3$ elements obtained by performing Breadth-First Search $\text{(BFS)}$ starting from the root. Let $B$ denote the set of first $3$ elements obtained by performing Depth-First Search $\text{(DFS)}$ starting from the root. The value of $\mid A-B \mid $ is _____________
Consider a complete binary tree with $7$ nodes. Let $A$ denote the set of first $3$ elements obtained by performing Breadth-First Search $\text{(BFS)}$ starting from the root. Let $B$ denote the set of first $3$ elements obtained by performing Depth-First Search $\text{(DFS)}$ starting from the root. The value of $\mid A-B \mid $ is _____________
asked Feb 18 in DS Arjun 282 views
0 votes
1 answer
2
GATE CSE 2021 Set 2 | Question: 17
Consider the following deterministic finite automaton $\text{(DFA)}$ The number of strings of length $8$ accepted by the above automaton is ___________
Consider the following deterministic finite automaton $\text{(DFA)}$ The number of strings of length $8$ accepted by the above automaton is ___________
asked Feb 18 in Theory of Computation Arjun 240 views
2 votes
2 answers
3
GATE CSE 2021 Set 2 | Question: 18
If $x$ and $y$ are two decimal digits and $(0.1101)_2 = (0.8xy5)_{10}$, the decimal value of $x+y$ is ___________
If $x$ and $y$ are two decimal digits and $(0.1101)_2 = (0.8xy5)_{10}$, the decimal value of $x+y$ is ___________
asked Feb 18 in Digital Logic Arjun 309 views
1 vote
2 answers
4
GATE CSE 2021 Set 2 | Question: 19
Consider a set-associative cache of size $\text{2KB (1KB} =2^{10}$ bytes$\text{)}$ with cache block size of $64$ bytes. Assume that the cache is byte-addressable and a $32$ -bit address is used for accessing the cache. If the width of the tag field is $22$ bits, the associativity of the cache is _________
Consider a set-associative cache of size $\text{2KB (1KB} =2^{10}$ bytes$\text{)}$ with cache block size of $64$ bytes. Assume that the cache is byte-addressable and a $32$ -bit address is used for accessing the cache. If the width of the tag field is $22$ bits, the associativity of the cache is _________
asked Feb 18 in CO and Architecture Arjun 389 views
1 vote
1 answer
5
GATE CSE 2021 Set 2 | Question: 20
Consider a computer system with $\text{DMA}$ support. The $\text{DMA}$ module is transferring one $8$-bit character in one $\text{CPU}$ cycle from a device to memory through cycle stealing at regular intervals. Consider a $\text{2 MHz}$ ... $\text{DMA}$, the data transfer rate of the device is __________ bits per second.
Consider a computer system with $\text{DMA}$ support. The $\text{DMA}$ module is transferring one $8$-bit character in one $\text{CPU}$ cycle from a device to memory through cycle stealing at regular intervals. Consider a $\text{2 MHz}$ processor. If $0.5 \%$ processor cycles are used for $\text{DMA}$, the data transfer rate of the device is __________ bits per second.
asked Feb 18 in CO and Architecture Arjun 344 views
1 vote
1 answer
6
GATE CSE 2021 Set 2 | Question: 21
A data file consisting of $1,50,000$ student-records is stored on a hard disk with block size of $4096$ bytes. The data file is sorted on the primary key $\textrm{RollNo}$. The size of a record pointer for this disk is $7$ bytes. ... that the records of data file and index file are not split across disk blocks. The number of blocks in the index file is ________
A data file consisting of $1,50,000$ student-records is stored on a hard disk with block size of $4096$ bytes. The data file is sorted on the primary key $\textrm{RollNo}$. The size of a record pointer for this disk is $7$ bytes. Each student-record has ... disk. Assume that the records of data file and index file are not split across disk blocks. The number of blocks in the index file is ________
asked Feb 18 in Operating System Arjun 313 views
2 votes
1 answer
7
GATE CSE 2021 Set 2 | Question: 22
For a given biased coin, the probability that the outcome of a toss is a head is $0.4$. This coin is tossed $1,000$ times. Let $X$ denote the random variable whose value is the number of times that head appeared in these $1,000$ tosses. The standard deviation of $X$ (rounded to $2$ decimal place) is _________
For a given biased coin, the probability that the outcome of a toss is a head is $0.4$. This coin is tossed $1,000$ times. Let $X$ denote the random variable whose value is the number of times that head appeared in these $1,000$ tosses. The standard deviation of $X$ (rounded to $2$ decimal place) is _________
asked Feb 18 in Probability Arjun 243 views
1 vote
1 answer
8
GATE CSE 2021 Set 2 | Question: 23
Consider the following $\text{ANSI C}$ function: int SomeFunction (int x, int y) { if ((x==1) || (y==1)) return 1; if (x==y) return x; if (x > y) return SomeFunction(x-y, y); if (y > x) return SomeFunction (x, y-x); } The value returned by $\textrm{SomeFunction(15, 255)}$ is __________
Consider the following $\text{ANSI C}$ function: int SomeFunction (int x, int y) { if ((x==1) || (y==1)) return 1; if (x==y) return x; if (x > y) return SomeFunction(x-y, y); if (y > x) return SomeFunction (x, y-x); } The value returned by $\textrm{SomeFunction(15, 255)}$ is __________
asked Feb 18 in Programming Arjun 246 views
2 votes
1 answer
9
GATE CSE 2021 Set 2 | Question: 24
Suppose that $P$ is a $4 \times 5$ matrix such that every solution of the equation $\text{Px=0}$ is a scalar multiple of $\begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T$. The rank of $P$ is __________
Suppose that $P$ is a $4 \times 5$ matrix such that every solution of the equation $\text{Px=0}$ is a scalar multiple of $\begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T$. The rank of $P$ is __________
asked Feb 18 in Linear Algebra Arjun 278 views
2 votes
2 answers
10
GATE CSE 2021 Set 2 | Question: 25
Suppose that $f: \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function on the interval $[-3, 3]$ and a differentiable function in the interval $(-3,3)$ such that for every $x$ in the interval, $f’(x) \leq 2$. If $f(-3)=7$, then $f(3)$ is at most __________
Suppose that $f: \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function on the interval $[-3, 3]$ and a differentiable function in the interval $(-3,3)$ such that for every $x$ in the interval, $f’(x) \leq 2$. If $f(-3)=7$, then $f(3)$ is at most __________
asked Feb 18 in Calculus Arjun 218 views
3 votes
3 answers
11
GATE CSE 2021 Set 2 | Question: 48
Consider a three-level page table to translate a $39$-bit virtual address to a physical address as shown below: The page size is $4$ KB = ($1$KB $=2^{10}$ bytes) and page table entry size at every level is $8$ ... to $2$ GB of physical memory. The minimum amount of memory required for the page table of $P$ across all levels is _________ KB
Consider a three-level page table to translate a $39$-bit virtual address to a physical address as shown below: The page size is $4$ KB = ($1$KB $=2^{10}$ bytes) and page table entry size at every level is $8$ bytes. A process $P$ ... which os mapped to $2$ GB of physical memory. The minimum amount of memory required for the page table of $P$ across all levels is _________ KB
asked Feb 18 in Operating System Arjun 505 views
3 votes
1 answer
12
GATE CSE 2021 Set 2 | Question: 49
Consider the following $\text{ANSI C}$ program #include <stdio.h> int foo(int x, int y, int q) { if ((x<=0) && (y<=0)) return q; if (x<=0) return foo(x, y-q, q); if (y<=0) return foo(x-q, y, q); return foo(x, ... ); } int main( ) { int r = foo(15, 15, 10); printf( %d , r); return 0; } The output of the program upon execution is _________
Consider the following $\text{ANSI C}$ program #include <stdio.h> int foo(int x, int y, int q) { if ((x<=0) && (y<=0)) return q; if (x<=0) return foo(x, y-q, q); if (y<=0) return foo(x-q, y, q); return foo(x, y-q, q) + foo(x-q, y, q); } int main( ) { int r = foo(15, 15, 10); printf(“%d”, r); return 0; } The output of the program upon execution is _________
asked Feb 18 in Programming Arjun 273 views
1 vote
2 answers
13
GATE CSE 2021 Set 2 | Question: 50
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________
asked Feb 18 in Set Theory & Algebra Arjun 358 views
0 votes
1 answer
14
GATE CSE 2021 Set 2 | Question: 51
Consider the following augmented grammar with $\{ \#, @, <, >, a, b, c \}$ ... $\text{GOTO(GOTO}(I_0<), <)$ is ___________
Consider the following augmented grammar with $\{ \#, @, <, >, a, b, c \}$ ... $I_0 = \text{CLOSURE}(\{S' \rightarrow \bullet S\})$. The number of items in the set $\text{GOTO(GOTO}(I_0<), <)$ is ___________
asked Feb 18 in Compiler Design Arjun 260 views
0 votes
1 answer
15
GATE CSE 2021 Set 2 | Question: 52
Consider a Boolean function $f(w,x,y,z)$ such that $\begin{array}{lll} f(w,0,0,z) & = & 1 \\ f(1,x,1,z) & =& x+z \\ f(w,1,y,z) & = & wz +y \end{array}$ The number of literals in the minimal sum-of-products expression of $f$ is _________
Consider a Boolean function $f(w,x,y,z)$ such that $\begin{array}{lll} f(w,0,0,z) & = & 1 \\ f(1,x,1,z) & =& x+z \\ f(w,1,y,z) & = & wz +y \end{array}$ The number of literals in the minimal sum-of-products expression of $f$ is _________
asked Feb 18 in Digital Logic Arjun 310 views
5 votes
2 answers
16
GATE CSE 2021 Set 2 | Question: 53
Consider a pipelined processor with $5$ stages, $\text{Instruction Fetch} (\textsf{IF})$, $\text{Instruction Decode} \textsf{(ID)}$, $\text{Execute } \textsf{(EX)}$, $\text{Memory Access } \textsf{(MEM)}$ ... $\textit{Speedup} $ achieved in executing the given instruction sequence on the pipelined processor (rounded to $2$ decimal places) is _____________
Consider a pipelined processor with $5$ stages, $\text{Instruction Fetch} (\textsf{IF})$, $\text{Instruction Decode} \textsf{(ID)}$, $\text{Execute } \textsf{(EX)}$, $\text{Memory Access } \textsf{(MEM)}$ ... $\textit{Speedup} $ achieved in executing the given instruction sequence on the pipelined processor (rounded to $2$ decimal places) is _____________
asked Feb 18 in CO and Architecture Arjun 508 views
1 vote
3 answers
17
GATE CSE 2021 Set 2 | Question: 54
Consider a network using the pure $\text{ALOHA}$ medium access control protocol, where each frame is of length $1,000$ bits. The channel transmission rate is $1$ Mbps ($=10^6$ bits per second). The aggregate number ... the average number of frames successfully transmitted per second. The throughput of the network (rounded to the nearest integer) is ______________
Consider a network using the pure $\text{ALOHA}$ medium access control protocol, where each frame is of length $1,000$ bits. The channel transmission rate is $1$ Mbps ($=10^6$ bits per second). The aggregate number of transmissions across all ... as the average number of frames successfully transmitted per second. The throughput of the network (rounded to the nearest integer) is ______________
asked Feb 18 in Computer Networks Arjun 354 views
1 vote
1 answer
18
GATE CSE 2021 Set 2 | Question: 55
In a directed acyclic graph with a source vertex $\textsf{s}$, the $\textit{quality-score}$ of a directed path is defined to be the product of the weights of the edges on the path. Further, for a vertex $v$ other than $\textsf{s}$, the quality ... $\textsf{s}$ is assumed to be $1$. The sum of the quality-scores of all vertices on the graph shown above is _______
In a directed acyclic graph with a source vertex $\textsf{s}$, the $\textit{quality-score}$ of a directed path is defined to be the product of the weights of the edges on the path. Further, for a vertex $v$ other than $\textsf{s}$, the quality-score of $v$ is ... quality-score of $\textsf{s}$ is assumed to be $1$. The sum of the quality-scores of all vertices on the graph shown above is _______
asked Feb 18 in Algorithms Arjun 372 views
0 votes
2 answers
19
GATE CSE 2021 Set 1 | Question: 16
In an undirected connected planar graph $G$, there are eight vertices and five faces. The number of edges in $G$ is _________.
In an undirected connected planar graph $G$, there are eight vertices and five faces. The number of edges in $G$ is _________.
asked Feb 18 in Graph Theory Arjun 213 views
0 votes
3 answers
20
GATE CSE 2021 Set 1 | Question: 17
Consider the following undirected graph with edge weights as shown: The number of minimum-weight spanning trees of the graph is ___________.
Consider the following undirected graph with edge weights as shown: The number of minimum-weight spanning trees of the graph is ___________.
asked Feb 18 in Algorithms Arjun 217 views
1 vote
1 answer
21
GATE CSE 2021 Set 1 | Question: 18
The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter $2$. For a randomly picked component of this type, the probability that its lifetime exceeds the expected lifetime (rounded to $2$ decimal places) is ____________.
The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter $2$. For a randomly picked component of this type, the probability that its lifetime exceeds the expected lifetime (rounded to $2$ decimal places) is ____________.
asked Feb 18 in Probability Arjun 241 views
2 votes
1 answer
22
GATE CSE 2021 Set 1 | Question: 19
There are $6$ jobs with distinct difficulty levels, and $3$ computers with distinct processing speeds. Each job is assigned to a computer such that: The fastest computer gets the toughest job and the slowest computer gets the easiest job. Every computer gets at least one job. The number of ways in which this can be done is ___________.
There are $6$ jobs with distinct difficulty levels, and $3$ computers with distinct processing speeds. Each job is assigned to a computer such that: The fastest computer gets the toughest job and the slowest computer gets the easiest job. Every computer gets at least one job. The number of ways in which this can be done is ___________.
asked Feb 18 in Combinatory Arjun 466 views
0 votes
2 answers
23
GATE CSE 2021 Set 1 | Question: 20
Consider the following expression. $\displaystyle \lim_{x\rightarrow-3}\frac{\sqrt{2x+22}-4}{x+3}$ The value of the above expression (rounded to 2 ddecimal places) is ___________.
Consider the following expression. $\displaystyle \lim_{x\rightarrow-3}\frac{\sqrt{2x+22}-4}{x+3}$ The value of the above expression (rounded to 2 ddecimal places) is ___________.
asked Feb 18 in Calculus Arjun 225 views
0 votes
2 answers
24
GATE CSE 2021 Set 1 | Question: 21
Consider the following sequence of operations on an empty stack. $\textsf{push}(54);\textsf{push}(52);\textsf{pop}();\textsf{push}(55);\textsf{push}(62);\textsf{s}=\textsf{pop}();$ ... $\textsf{s+q}$ is ___________.
Consider the following sequence of operations on an empty stack. $\textsf{push}(54);\textsf{push}(52);\textsf{pop}();\textsf{push}(55);\textsf{push}(62);\textsf{s}=\textsf{pop}();$ ... $\textsf{s+q}$ is ___________.
asked Feb 18 in DS Arjun 249 views
0 votes
3 answers
25
GATE CSE 2021 Set 1 | Question: 22
Consider a computer system with a byte-addressable primary memory of size $2^{32}$ bytes. Assume the computer system has a direct-mapped cache of size $\text{32 KB}$ ($\text{1 KB}$ = $2^{10}$ bytes), and each cache block is of size $64$ bytes. The size of the tag field is __________ bits.
Consider a computer system with a byte-addressable primary memory of size $2^{32}$ bytes. Assume the computer system has a direct-mapped cache of size $\text{32 KB}$ ($\text{1 KB}$ = $2^{10}$ bytes), and each cache block is of size $64$ bytes. The size of the tag field is __________ bits.
asked Feb 18 in CO and Architecture Arjun 182 views
1 vote
1 answer
26
GATE CSE 2021 Set 1 | Question: 23
A relation $r(A, B)$ in a relational database has $1200$ tuples. The attribute $A$ has integer values ranging from $6$ to $20$, and the attribute $B$ has integer values ranging from $1$ to $20$. Assume that the attributes $A$ and $B$ are independently distributed. The estimated number of tuples in the output of $\sigma _{(A>10)\vee(B=18)}(r)$ is ____________.
A relation $r(A, B)$ in a relational database has $1200$ tuples. The attribute $A$ has integer values ranging from $6$ to $20$, and the attribute $B$ has integer values ranging from $1$ to $20$. Assume that the attributes $A$ and $B$ are independently distributed. The estimated number of tuples in the output of $\sigma _{(A>10)\vee(B=18)}(r)$ is ____________.
asked Feb 18 in Databases Arjun 811 views
0 votes
4 answers
27
GATE CSE 2021 Set 1 | Question: 24
Consider the following representation of a number in $\text{IEEE 754}$ single-precision floating point format with a bias of $127$. $S: 1\quad\quad E:\; 10000001\quad\quad F:\;11110000000000000000000$ Here, $S, \;E$ ... the floating point representation. The decimal value corresponding to the above representation (rounded to $2$ decimal places) is ____________.
Consider the following representation of a number in $\text{IEEE 754}$ single-precision floating point format with a bias of $127$. $S: 1\quad\quad E:\; 10000001\quad\quad F:\;11110000000000000000000$ Here, $S, \;E$ and $F$ denote ... components of the floating point representation. The decimal value corresponding to the above representation (rounded to $2$ decimal places) is ____________.
asked Feb 18 in Digital Logic Arjun 204 views
0 votes
4 answers
28
GATE CSE 2021 Set 1 | Question: 25
Three processes arrive at time zero with $\text{CPU}$ bursts of $16,\;20$ and $10$ milliseconds. If the scheduler has prior knowledge about the length of the $\text{CPU}$ bursts, the minimum achievable average waiting time for these three processes in a non-preemptive scheduler (rounded to nearest integer) is _____________ milliseconds.
Three processes arrive at time zero with $\text{CPU}$ bursts of $16,\;20$ and $10$ milliseconds. If the scheduler has prior knowledge about the length of the $\text{CPU}$ bursts, the minimum achievable average waiting time for these three processes in a non-preemptive scheduler (rounded to nearest integer) is _____________ milliseconds.
asked Feb 18 in Operating System Arjun 182 views
0 votes
1 answer
29
GATE CSE 2021 Set 1 | Question: 48
Consider the following $\text{ANSI C}$ function: int SimpleFunction(int Y[], int n, int x) { int total = Y[0], loopIndex; for (loopIndex=1; loopIndex<=n-1; loopIndex++) total=x*total +Y[loopIndex]; return total; } Let $\textsf{Z}$ be an array ... $i$ such that $0 \leq i \leq 9$. The value returned by $\textsf{SimpleFunction(Z},10,2)$ is __________
Consider the following $\text{ANSI C}$ function: int SimpleFunction(int Y[], int n, int x) { int total = Y[0], loopIndex; for (loopIndex=1; loopIndex<=n-1; loopIndex++) total=x*total +Y[loopIndex]; return total; } Let $\textsf{Z}$ be an array of $10$ elements with $\textsf{Z}[i]=1$, for all $i$ such that $0 \leq i \leq 9$. The value returned by $\textsf{SimpleFunction(Z},10,2)$ is __________
asked Feb 18 in Programming Arjun 157 views
0 votes
1 answer
30
GATE CSE 2021 Set 1 | Question: 49
Consider the sliding window flow-control protocol operating between a sender and a receiver over a full-duplex error-free link. Assume the following: The time taken for processing the data frame by the receiver is negligible. The time taken for ... number of frames, (rounded to the nearest integer) needed to achieve a link utilization of $50\%$ is_____________.
Consider the sliding window flow-control protocol operating between a sender and a receiver over a full-duplex error-free link. Assume the following: The time taken for processing the data frame by the receiver is negligible. The time taken for processing the ... of the number of frames, (rounded to the nearest integer) needed to achieve a link utilization of $50\%$ is_____________.
asked Feb 18 in Computer Networks Arjun 633 views
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