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Recent activity by Soumya29
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1
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1
CombinatoricsKenneth Rosen(Ex5.1 23c)
How many strings of three decimal digits can be formed such that they have exactly two digits that are 4's. My approach as to select 2 positions for these 4's in $\binom{3}{2}$ ways and the last bit will have 10 choices.Now I can permute the string formed in $ ... total such strings should be $\binom{3}{2}$ * 10*$\frac{3!}{2!}$ = 90. But the answer is 27. How?
commented
2 hours
ago
in
Combinatory

9
views
kennethrosen
permutationsandcombinations
4
answers
2
GATE20001.16
Aliasing in the context of programming languages refers to multiple variables having the same memory location multiple variables having the same value multiple variables having the same identifier multiple uses of the same variable
commented
2 hours
ago
in
Programming

1.6k
views
gate2000
programming
easy
aliasing
1
answer
3
You want to check whether a given set of items is sorted or not
commented
8 hours
ago
in
Algorithms

39
views
4
answers
4
GATE2004IT44
The function AB'C + A'BC + ABC' + A'B'C + AB'C' is equivalent to AC' + AB + A'C AB' + AC' + A'C A'B + AC' + AB' A'B + AC + AB'
comment edited
9 hours
ago
in
Digital Logic

875
views
gate2004it
digitallogic
booleanexpressions
easy
1
answer
5
doubt in propositional logic
can someone explain NULL QUANTIFICATION in depth??
answer selected
1 day
ago
in
Mathematical Logic

72
views
4
answers
6
GATE200338
Consider the set \(\{a, b, c\}\) with binary operators \(+\) and \(*\) defined as follows. + a b c a b a c b a b c c a c b * a b c a a b c b b c a c c c b For example, \(a + c = c, c + a = a, c * b = c\) and \(b * c = a\). Given the following set of ... x) + (a * y) = c \\ (b * x) + (c * y) = c$$ The number of solution(s) (i.e., pair(s) (x, y) that satisfy the equations) is 0 1 2 3
answer edited
2 days
ago
in
Set Theory & Algebra

995
views
gate2003
settheory&algebra
normal
binaryoperation
4
answers
7
GATE2016209
Let $X$ be the number of distinct $16$bit integers in $2's$ complement representation. Let $Y$ be the number of distinct $16$bit integers in sign magnitude representation Then $X  Y$ is______.
answer selected
3 days
ago
in
Digital Logic

2.7k
views
gate20162
digitallogic
numberrepresentation
normal
numericalanswers
6
answers
8
GATE2016107
The $16 bi$ $2's$ complement representation of an integer is $1111 \quad 1111 \quad 1111 \quad 0101$; its decimal representation is ______________
commented
3 days
ago
in
Digital Logic

3.1k
views
gate20161
digitallogic
numberrepresentation
normal
numericalanswers
2
answers
9
GATE2008IT1
A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those. Which of the following sets of connectives is NOT functionally complete? EXNOR implication, negation OR, negation NAND
commented
4 days
ago
in
Digital Logic

1.3k
views
gate2008it
digitallogic
easy
functionalcompleteness
4
answers
10
GATE19992.9
Which of the following sets of component(s) is/are sufficient to implement any arbitrary Boolean function? XOR gates, NOT gates 2 to 1 multiplexers AND gates, XOR gates Threeinput gates that output (A.B) + C for the inputs A, B and C.
commented
5 days
ago
in
Digital Logic

3.1k
views
gate1999
digitallogic
normal
functionalcompleteness
3
answers
11
GATE2017121
Consider the Karnaugh map given below, where $X$ represents "don't care" and blank represents $0$. Assume for all inputs $\left ( a,b,c,d \right )$, the respective complements $\left ( \bar{a}, \bar{b}, \bar{c}, \bar{d} \right )$ are also available. The above logic is implemented using $2$input $\text{NOR}$ gates only. The minimum number of gates required is ____________ .
commented
Jun 16
in
Digital Logic

2.9k
views
gate20171
digitallogic
kmap
numericalanswers
normal
5
answers
12
GATE19975.1
Let $f(x, y, z)=\bar{x} + \bar{y}x + xz$ be a switching function. Which one of the following is valid? $\bar{y} x$ is a prime implicant of $f$ $xz$ is a minterm of $f$ $xz$ is an implicant of $f$ $y$ is a prime implicant of $f$
answer selected
Jun 16
in
Digital Logic

1.8k
views
gate1997
digitallogic
normal
primeimplicants
3
answers
13
GATE201113
Which one of the following circuits is NOT equivalent to a $2$input $XNOR$ (exclusive $NOR$) gate?
answer edited
Jun 15
in
Digital Logic

945
views
gate2011
digitallogic
normal
logicgates
3
answers
14
GATE20021.12
Minimum sum of product expression for f(w,x,y,z) shown in Karnaughmap below xz + y'z xz' + zx' x'y + zx' None of the above
answer selected
Jun 15
in
Digital Logic

514
views
gate2002
digitallogic
kmap
normal
4
answers
15
GATE19962.24
What is the equivalent Boolean expression in productofsums form for the Karnaugh map given in Fig $B\overline{D} + \overline{B}D$ $(B + \overline{C} +D) (\overline{B} + C + \overline{D})$ $(B + {D})(\overline{B} +\overline{ D})$ $(B + \overline{D})(\overline{B} + {D})$
answer selected
Jun 15
in
Digital Logic

1.1k
views
gate1996
digitallogic
kmap
easy
7
answers
16
GATE2015343
The total number of prime implicants of the function $f(w, x, y, z) = \sum (0, 2, 4, 5, 6, 10)$ is __________
commented
Jun 15
in
Digital Logic

2.5k
views
gate20153
digitallogic
canonicalnormalform
normal
numericalanswers
2
answers
17
GATE200826
If $P, Q, R$ are Boolean variables, then $(P + \bar{Q}) (P.\bar{Q} + P.R) (\bar{P}.\bar{R} + \bar{Q})$ simplifies to $P.\bar{Q}$ $P.\bar{R}$ $P.\bar{Q} + R$ $P.\bar{R} + Q$
commented
Jun 14
in
Digital Logic

1.3k
views
gate2008
easy
digitallogic
booleanexpressions
3
answers
18
GATE19952.5
What values of $A, B, C$ and $D$ satisfy the following simultaneous Boolean equations? $\overline{A} + AB =0, AB=AC, AB+A\overline{C}+CD=\overline{C}D$ $A=1, B=0, C=0, D=1$ $A=1, B=1, C=0, D=0$ $A=1, B=0, C=1, D=1$ $A=1, B=0, C=0, D=0$
commented
Jun 14
in
Digital Logic

589
views
gate1995
digitallogic
booleanexpressions
easy
1
answer
19
GATE19944
Let $*$ be a Boolean operation defined as $A*B = AB + \overline{A}\;\overline{B}$. If $C=A*B$ then evaluate and fill in the blanks: $A*A=$____ $C*A=$____ Solve the following boolean equations for the values of $A, B$ and $C$: $AB+\overline{A}C=1$ $AC+B=0$
comment edited
Jun 14
in
Digital Logic

452
views
gate1994
digitallogic
normal
booleanexpressions
4
answers
20
GATE20002.10
The simultaneous equations on the Boolean variables x, y, z and w, $$x + y + z = 1 \\xy = 0\\xz + w = 1\\xy + \bar{z}\bar{w} = 0$$ have the following solution for x, y, z and w, respectively: 0 1 0 0 1 1 0 1 1 0 1 1 1 0 0 0
commented
Jun 14
in
Digital Logic

1.1k
views
gate2000
digitallogic
booleanalgebra
easy
2
answers
21
Distributive Lattice
Is below diagram is distributive lattice?
commented
Jun 11
in
Set Theory & Algebra

111
views
lattice
discretemathematics
2
answers
22
GATE20059
The following is the Hasse diagram of the poset $\left[\{a,b,c,d,e\},≺\right]$ The poset is : not a lattice a lattice but not a distributive lattice a distributive lattice but not a Boolean algebra a Boolean algebra
commented
Jun 11
in
Set Theory & Algebra

1.2k
views
gate2005
settheory&algebra
lattice
normal
1
answer
23
self made doubt
How to know that the language needs 1 stack or more than one stack in order to know about it is regular, contextfree or not. example L1={$a^i b^j c^k│i<j<k$} L2={$a^i b^j c^k│i<j \ or \ k<j$} L3={$a^i b^j c^k│i<j \ and \ k<j$}
edited
Jun 11
in
Theory of Computation

45
views
contextfreelanguage
regularlanguages
theoryofcomputation
4
answers
24
TIFR2013B4
A set $S$ together with partial order $\ll$ is called a well order if it has no infinite descending chains, i.e. there is no infinite sequence $x_1, x_2,\ldots$ of elements from $S$ such that $x_{i+1} \ll x_i$ and $x_{i+1} \neq x_i$ for all $i$. Consider the set ... are only $2^{24}$ words. $W$ is not a partial order. $W$ is a partial order but not a well order. $W$ is a well order.
commented
Jun 9
in
Set Theory & Algebra

431
views
tifr2013
settheory&algebra
partialorder
7
answers
25
GATE200473
The inclusion of which of the following sets into $S = \left\{ \left\{1, 2\right\}, \left\{1, 2, 3\right\}, \left\{1, 3, 5\right\}, \left\{1, 2, 4\right\}, \left\{1, 2, 3, 4, 5\right\} \right\} $ is necessary and sufficient to make $S$ a complete lattice under the partial order defined by set containment? ... \{2, 3\}$ $\{1\}, \{1, 3\}$ $\{1\}, \{1, 3\}, \{1, 2, 3, 4\}, \{1, 2, 3, 5\}$
commented
Jun 9
in
Set Theory & Algebra

1.6k
views
gate2004
settheory&algebra
partialorder
normal
1
answer
26
Distinguishable objects and indistinguishable boxes
commented
Jun 9
in
Mathematical Logic

75
views
permutationsandcombinations
2
answers
27
pipelining
A CPU has fivestage pipeline where each stage takes 1ns, 2ns, 1.5ns, 3ns, 2.5ns. Instruction fetch happens in the first stage of the pipeline. Branch instructions are not overlapped. i.e., the instruction after the branch is not fetched ... one clock cycle. 30% of the instructions are conditional branches. Find the average execution time of the program for 1200 instructions is ________
commented
Jun 9
in
CO & Architecture

69
views
0
answers
28
Self doubt regarding complete lattice related to https://gateoverflow.in/27341/tifr2014b16
commented
Jun 8
in
Set Theory & Algebra

69
views
discretemathematics
settheory&algebra
lattice
3
answers
29
TIFR2014B16
Consider the ordering relation $x\mid y \subseteq N \times N$ over natural numbers $N$ such that $x \mid y$ if there exists $z \in N$ such that $x ∙ z = y$. A set is called lattice if every finite subset has a least upper bound and greatest lower bound. It is ... $\mid$ is a total order. $(N, \mid)$ is a complete lattice. $(N, \mid)$ is a lattice but not a complete lattice.
commented
Jun 8
in
Set Theory & Algebra

588
views
tifr2014
settheory&algebra
partialorder
1
answer
30
Non Regular Language
Non regular language closed under which of the following operations? I)Union II) Intersection III)Complementation
answer selected
Jun 8
in
Theory of Computation

55
views
theoryofcomputation
regularlanguages
1
answer
31
Galvin
The Following processes are being scheduled using a Premptive RR scheduling Alogrithm. Each Process is Assigned a numeric Proirity, with higher number indicating higher priority. In addition it also has ideal task which consumes no CPU Resources and is identified by Pidle. This task ... 10 105 A. Turn Around Time of Each Process ? B. Waiting time of Each Process ? C. CPU Utilization Rate ?
commented
Jun 8
in
Operating System

27
views
operatingsystem
1
answer
32
Fork Output
#include<stdio.h> #include<sys/types.h> #include<unistd.h> void forkexample() { int x = 1; if (fork() == 0) printf("Child has x = %d\n", ++x); else printf("Parent has x = %d\n", x); } int main() { forkexample(); return 0; ... = 2 (or) Child has x = 2 Parent has x = 0 I guess both because we dont know who will return first parent or child is it ?
commented
Jun 7
in
Operating System

91
views
operatingsystem
fork
1
answer
33
Quasi Order Relations
What are the conditions for a relation to be quasiordered? In NPTEL video lectures, I found conditions for it to be Irreflexive and Transitive. But on Wikipedia and other resources, it's given that a binary relation R on a set A quasiorder if it is Reflexive and Transitive. Which one is correct ? or Am I missing something?
commented
Jun 6
in
Set Theory & Algebra

25
views
settheory&algebra
discretemathematics
relations
1
answer
34
Find the language
1)$L_{1}=\left \{ a^{2^{n}} \right \}$ where n is a positive integer. Is it Reguler, CFL or CSL? 2)$L_{2}=\left \{ (a^{n})^{m}.b^{n}n,m\geq 1 \right \}$ Is it Regular CFL or CSL?
answer edited
Jun 6
in
Theory of Computation

206
views
theoryofcomputation
3
answers
35
ISICAL MTech 2014 CS
How many asterisks $(*)$ in terms of $k$ will be printed by the following C function, when called as $\text{count}(m)$ where $m = 3^k \ ?$ Justify your answer. Assume that $4$ bytes are used to store an integer in C and $k$ is such that $3^k$ can be stored in $4$ bytes. void count(int n){ printf("*"); if(n>1){ count(n/3); count(n/3); count(n/3); } }
answer selected
Jun 6
in
Programming

431
views
programminginc
recursion
isi2014
2
answers
36
set theory
How many relation possible with $n$ elements of a set which are symmetric but not antisymmetric ?
answered
Jun 5
in
Set Theory & Algebra

37
views
engineeringmathematics
discretemathematics
settheory&algebra
2
answers
37
TIFR2011B23
Suppose $(S_{1}, S_{2},...,S_{m})$ is a finite collection of nonempty subsets of a universe U. Note that the sets in this collection need not to be distinct. Consider the following basic step to be performed on this sequence. While there exist sets $S_{i} ... of subsets of a finite universe $U$ and a choice of $S_{i}$ and $S_{j}$ in each step such that the process does not terminate.
answer edited
Jun 4
in
Set Theory & Algebra

176
views
tifr2011
settheory&algebra
sets
2
answers
38
GATE2015135
What is the output of the following C code? Assume that the address of $x$ is $2000$ (in decimal) and an integer requires four bytes of memory. int main () { unsigned int x [4] [3] = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}, {10, 11, 12}}; printf ("%u, %u, %u", x + 3, *(x + 3), *(x + 2) + 3); } $2036, 2036, 2036$ $2012, 4, 2204$ $2036, 10, 10$ $2012, 4, 6$
recategorized
Jun 3
in
Programming

4.8k
views
gate20151
programming
programminginc
normal
5
answers
39
GATE2015111
The output of the following C program is_____________. void f1 ( int a, int b) { int c; c = a; a = b; b = c; } void f2 ( int * a, int * b) { int c; c = * a; *a = *b; *b = c; } int main () { int a = 4, b = 5, c = 6; f1 ( a, b); f2 (&b, &c); printf ("%d", c  a  b); }
answer selected
Jun 3
in
Programming

1.8k
views
gate20151
programming
programminginc
easy
numericalanswers
1
answer
40
Automata
Logic and PDA for L = $\{a^{n1} b^{2n+1} \  n \geq1\}.$
edited
Jun 3
in
Theory of Computation

29
views
theoryofcomputation
36,164
questions
43,622
answers
124,010
comments
42,881
users