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Syllabus: Sets, Relations, Functions, Partial orders, Lattices, Monoids, Groups.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2024-1} &\textbf{2024-2} &\textbf{2023} & \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} &1&1&0& 1&0&1&0&0.83&1
\\\hline\textbf{2 Marks Count} &1&1&2& 0 &2&1&0&1.16&2
\\\hline\textbf{Total Marks} & 3&3&4&1&4&3&\bf{1}&\bf{3}&\bf{4}\\\hline
\end{array}}}$$

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Recent questions in Set Theory & Algebra

#321
744
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1 answers
3 votes
NIELIT 2016 DEC Scientist B (IT) - Section B: 21
Consider the set $S=\{1,\omega,\omega ^2​\}$, where $\omega$ and $\omega^2​$ are cube roots of unity. If $*$ denotes the multiplication operation, the structure $(S,*)$ forms:A groupA ringAn integral domainA field
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#322
575
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2 answers
1 votes
NIELIT 2016 DEC Scientist B (IT) - Section B: 28
What is the possible number of reflexive relation on a set of $5$ elements?$2^{10}$2^{15}$2^{20}$2^{25}$
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#323
827
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1 answers
3 votes
NIELIT 2016 DEC Scientist B (CS) - Section B: 28
Which one of the following is NOT necessarily a property of a Group?CommutativityAssociativityExistence of inverse for every elementExistence of identity
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#324
530
views
1 answers
2 votes
NIELIT 2016 DEC Scientist B (CS) - Section B: 34
How many onto (or surjective) functions are there from an $n$-element $(n>=2)$ set to a $2$-element set?$2^n$2^n-1$2^n-2$2(2^n-2)$
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#325
564
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2 answers
1 votes
NIELIT 2017 July Scientist B (IT) - Section B: 9
Power set of empty set has exactly _______ subsetOneTwoZeroThree
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#326
517
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1 answers
3 votes
NIELIT 2017 July Scientist B (IT) - Section B: 10
What is the Cartesian product of $A=\{1,2\}$ and $B=\{a,b\}$?$\{(1,a),(1,b),(2,a),(b,b)\}$\{(1,1),(2,2),(a,a),(b,b)\}$\{(1,a),(2,a),(1,b),(2,b)\}$\{(1,1),(a,a),(2,a),(1,b)\}$
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#327
613
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3 answers
1 votes
NIELIT 2017 July Scientist B (IT) - Section B: 11
What is the Cardinality of the Power set of the set $\{0,1,2\}$?$8$6$7$9$
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#328
683
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1 answers
0 votes
NIELIT 2017 July Scientist B (IT) - Section B: 16
A partial ordered relation is transitive, reflexive andantisymmetricbisymmetricantireflexiveasymmetric
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#329
9.6k
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1 answers
1 votes
NIELIT 2017 July Scientist B (IT) - Section B: 17
​ Let $N=\{1,2,3,\dots\}$ be ordered by divisibility, which of the following subset is totally ordered?$(2,6,24)$(3,5,15)$(2,9,16)$(4,15,30)$
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#330
2.0k
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1 answers
2 votes
NIELIT 2017 July Scientist B (IT) - Section B: 18
If $B$ is a Boolean algebra, then which of the following is true?$B$ is a finite but not complemented lattice$B$ is a finite, complemented and ... $B$ is a finite,distributive but not complemented lattice$B$ is not distributive lattice
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#331
455
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1 answers
2 votes
NIELIT 2017 July Scientist B (IT) - Section B: 20
If $A$ and $B$ are two sets and $A \cup B = A ​ \cap ​ B$ then$A=\phi$B=\phi$A\neq B$A=B$
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#332
485
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1 answers
1 votes
NIELIT 2017 July Scientist B (IT) - Section B: 21
The relation $\{(1,2),(1,3)(3,1),(1,1),(3,3),(3,2),(1,4),(4,2),(3,4)\}$ is ReflexiveTransitiveSymmetricAsymmetric
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#333
2.0k
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1 answers
2 votes
NIELIT 2017 July Scientist B (IT) - Section B: 22
Let $L$ be a lattice. Then for every $a$ and $b$ in $L$ which one of the following is correct?$a\lor b = a​\land \:b$a\lor(b\lor c)=(a\lor b)\lor c$a\lor(b​\land \:c)=a$a\lor(b\lor c)=b$
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#334
1.0k
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4 answers
1 votes
NIELIT 2017 DEC Scientist B - Section B: 46
The number of integers between $1$ and $500$(both inclusive) that are divisible by $3$ or $5$ or $7$ is _________.$269$270$271$272$
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#335
1.9k
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5 answers
4 votes
NIELIT 2017 DEC Scientist B - Section B: 48
On a set $A = \{a,b,c,d\}$ a binary operation $*$ ... isCommutative but not associativeNeither commutative nor associativeBoth commutative and associativeAssociative but not commutative
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#336
1.4k
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1 answers
0 votes
UGC NET CSE | June 2005 | Part 2 | Question: 3
The transitive closure of a relation $R$ on set $A$ whose relation matrix $\begin{bmatrix}0 & 1 & 0\\ 0 & 0 & 1 \\ 1 & 0 & 0\end{bmatrix}$ ... }$\begin{bmatrix}0 & 1 & 1\\ 0 & 1 & 1 \\ 0 & 1 & 1\end{bmatrix}$
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#337
374
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1 answers
0 votes
UGC NET CSE | December 2004 | Part 2 | Question: 2
If $f (x)=x+1\:\text{and}\:g(x)=x+3$ then $f 0 f 0 f 0 f$ is :$g$g+1$g^4$None of these
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#338
1.0k
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3 answers
1 votes
UGC NET CSE | January 2017 | Part 2 | Question: 3
The functions mapping $R$ into $R$ are defined as :$f\left(x \right)=x^{3} - 4x, g\left(x \right)=\frac{1}{x^{2}+1}$ and $h\left(x \right)=x^{4}.$Then find the value of ... $\left [ \left ( x^{3}-4x \right )^{2}+1 \right ]^{-4}$
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#339
1.0k
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2 answers
0 votes
UGC NET CSE | January 2017 | Part 2 | Question: 4
How many multiples of $6$ are there between the following pairs of numbers?$0$ and $100$ and $-6$ and $34$1$ and $6$17$ and $6$17$ and $7$16$ and $7$
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#340
923
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1 answers
1 votes
JEST 2020
X AND Y is an arbitrary sets, F: $X\rightarrow Y$ show that a and b are equivalent F is one-oneFor all set Z and function g1: $Z\rightarrow X$ and g2: ... $f \bigcirc g1 \neq f \bigcirc g2$ Where $\bigcirc$ is a fucntion composition.
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