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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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Most viewed questions in Set Theory & Algebra

18 votes
4 answers
183
GATE CSE 1994 | Question: 2.9
The Hasse diagrams of all the lattices with up to four elements are ________ (write all the relevant Hasse diagrams)
The Hasse diagrams of all the lattices with up to four elements are ________ (write all the relevant Hasse diagrams)
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29 votes
3 answers
184
GATE CSE 1993 | Question: 8.6
Let $A$ and $B$ be sets with cardinalities $m$ and $n$ respectively. The number of one-one mappings from $A$ to $B$, when $m < n$, is $m^n$ $^nP_m$ $^mC_n$ $^nC_m$ $^mP_n$
Let $A$ and $B$ be sets with cardinalities $m$ and $n$ respectively. The number of one-one mappings from $A$ to $B$, when $m < n$, is$m^n$$^nP_m$$^mC_n$$^nC_m$$^mP_n$
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13 votes
4 answers
186
GATE CSE 1998 | Question: 10b
Let $R$ be a binary relation on $A = \{a, b, c, d, e, f, g, h\}$ represented by the following two component digraph. Find the smallest integers $m$ and $n$ such that $m < n$ and $R^m = R^n$.
Let $R$ be a binary relation on $A = \{a, b, c, d, e, f, g, h\}$ represented by the following two component digraph. Find the smallest integers $m$ and $n$ such that $m <...
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21 votes
2 answers
187
GATE CSE 1995 | Question: 25b
Determine the number of positive integers $(\leq 720)$ which are not divisible by any of $2,3$ or $5.$
Determine the number of positive integers $(\leq 720)$ which are not divisible by any of $2,3$ or $5.$
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3 votes
2 answers
188
TIFR2010-Maths-A-1
A cyclic group of order 60 has 12 Generators 15 Generators 16 Generators 20 Generators
A cyclic group of order 60 has12 Generators15 Generators16 Generators20 Generators
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8 votes
3 answers
191
ISRO2018-17
$(\text{G}, \ast )$ is an abelian group. Then $x= x^{-1}$ for any $x$ belonging to $\text{G}$ $x=x^{2}$ for any $x$ belonging to $\text{G}$ $\left( x \ast y \right )^{2}= x^{2} \ast y^{2}$ , for any $x, y$ belonging to $\text{G}$ $\text{G}$ is of finite order
$(\text{G}, \ast )$ is an abelian group. Then$x= x^{-1}$ for any $x$ belonging to $\text{G}$$x=x^{2}$ for any $x$ belonging to $\text{G}$$\left( x \ast y \right )^{2}= x^...
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24 votes
3 answers
193
GATE CSE 1987 | Question: 9b
How many one-to-one functions are there from a set $A$ with $n$ elements onto itself?
How many one-to-one functions are there from a set $A$ with $n$ elements onto itself?
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28 votes
3 answers
194
GATE CSE 2000 | Question: 4
Let $S= \{0, 1, 2, 3, 4, 5, 6, 7\}$ and $⊗$ denote multiplication modulo $8,$ that is, $x ⊗ y= (xy) \mod 8$ Prove that $( \{ 0, 1\}, ⊗)$ is not a group. Write three distinct groups $(G, ⊗)$ where $G ⊂ S$ and $G$ has $2$ elements.
Let $S= \{0, 1, 2, 3, 4, 5, 6, 7\}$ and $⊗$ denote multiplication modulo $8,$ that is, $x ⊗ y= (xy) \mod 8$Prove that $( \{ 0, 1\}, ⊗)$ is not a group.Write three d...
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21 votes
2 answers
199
GATE CSE 1990 | Question: 2-x
Match the pairs in the following questions: ...
Match the pairs in the following questions:$$\begin{array}{|ll|ll|}\hline (a) & \text{Groups} & (p) & \text{Associativity} \\\hline (b) & \text{Semigroups} & (q) & \text...
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