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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 answered questions in Set Theory & Algebra

22 votes
5 answers
65
GATE CSE 1996 | Question: 1.2
Let $X = \{2, 3, 6, 12, 24\}$, Let $\leq$ be the partial order defined by $X \leq Y$ if $x$ divides $y$. Number of edges in the Hasse diagram of $(X, \leq)$ is $3$ $4$ $9$ None of the above
Let $X = \{2, 3, 6, 12, 24\}$, Let $\leq$ be the partial order defined by $X \leq Y$ if $x$ divides $y$. Number of edges in the Hasse diagram of $(X, \leq)$ is$3$$4$$9$No...
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27 votes
5 answers
66
GATE CSE 1995 | Question: 21
Let $G_1$ and $G_2$ be subgroups of a group $G$. Show that $G_1 \cap G_2$ is also a subgroup of $G$. Is $G_1 \cup G_2$ always a subgroup of $G$?.
Let $G_1$ and $G_2$ be subgroups of a group $G$.Show that $G_1 \cap G_2$ is also a subgroup of $G$.Is $G_1 \cup G_2$ always a subgroup of $G$?.
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21 votes
5 answers
67
GATE CSE 1994 | Question: 3.9
Every subset of a countable set is countable. State whether the above statement is true or false with reason.
Every subset of a countable set is countable.State whether the above statement is true or false with reason.
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42 votes
5 answers
69
GATE CSE 2012 | Question: 37
How many onto (or surjective) functions are there from an $n$-element $(n ≥ 2)$ set to a $2$-element set? $ 2^{n}$ $2^{n} – 1$ $2^{n} – 2$ $2(2^{n} – 2)$
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$$2(2^{n} – 2)$
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20 votes
5 answers
71
GATE CSE 1998 | Question: 1.6
Suppose $A$ is a finite set with $n$ elements. The number of elements in the largest equivalence relation of A is $n$ $n^2$ $1$ $n+1$
Suppose $A$ is a finite set with $n$ elements. The number of elements in the largest equivalence relation of A is$n$$n^2$$1$$n+1$
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60 votes
5 answers
73
GATE CSE 2007 | Question: 21
How many different non-isomorphic Abelian groups of order $4$ are there? $2$ $3$ $4$ $5$
How many different non-isomorphic Abelian groups of order $4$ are there?$2$$3$$4$$5$
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26 votes
5 answers
74
GATE CSE 2005 | Question: 8
Let $A, B$ and $C$ be non-empty sets and let $X = ( A - B ) - C$ and $Y = ( A - C ) - ( B - C ).$ Which one of the following is TRUE? $X = Y$ $X ⊂ Y$ $Y ⊂ X$ None of these
Let $A, B$ and $C$ be non-empty sets and let $X = ( A - B ) - C$ and $Y = ( A - C ) - ( B - C ).$ Which one of the following is TRUE?$X = Y$$X ⊂ Y$$Y ⊂ X$None of thes...
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