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

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1&0&1&2&1&1&0&2&0&0&0&0.8&2
\\\hline\textbf{2 Marks Count} & 0 &2&1&0&0&1&1&0&1&2&0&0.8&2
\\\hline\textbf{Total Marks} & 1&4&3&2&1&3&2&2&2&4&\bf{1}&\bf{2.4}&\bf{4}\\\hline
\end{array}}}$$

Recent questions in Set Theory & Algebra

28 votes
6 answers
1561
3 votes
0 answers
1562
21 votes
5 answers
1563
17 votes
4 answers
1564
The Hasse diagrams of all the lattices with up to four elements are ________ (write all the relevant Hasse diagrams)
31 votes
4 answers
1565
23 votes
3 answers
1566
Amongst the properties $\left\{\text{reflexivity, symmetry, anti-symmetry, transitivity}\right\}$ the relation $R=\{(x, y) \in N^2|x \neq y\}$ satisfies _________
39 votes
4 answers
1567
41 votes
3 answers
1568
30 votes
4 answers
1569
42 votes
4 answers
1570
Out of a group of $21$ persons, $9$ eat vegetables, $10$ eat fish and $7$ eat eggs. $5$ persons eat all three. How many persons eat at least two out of the three dishes?
28 votes
3 answers
1571
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$
27 votes
3 answers
1573
Let A be a finite set of size n. The number of elements in the power set of $A\times A$ is:$2^{2^n}$$2^{n^2}$$\left(2^n\right)^2$$\left(2^2\right)^n$None of the above
54 votes
6 answers
1577
27 votes
4 answers
1579
A polynomial $p(x)$ is such that $p(0) = 5, p(1) = 4, p(2) = 9$ and $p(3) = 20$. The minimum degree it should have is$1$$2$$3$$4$
24 votes
4 answers
1580
In the lattice defined by the Hasse diagram given in following figure, how many complements does the element ‘$e$’ have?$2$$3$$0$$1$