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

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

Recent questions in Set Theory & Algebra

#741
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The set of all English words ordered in a dictionary is ________$A)$ not a poset$B)$ a poset but not totally ordered$C)$ a totally ordered set but not well ordered$D)$ a well ordered set
#742
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1 votes
Consider the following system of sets and operations an them:$(1)(Z,\geq ),$ where $'Z'$ is the set of an integer$(2) (Z^{+},1),$where $'1'$ is the divisibility ... $(3)$ only$C) (1)$ and $(3)$ only$D)$ All are partial ordering
#743
685
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Number of possible Boolean functions of two binary variables excluding True and False are______
#744
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1 answers
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A) {0,g,h,i}B) {0,h,s}C) {d,e,f,g,h,i,0}D) {0,h,e}
#745
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1 answers
2 votes
If Irreflexive relation are represented as directed graphs, then the partitions of an equivalence relation manifest in the form of ______A) Strongly connected component B) Unilaterally connected componentC) CliqueD) None of these
#746
416
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2 answers
1 votes
For given R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(3,4),(4,3)}Is the given relation transitive?
#747
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1 answers
2 votes
Which of the following is not a subset of $P(P(P(\phi)))$?$A)$ {$\phi$}$B)$ { {$\phi$} }$C)$ { {$\phi$} , { {$\phi$} } }$D)$ { { { {$\phi$} } } }
#748
164
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#749
159
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#750
486
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#751
647
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#752
718
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https://gateoverflow.in/18503/tifr2010-a-11Here how points are taken and and calculation has been done?Can anybody tell me why (x,y) taking all decimal value?I am not getting , plz somebody explain
#754
861
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1 answers
2 votes
FIELD AND RING ARE IN SYLLABUS???
#755
2.7k
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2 answers
2 votes
Number of non isomorphic group of order 10
#756
668
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4 votes
How to test whether function is onto and one-to-one when function is in two variables?Determine whether below function $f:Z\,X\,Z\rightarrow\,Z$ is one-to-one, or onto or none?(a)$f(m,n)=2m-n$(b)$f(m,n)=m^2-n^2$
#757
137
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In discrete,can we use X-OR condition if the question uses ''either-or" or it has to be "either-or but not both"?
#758
182
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Let $f \: \circ \: g$ denote function composition such that $(f \circ g)(x) = f(g(x))$. Let $f: A \rightarrow B$ ... ://gateoverflow.in/95289/tifr2017-a-11i'm not able to understand why f should be one-to-one
#759
1.1k
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1 answers
1 votes
How many different non-isomorphic Abelian groups of order 16 are there?
#760
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1 answers
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State True or False?Empty set Φ is an equivalence relation.