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

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

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Most answered questions in Set Theory & Algebra

2 votes
4 answers
101
TIFR-2014-Maths-B-4
Let $H_{1}$, $H_{2}$ be two distinct subgroups of a finite group $G$, each of order $2$. Let $H$ be the smallest subgroup containing $H_{1}$ and $H_{2}$. Then the order of $H$ is Always 2 Always 4 Always 8 None of the above
Let $H_{1}$, $H_{2}$ be two distinct subgroups of a finite group $G$, each of order $2$. Let $H$ be the smallest subgroup containing $H_{1}$ and $H_{2}$. Then the order o...
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4 votes
4 answers
105
How many number of possible relations in a antisymmetric set?
I just want to know how the value in the answers come like 2^n2 and 2^n^2-1 etc. Please make it clear.
I just want to know how the value in the answers come like 2^n2 and 2^n^2-1 etc. Please make it clear.
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1 votes
4 answers
106
functions -which of following is false
Let A={x|x∈R and x!=2} and B={x|x∈R and x!=1} define f:A->B and g:B->A by  f(x)=x/(x-2) and g(x)=2x/(x-1) then which of following is false? 1)f∘g=g∘f    2)f∘g=Ib     Ib is identity function on set B 3)f=g-1      4) f∘g is bijection  
Let A={x|x∈R and x!=2} and B={x|x∈R and x!=1} define f:A->B and g:B->A by f(x)=x/(x-2) and g(x)=2x/(x-1) thenwhich of following is false?1)f∘g=g∘f    2)f∘g=I...
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29 votes
4 answers
107
GATE CSE 2015 Set 1 | Question: 5
If $g(x) = 1 - x$ and $h(x) = \frac{x}{x-1}$, then $\frac{g(h(x))}{h(g(x))}$ is: $\frac{h(x)}{g(x)}$ $\frac{-1}{x}$ $\frac{g(x)}{h(x)}$ $\frac{x}{(1-x)^{2}}$
If $g(x) = 1 - x$ and $h(x) = \frac{x}{x-1}$, then $\frac{g(h(x))}{h(g(x))}$ is:$\frac{h(x)}{g(x)}$$\frac{-1}{x}$$\frac{g(x)}{h(x)}$$\frac{x}{(1-x)^{2}}$
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4 votes
4 answers
108
No of surjective functions
The number of surjective (onto) functions defined from $A$ to $B$ where |A| = 5, |B| = 4, is _______
The number of surjective (onto) functions defined from $A$ to $B$ where |A| = 5, |B| = 4, is _______
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17 votes
4 answers
113
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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31 votes
4 answers
114
GATE CSE 1994 | Question: 2.4
The number of subsets $\left\{ 1,2, \dots, n\right\}$ with odd cardinality is ___________
The number of subsets $\left\{ 1,2, \dots, n\right\}$ with odd cardinality is ___________
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39 votes
4 answers
115
GATE CSE 1994 | Question: 2.2
On the set $N$ of non-negative integers, the binary operation ______ is associative and non-commutative.
On the set $N$ of non-negative integers, the binary operation ______ is associative and non-commutative.
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32 votes
4 answers
116
GATE CSE 1993 | Question: 28
Let $\left(\{ p,q \},*\right)$ be a semigroup where $p*p=q$. Show that: $p*q=q*p$ and $q*q=q$
Let $\left(\{ p,q \},*\right)$ be a semigroup where $p*p=q$. Show that:$p*q=q*p$ and$q*q=q$
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42 votes
4 answers
117
GATE CSE 1993 | Question: 17
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?
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?
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27 votes
4 answers
120
GATE CSE 1997 | Question: 4.4
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$
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$
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