Register

Web Page

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

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

Filter

Previous GATE Questions in Set Theory & Algebra

41 votes
5 answers
22
GATE CSE 2017 Set 2 | Question: 24
Consider the quadratic equation $x^2-13x+36=0$ with coefficients in a base $b$. The solutions of this equation in the same base $b$ are $x=5$ and $x=6$. Then $b=$ _____
Consider the quadratic equation $x^2-13x+36=0$ with coefficients in a base $b$. The solutions of this equation in the same base $b$ are $x=5$ and $x=6$. Then $b=$ _____
User Avatar
25 votes
2 answers
23
GATE CSE 1988 | Question: 13ii
If the set $S$ has a finite number of elements, prove that if $f$ maps $S$ onto $S$, then $f$ is one-to-one.
If the set $S$ has a finite number of elements, prove that if $f$ maps $S$ onto $S$, then $f$ is one-to-one.
User Avatar
1 votes
1 answer
24
GATE CSE 1988 | Question: 13ic
Verify whether the following mapping is a homomorphism. If so, determine its kernel. $f(x)=x^3$, for all $x$ belonging to $G$.
Verify whether the following mapping is a homomorphism. If so, determine its kernel.$f(x)=x^3$, for all $x$ belonging to $G$.
User Avatar
1 votes
0 answers
25
GATE CSE 1988 | Question: 13ia
Verify whether the following mapping is a homomorphism. If so, determine its kernel. $G$ is the group of non zero real numbers under multiplication.
Verify whether the following mapping is a homomorphism. If so, determine its kernel.$G$ is the group of non zero real numbers under multiplication.
User Avatar
15 votes
2 answers
26
GATE CSE 1988 | Question: 2xviii
Show that if $G$ is a group such that $(a. b)^2 = a^2.b^2$ for all $a, b$ belonging to $G$, then $G$ is an abelian.
Show that if $G$ is a group such that $(a. b)^2 = a^2.b^2$ for all $a, b$ belonging to $G$, then $G$ is an abelian.
User Avatar
25 votes
4 answers
27
GATE CSE 1989 | Question: 13c
Find the number of single valued functions from set $A$ to another set $B,$ given that the cardinalities of the sets $A$ and $B$ are $m$ and $n$ respectively.
Find the number of single valued functions from set $A$ to another set $B,$ given that the cardinalities of the sets $A$ and $B$ are $m$ and $n$ respectively.
User Avatar
0 votes
0 answers
28
GATE CSE 1988 | Question: 2iv
Give one property of the field of real numbers which no longer holds when we compute using finite-precision floating point numbers.
Give one property of the field of real numbers which no longer holds when we compute using finite-precision floating point numbers.
User Avatar
22 votes
6 answers
29
GATE CSE 1988 | Question: 1vii
The complement(s) of the element $'a'$ in the lattice shown in below figure is (are) ____
The complement(s) of the element $'a'$ in the lattice shown in below figure is (are) ____
User Avatar
43 votes
2 answers
30
GATE CSE 1989 | Question: 1-v
The number of possible commutative binary operations that can be defined on a set of $n$ elements (for a given $n$) is ___________.
The number of possible commutative binary operations that can be defined on a set of $n$ elements (for a given $n$) is ___________.
User Avatar
23 votes
6 answers
31
GATE CSE 1989 | Question: 1-iv
The transitive closure of the relation $\left\{(1, 2), (2, 3), (3, 4), (5, 4)\right\}$ on the set $\left\{1, 2, 3, 4, 5\right\}$ is ___________.
The transitive closure of the relation $\left\{(1, 2), (2, 3), (3, 4), (5, 4)\right\}$ on the set $\left\{1, 2, 3, 4, 5\right\}$ is ___________.
User Avatar
9 votes
2 answers
32
GATE CSE 1990 | Question: 17c
Show that the elements of the lattice $(N, \leq)$, where $N$ is the set of positive intergers and $a \leq b$ if and only if $a$ divides $b$, satisfy the distributive property.
Show that the elements of the lattice $(N, \leq)$, where $N$ is the set of positive intergers and $a \leq b$ if and only if $a$ divides $b$, satisfy the distributive prop...
User Avatar
21 votes
2 answers
33
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...
User Avatar
26 votes
2 answers
35
GATE CSE 1987 | Question: 9e
How many true inclusion relations are there of the form $A \subseteq B$, where $A$ and $B$ are subsets of a set $S$ with $n$ elements?
How many true inclusion relations are there of the form $A \subseteq B$, where $A$ and $B$ are subsets of a set $S$ with $n$ elements?
User Avatar
24 votes
3 answers
36
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?
User Avatar
25 votes
4 answers
37
GATE CSE 1987 | Question: 9a
How many binary relations are there on a set $A$ with $n$ elements?
How many binary relations are there on a set $A$ with $n$ elements?
User Avatar
23 votes
4 answers
38
GATE CSE 1987 | Question: 2d
State whether the following statements are TRUE or FALSE: The union of two equivalence relations is also an equivalence relation.
State whether the following statements are TRUE or FALSE:The union of two equivalence relations is also an equivalence relation.
User Avatar
8 votes
2 answers
40
GATE CSE 1992 | Question: 15.b
Let $S$ be the set of all integers and let $n > 1$ be a fixed integer. Define for $a,b \in S, a R b$ iff $a-b$ is a multiple of $n$. Show that $R$ is an equivalence relation and find its equivalence classes for $n = 5$.
Let $S$ be the set of all integers and let $n 1$ be a fixed integer. Define for $a,b \in S, a R b$ iff $a-b$ is a multiple of $n$. Show that $R$ is an equivalence relat...
User Avatar
Page: