Monoids and Groups: GATE CS previous year questions (Engineering Mathematics)

GATE CS 2025 Set 1MSQ2 marksEasy (estimate)
GATE CS 2025 Set 1, Q.49
$A = {0, 1, 2, 3, \dots}$ is the set of non-negative integers. Let $F$ be the set of functions from $A$ to itself. For any two functions, $f_{1}, f_{2} \in F$ , we define…
Monoids and Groups
GATE CS 2024 Set 1MSQ2 marksEasy (estimate)
GATE CS 2024 Set 1, Q.52
Consider the operators $⋄$ and $□$ defined by $a ⋄ b = a + 2 b, a □ b = ab$ , for positive integers. Which of the following statements is/are TRUE?
Monoids and Groups
GATE CS 2024 Set 2NAT2 marksEasy (estimate)
GATE CS 2024 Set 2, Q.63
Let $Z_{n}$ be the group of integers ${0, 1, 2, \dots, n - 1}$ with addition modulo $n$ as the group operation. The number of elements in the group $Z_{2} \times Z_{3} \times Z_{4}$ t...
Monoids and Groups
GATE CS 2023MSQ2 marksMedium (estimate)
GATE CS 2023, Q.51
Let $X$ be a set and $2^{X}$ denote the powerset of $X$ . Define a binary operation $Δ$ on $2^{X}$ as follows: $A Δ B = (A - B) \cup (B - A) .$ Let $H = (2^{X}, Δ)$ . Wh...
Monoids and Groups · Sets, Relations, Functions, Partial Orders and Lattices
GATE CS 2022MSQ1 markMedium (estimate)
GATE CS 2022, Q.27
Which of the following statements is/are TRUE for a group G ?
Monoids and Groups
GATE CS 2021 Set 1MCQ2 marksMedium (estimate)
GATE CS 2021 Set 1, Q.44 (CS Q.34)
Let $G$ be a group of order 6, and $H$ be a subgroup of $G$ such that $1 < ∣ H ∣ < 6$ . Which one of the following options is correct?
Monoids and Groups
GATE CS 2020NAT1 markEasy (estimate)
GATE CS 2020, Q.28 (CS Q.18)
Let $G$ be a group of 35 elements. Then the largest possible size of a subgroup of $G$ other than $G$ itself is _______.
Monoids and Groups
GATE CS 2019MCQ1 markEasy (estimate)
GATE CS 2019, Q.20 (CS Q.10)
Let $G$ be an arbitrary group. Consider the following relations on $G$ : $R_{1}$ : $\forall a, b \in G$ , $a R_{1} b$ if and only if $\exists g \in G$ such that $a = g^{- 1} b g$ $R_{2}$ …
Monoids and Groups
GATE CS 2019NAT1 markEasy (estimate)
GATE CS 2019, Q.31 (CS Q.21)
The value of $3^{51} (mod 5)$ is ________.
Monoids and Groups
GATE CS 2018NAT1 markEasy (estimate)
GATE CS 2018, Q.29 (CS Q.19)
Let $G$ be a finite group on 84 elements. The size of a largest possible proper subgroup of $G$ is ________.
Monoids and Groups
GATE CS 2018MCQ2 marksMedium (estimate)
GATE CS 2018, Q.37 (CS Q.27)
Let $N$ be the set of natural numbers. Consider the following sets. P: Set of Rational numbers (positive and negative) Q: Set of functions from {0, 1} to $N$ R...
Monoids and Groups
GATE CS 2014 Set 3NAT1 markEasy (estimate)
GATE CS 2014 Set 3, Q.13 (CS Q.3)
Let $G$ be a group with 15 elements. Let $L$ be a subgroup of $G$ . It is known that $L \neq = G$ and that the size of $L$ is at least 4. The size of $L$ is _____.
Monoids and Groups
GATE CS 2014 Set 3NAT2 marksMedium (estimate)
GATE CS 2014 Set 3, Q.60 (CS Q.50)
There are two elements $x, y$ in a group $(G, *)$ such that every element in the group can be written as a product of some number of $x$ 's and $y$ 's in some order. It is known t...
Monoids and Groups
GATE CS 2013MCQ1 markEasy (estimate)
GATE CS 2013, Q.1 (CS Q.1)
A binary operation $\oplus$ on a set of integers is defined as $x \oplus y = x^{2} + y^{2}$ . Which one of the following statements is TRUE about $\oplus$ ?
Monoids and Groups

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