Recent questions tagged goclasses_2025_cs_dm_tw

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GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 3 | Question: 9
The multiplication table $\left({ }^*\right)$ for a group $\mathrm{G}=\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d})$ ... /are false? $d \ast b=d$ $b \ast c=d$ $\left(c\ast d\right) \ast c=d$ $G$ is a cyclic group.

The multiplication table $\left({ }^*\right)$ for a group $\mathrm{G}=\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d})$ is given below.$$\begin{array}{|c|c|c|c|c|}\hline...

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GO Classes asked May 4, 2023

3 votes

1 answer

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GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 3 | Question: 5
What is the order of smallest non-cyclic group?

What is the order of smallest non-cyclic group?

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GO Classes asked May 29, 2022

6 votes

3 answers

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GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 3 | Question: 1
Let $\text{G}$ be a cyclic group with generator ‘$a$’. Order of ‘$a$’ is $29.$ The number of subgroups $\text{G}$ has ________

Let $\text{G}$ be a cyclic group with generator ‘$a$’. Order of ‘$a$’ is $29.$ The number of subgroups $\text{G}$ has ________

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GO Classes asked May 29, 2022

6 votes

2 answers

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GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 3 | Question: 2
In a group $\text{G},$ every element other than the identity element has order $2$ then $\mathrm{G}$ is? Abelian group Cyclic group Non-abelian group Non-cyclic group

In a group $\text{G},$ every element other than the identity element has order $2$ then $\mathrm{G}$ is?Abelian groupCyclic groupNon-abelian groupNon-cyclic group

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GO Classes asked May 29, 2022

7 votes

1 answer

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GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 3| Question: 6
Let $\text{R}$ be the set of all real numbers. Let $\text{S = R} \backslash\{-1\}$ and define a binary operation on $\text{S}$ by $a \ast b=a+b+a b$ ... not abelian. $(\mathrm{S}, \ast)$ is a cyclic group. $(\mathrm{S}, \ast)$ is an abelian group but not cyclic.

Let $\text{R}$ be the set of all real numbers.Let $\text{S = R} \backslash\{-1\}$ and define a binary operation on $\text{S}$ by $a \ast b=a+b+a b$.Which of the following...

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GO Classes asked May 29, 2022

4 votes

2 answers

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GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 3 | Question: 7
Which of the following multiplication tables defined on the set $G = \{a, b, c, d\}$ form a group?

Which of the following multiplication tables defined on the set $G = \{a, b, c, d\}$ form a group?

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GO Classes asked May 29, 2022

3 votes

1 answer

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GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 3| Question: 8
Let $G$ be a group under binary operation $\ast.$ Let $g \in G$. We define $\langle g\rangle$ as follows : $\langle g\rangle=\left\{g^{n} \mid n \in \mathbb{Z}\right\}$ ... $\langle g\rangle$ is abelian. If $H \leq G$ and $g \in H$, then $\langle g\rangle \leq H$.

Let $G$ be a group under binary operation $\ast.$ Let $g \in G$.We define $\langle g\rangle$ as follows :$$\langle g\rangle=\left\{g^{n} \mid n \in \mathbb{Z}\right\}$$Wh...

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GO Classes asked May 29, 2022

7 votes

2 answers

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GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 3 | Question: 4
What is the smallest positive integer $n$ such that there is a group of order $n$ which is not abelian?

What is the smallest positive integer $n$ such that there is a group of order $n$ which is not abelian?

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GO Classes asked Apr 27, 2022

8 votes

2 answers

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GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 3 | Question: 10
Let $\text{G}$ be a group and let $\text{H} = \{x^{–1} | x \in \text{G}\}$ then which of the following is true? $\text{G} \subseteq \text{H}$ but $\text{G}$ may not be same as $H$ $\text{H} \subseteq \text{G}$ but $\text{H}$ may not be same as $\text{G}$ $\text{H = G}$ $\text{H}$ may not be a group.

Let $\text{G}$ be a group and let $\text{H} = \{x^{–1} | x \in \text{G}\}$ then which of the following is true?$\text{G} \subseteq \text{H}$ but $\text{G}$ may not be s...

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GO Classes asked Apr 27, 2022

6 votes

3 answers

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GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 3 | Question: 3
Let $\mathbf{Z}$ be the group of all integers under the operation of addition. Which of the following subsets of $\mathbf{Z}$ is/are NOT a subgroup of $\mathbf{Z}?$ $\{0\}$ $\{n \in \mathbf{Z} : n > 0\}$ ... $\{n \in \mathbf{Z} : n \;\text{is divisible by both 6 and 9}\}$

Let $\mathbf{Z}$ be the group of all integers under the operation of addition. Which of the following subsets of $\mathbf{Z}$ is/are NOT a subgroup of $\mathbf{Z}?$$\{0\}...

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GO Classes asked Apr 27, 2022

6 votes

2 answers

11

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 3 | Question: 11
Let $\text{G}_{1}$ and $\text{G}_{2}$ be two groups as following: $G_1$ is a group such that $\forall x, y, z \in \text{G}_{1}$ $xy = zx$ implies $y = z$ $\text{G}_{2}$ ... $\text{G}_{1}$. Neither of $\text{G}_{1}$ and $\text{G}_{2}$ is abelian.

Let $\text{G}_{1}$ and $\text{G}_{2}$ be two groups as following:$G_1$ is a group such that $\forall x, y, z \in \text{G}_{1}$ $xy = zx$ implies $y = z$$\text{G}...

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GO Classes asked Apr 27, 2022

7 votes

2 answers

12

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 3 | Question: 12
Let $\mathbf{Z}$ be set of integers, and $+$ be an integer addition operation. Let $p, q$ be distinct primes. If $\text{J}$ is a proper subgroup of $(\mathbf{Z}, +)$ containing exactly three of $\{p, p + q, pq, p^q, q^p\},$ ... $\{pq, p^{q}, q^{p}\}$ $\{p, pq, p^{q}\}$ $\{p, pq, q^{p}\}$

Let $\mathbf{Z}$ be set of integers, and “$+$” be an integer addition operation.Let $p, q$ be distinct primes. If $\text{J}$ is a proper subgroup of $(\mathbf{Z}, +)$...

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GO Classes asked Apr 27, 2022

7 votes

3 answers

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GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 3 | Question: 13
A binary operation $\ast$ on a set $\text{A}$ is a function from $\text{A} \times \text{A}$ to $\text{A},$ which maps pair $(a, b)$ to $a \ast b.$ Binary operation $\ast$ on a set ... The total number of different commutative binary operations on a set of four elements is?

A binary operation “$\ast$” on a set $\text{A}$ is a function from $\text{A} \times \text{A}$ to $\text{A},$ which maps pair $(a, b)$ to $a \ast b.$Binary operation �...

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GO Classes asked Apr 27, 2022

7 votes

1 answer

14

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 3 | Question: 15
Consider the following statements : Suppose $\text{G}$ is a group and $a,x \in \text{G}.$ If order of $x=2,$ Then $(a x a^{-1})$ has order $2.$ A finite group is never the union of two of its proper subgroups. Which of the above statements is/are true? Only $1$ Only $2$ Both None

Consider the following statements :Suppose $\text{G}$ is a group and $a,x \in \text{G}.$ If order of $x=2,$ Then $(a x a^{-1})$ has order $2.$A finite group is never the ...

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GO Classes asked Apr 27, 2022

3 votes

1 answer

15

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 3 | Question: 14
Let $\text{S}$ be the set of all functions $f : \text{R} \rightarrow \text{R}.$ Consider the two binary operations $+$ and $\ast$ on $\text{S}$ ... All II only Ill only II and III only

Let $\text{S}$ be the set of all functions $f : \text{R} \rightarrow \text{R}.$ Consider the two binary operations $+$ and $\ast$ on $\text{S}$ defined as pointwise addit...

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GO Classes asked Apr 27, 2022

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