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Recent questions tagged goclasses_wq12
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GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 1
What is the order of smallest non-cyclic group?
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GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 2
Let $\text{G}$ is a cyclic group with generator ‘$a$’. Order of ‘$a$’ is $29.$ The number of subgroups $\text{G}$ has ________
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GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 3
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
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GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 4
The set $\{1, 2, 3, \dots , n - 1\}$ is a group under multiplication modulo $n.$ Then the smallest value of $n$ between $20$ and $30$ is $(20, 30$ included $)\;$ _______
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GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 5
Consider the group $0,1,2,3,4,+{ }_{5}$. What will be the value of $2^{-3}$ and $3^{-2}$ for the given group? $1$ and $1$ $2$ and $3$ $4$ and $4$ $3$ and $2$
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6
GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 6
Let $f$ be a function from a set $X$ to a set $Y$. Consider the following statements. $P:$ For each $x \in X$, there exists $y \in Y$ such that $f(x)=y$. $Q$ : For each $y \in Y$, there exists $x \in X$ ... to-one and onto $Y$ " is $P$ or not $R$ $R$ or not $P$ $R$ or not $Q$ $P$ and not $R$
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7
GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 7
Let $R$ be the set of all real numbers. Let $S=R \backslash\{-1\}$ and define a binary operation on $S$ by $a \ast b=a+b+a b$. Which of the following is true? $(\mathrm{S}, \ast)$ is a not a group. ... not abelian. $(\mathrm{S}, \ast)$ is a cyclic group. $(\mathrm{S}, \ast)$ is an abelian group but not cyclic.
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8
GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 8
Which of the following associative multiplication tables defined on the set $G = \{a, b, c, d\}$ form a group?
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9
GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 9
The group $Z_{n}$ consists of the elements $\{0,1,2, \ldots, n-1\}$ with addition $\bmod n$ as the operation. How many subgroups of $Z_{9}$ are there?
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10
GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 10
Let $Z$ be the set of all integers. Let $n \in Z$ and $nZ = {nk : k \in Z}.$ Which of the following is/are true? $nZ$ is a subgroup of $Z$ (under addition operation) for all $n \in Z.$ Every subgroup of ... some $n.$ $3Z$ is the smallest subgroup of $(Z,+)$ containing $3.$ $nZ$ is a cyclic subgroup of $Z.$
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11
GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 11
The set $Z_{\mathrm{n}}^{*}$ consists of the elements $\{1,2, \ldots, \mathrm{n}-1\}$ with multiplication $\bmod n$ as the operation. The group $Z_{n}$ consists of the elements $\{0,1,2, \ldots, n-1\}$ ... then $\mathrm{G}$ is a cyclic group. The number of elements in $Z_{8}^{*}$ which have an inverse is $4.$
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12
GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 12
Consider the standard groups $Z_{\mathrm{n}}, \mathrm{R}^{*}, \mathrm{C}^{*}$ under their standard group operation. Here, $\mathrm{R}^{*}, \mathrm{C}^{*}$ are set of non-zero real numbers, set of non-zero complex numbers, ... $\sqrt{3} \in \mathrm{R}^{*}$ $-\mathrm{i} \in \mathrm{C}^{*}$
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13
GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 13
Which of the following functions are one-to-one but not onto. $f: \mathbb{R} \rightarrow \mathbb{R}$ defined by $f(x)=e^{x}$ $f: \mathbb{Z} \rightarrow \mathbb{Z}$ defined by $f(n)=n^{2}+3$ ... $f(x)=\sin x$ $f: \mathbb{Z} \rightarrow \mathbb{Z}$ defined by $f(x)=x^{2}$
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14
GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 14
Let $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$ and $\mathrm{g}: \mathrm{B} \rightarrow \mathrm{C}$ be maps. Which of the following is/are true? If $f$ and $g$ are both one-to-one functions, then $gof$ is one-to-one. ... $g \circ f$ is one-to-one and $f$ is onto, then $g$ is one-to-one.
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15
GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 15
Let $G$ be a group under binary operation *. Let $g \in G$. We define $<g>$ as follows : $\langle g\rangle=\left\{g^{n} \mid n \in \mathbb{Z}\right\}$ ... $G$. $<g>$ is abelian. If $H \leq G$ and $g \in H$, then $< g>\leq H$.
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