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Recent questions tagged go2025-dm-3

6 votes
1 answer
2
GATE Overflow Test Series | Discrete Mathematics | Test 3 | Question: 2
Let $G$ be a group with order $45$, and $H$ a non-abelian subgroup of $G$. Assuming $H \neq G$, what is the smallest possible order of $H$?
Let $G$ be a group with order $45$, and $H$ a non-abelian subgroup of $G$. Assuming $H \neq G$, what is the smallest possible order of $H$?
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3 votes
2 answers
3
GATE Overflow Test Series | Discrete Mathematics | Test 3 | Question: 3
Let $G=\langle{a\rangle}$. The smallest subgroup of $G$ containing $a^{2020}$ and $a^{1719}$ is _________ $a^{4}$ $a^{1719}$ $a^{2020}$ $a^{1}$
Let $G=\langle{a\rangle}$. The smallest subgroup of $G$ containing $a^{2020}$ and $a^{1719}$ is _________$a^{4}$$a^{1719}$$a^{2020}$$a^{1}$
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2 votes
2 answers
6
GATE Overflow Test Series | Discrete Mathematics | Test 3 | Question: 6
What is the solution to the recurrence relation $a_{n} = a_{n-1} + n$ with $a_{0} = 0$? $a_{n} = \dfrac{n(n-1)}{2} $ $a_{n} = \dfrac{(n-1)(n+1)}{2} $ $a_{n} = \dfrac{(n-1)(n+1)}{4} $ $a_{n} = \dfrac{n(n+1)}{2} $
What is the solution to the recurrence relation $a_{n} = a_{n-1} + n$ with $a_{0} = 0$?$a_{n} = \dfrac{n(n-1)}{2} $$a_{n} = \dfrac{(n-1)(n+1)}{2} $$a_{n} = \dfrac{(n-1)(n...
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3 votes
1 answer
7
GATE Overflow Test Series | Discrete Mathematics | Test 3 | Question: 7
Consider a prime number $p$ and a positive integer $a$ such that $p$ divides $a$. The remainder when $a^{p-1}$ is divided by $p$ is $1$ $0$ $p-1$ Cannot be determined
Consider a prime number $p$ and a positive integer $a$ such that $p$ divides $a$. The remainder when $a^{p-1}$ is divided by $p$ is$1$$0$$p-1$Cannot be determined
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2 votes
2 answers
10
GATE Overflow Test Series | Discrete Mathematics | Test 3 | Question: 10
Let $(G,\ast)$ be a group of order $P$, where $P$ is a prime number. The number of subgroups of $G$ is ________ $0$ $P^{2}$ $P^{2}-2$ $2$
Let $(G,\ast)$ be a group of order $P$, where $P$ is a prime number. The number of subgroups of $G$ is ________$0$$P^{2}$$P^{2}-2$$2$
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1 votes
1 answer
11
GATE Overflow Test Series | Discrete Mathematics | Test 3 | Question: 11
The value of $x_5$ for the recurrence relation defined by $x_n = 5x_{n-1} + 3$ with initial condition $x_1 = 3$ is _________
The value of $x_5$ for the recurrence relation defined by $x_n = 5x_{n-1} + 3$ with initial condition $x_1 = 3$ is _________
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2 votes
1 answer
14
GATE Overflow Test Series | Discrete Mathematics | Test 3 | Question: 14
The following Hasse diagram describes a Join semi lattice Meet semi lattice Lattice None of the above
The following Hasse diagram describes a Join semi latticeMeet semi latticeLatticeNone of the above
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2 votes
1 answer
16
GATE Overflow Test Series | Discrete Mathematics | Test 3 | Question: 16
The solution to the recurrence relation $a_{n}=a_{n-1}+2^{n}$ with $a_{0}=1$ is ________ $a_{n} = 2^{n} - 1 $ $a_{n} = 2^{n+1} - 2 $ $a_{n} = 2^{n+1} - 1 $ $a_{n} = 2^{n-1} - 1 $
The solution to the recurrence relation $a_{n}=a_{n-1}+2^{n}$ with $a_{0}=1$ is ________$a_{n} = 2^{n} - 1 $$a_{n} = 2^{n+1} - 2 $$a_{n} = 2^{n+1} - 1 $$a_{n} = 2^{n-1} -...
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2 votes
1 answer
19
GATE Overflow Test Series | Discrete Mathematics | Test 3 | Question: 19
Let $G$ be a finite group on $243$ elements. The size of the largest possible proper subgroup of $G$ is ________
Let $G$ be a finite group on $243$ elements. The size of the largest possible proper subgroup of $G$ is ________
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3 votes
1 answer
24
GATE Overflow Test Series | Discrete Mathematics | Test 3 | Question: 24
How many ways can we fill the following table so that the binary operation $\ast$ is commutative? $\begin{array}{| c | c| c | c | c |} \hline \textbf{$ ... $2$ $3$ $1$ $4$
How many ways can we fill the following table so that the binary operation $\ast$ is commutative?$$\begin{array}{| c | c| c | c | c |}\hline\textbf{$\ast$} & \textbf{a} &...
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4 votes
1 answer
27
GATE Overflow Test Series | Discrete Mathematics | Test 3 | Question: 27
Suppose $G$ is a group that has exactly $48$ distinct elements of order $5$. How many distinct subgroups of order $5$ does $G$ have? $12$ $6$ $1$ $4$
Suppose $G$ is a group that has exactly $48$ distinct elements of order $5$. How many distinct subgroups of order $5$ does $G$ have?$12$$6$$1$$4$
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1 votes
1 answer
28
GATE Overflow Test Series | Discrete Mathematics | Test 3 | Question: 28
What is the solution to the recurrence relation $f_{n} = f_{n-1} + f_{n-2} \quad \text{ with } f_{0} = 0,f_{1} = 1?$ ...
What is the solution to the recurrence relation$$f_{n} = f_{n-1} + f_{n-2} \quad \text{ with } f_{0} = 0,f_{1} = 1?$$$f_{n} =\dfrac{1}{\sqrt{5}}\bigg(\dfrac{(1 + \sqrt{5}...
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2 votes
2 answers
29
GATE Overflow Test Series | Discrete Mathematics | Test 3 | Question: 29
Calculate $a_{100} + a_{99}$ where $a_n$ is given by the recurrence relation $a_{n} = 2a_{n-1} - a_{n-2}$ with $a_{0} = 5,a_{1} = 4$?
Calculate $a_{100} + a_{99}$ where $a_n$ is given by the recurrence relation $a_{n} = 2a_{n-1} - a_{n-2}$ with $a_{0} = 5,a_{1} = 4$?
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1 votes
1 answer
30
GATE Overflow Test Series | Discrete Mathematics | Test 3 | Question: 30
The number of maximal and minimal elements for the poset $[\:\: \{2,4,6,9,12,18,27,36,48,60,72\},\: \mid\:\: ],$ where $\mid$ is the "divides" relation is $2,1$ $4,1$ $3,2$ $4,2$
The number of maximal and minimal elements for the poset $[\:\: \{2,4,6,9,12,18,27,36,48,60,72\},\: \mid\:\: ],$ where $\mid$ is the "divides" relation is$2,1$$4,1$$3,2$$...
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