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Previous GATE Questions in Discrete Mathematics

23 votes
9 answers
91
GATE CSE 1987 | Question: 10e
Show that the conclusion $(r \to q)$ follows from the premises$:p, (p \to q) \vee (p \wedge (r \to q))$
Show that the conclusion $(r \to q)$ follows from the premises$:p, (p \to q) \vee (p \wedge (r \to q))$
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36 votes
8 answers
92
GATE CSE 1987 | Question: 10b
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
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25 votes
2 answers
94
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?
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11 votes
1 answer
95
GATE CSE 1987 | Question: 9d
Specify an adjacency-lists representation of the undirected graph given above.
Specify an adjacency-lists representation of the undirected graph given above.
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15 votes
3 answers
96
GATE CSE 1987 | Question: 9c
Show that the number of odd-degree vertices in a finite graph is even.
Show that the number of odd-degree vertices in a finite graph is even.
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23 votes
3 answers
97
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?
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24 votes
4 answers
98
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?
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2 votes
2 answers
99
GATE CSE 1987 | Question: 2f
State whether the following statements are TRUE or FALSE: Every infinite cyclic group is isomorphic to the infinite cyclic group of integers under addition.
State whether the following statements are TRUE or FALSE:Every infinite cyclic group is isomorphic to the infinite cyclic group of integers under addition.
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4 votes
1 answer
100
GATE CSE 1987 | Question: 2e
State whether the following statement is TRUE or FALSE: There is a linear-time algorithm for testing the planarity of finite graphs.
State whether the following statement is TRUE or FALSE:There is a linear-time algorithm for testing the planarity of finite graphs.
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22 votes
4 answers
101
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.
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7 votes
2 answers
103
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...
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67 votes
10 answers
108
GATE CSE 2016 Set 1 | Question: 27
Consider the recurrence relation $a_1 =8 , a_n =6n^2 +2n+a_{n-1}$. Let $a_{99}=K\times 10^4$. The value of $K$ is __________.
Consider the recurrence relation $a_1 =8 , a_n =6n^2 +2n+a_{n-1}$. Let $a_{99}=K\times 10^4$. The value of $K$ is __________.
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57 votes
17 answers
109
GATE CSE 2016 Set 1 | Question: 26
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
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