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Previous GATE Questions in Engineering Mathematics

18 votes
1 answer
151
GATE CSE 1990 | Question: 1-viii
A graph which has the same number of edges as its complement must have number of vertices congruent to ________ or ________ modulo $4$.
A graph which has the same number of edges as its complement must have number of vertices congruent to ________ or ________ modulo $4$.
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23 votes
9 answers
152
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
153
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
155
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
156
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
157
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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24 votes
3 answers
158
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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25 votes
4 answers
159
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
160
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
161
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
162
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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18 votes
3 answers
164
GATE CSE 1987 | Question: 1-xxiii
A square matrix is singular whenever The rows are linearly independent The columns are linearly independent The row are linearly dependent None of the above
A square matrix is singular whenever The rows are linearly independentThe columns are linearly independentThe row are linearly dependentNone of the above
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16 votes
5 answers
165
GATE CSE 1987 | Question: 1-xxii
The equation $7x^{7}+14x^{6}+12x^{5}+3x^{4}+12x^{3}+10x^{2}+5x+7=0$ has All complex roots At least one real root Four pairs of imaginary roots None of the above
The equation $7x^{7}+14x^{6}+12x^{5}+3x^{4}+12x^{3}+10x^{2}+5x+7=0$ hasAll complex rootsAt least one real rootFour pairs of imaginary rootsNone of the above
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12 votes
4 answers
166
GATE CSE 1987 | Question: 1-xxi
If $a, b,$ and $c$ are constants, which of the following is a linear inequality? $ax+bcy=0$ $ax^{2}+cy^{2}=21$ $abx+a^{2}y \geq 15$ $xy+ax \geq 20$
If $a, b,$ and $c$ are constants, which of the following is a linear inequality?$ax+bcy=0$$ax^{2}+cy^{2}=21$$abx+a^{2}y \geq 15$$xy+ax \geq 20$
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7 votes
2 answers
168
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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