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Previous GATE Questions in Engineering Mathematics

8 votes
3 answers
122
GATE CSE 1988 | Question: 16i
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lower-triangular with all diagonal elements equal to $1, U$ is upper-triangular, and $P$ ... $L, U,$ and $P$ using Gaussian elimination with partial pivoting.
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lower-triangular with all diagonal elements equal to $1, U$ is upper-triangula...
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1 votes
1 answer
124
GATE CSE 1988 | Question: 14i
Consider the following well-formed formula: $\exists x \forall y [ \neg \: \exists z [ p (y, z) \wedge p (z, y) ] \equiv p(x,y)]$ Express the above well-formed formula in clausal form.
Consider the following well-formed formula:$\exists x \forall y [ \neg \: \exists z [ p (y, z) \wedge p (z, y) ] \equiv p(x,y)]$Express the above well-formed formula in c...
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7 votes
3 answers
125
GATE CSE 1988 | Question: 13iii
Are the two digraphs shown in the above figure isomorphic? Justify your answer.
Are the two digraphs shown in the above figure isomorphic? Justify your answer.
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25 votes
2 answers
126
GATE CSE 1988 | Question: 13ii
If the set $S$ has a finite number of elements, prove that if $f$ maps $S$ onto $S$, then $f$ is one-to-one.
If the set $S$ has a finite number of elements, prove that if $f$ maps $S$ onto $S$, then $f$ is one-to-one.
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1 votes
1 answer
127
GATE CSE 1988 | Question: 13ic
Verify whether the following mapping is a homomorphism. If so, determine its kernel. $f(x)=x^3$, for all $x$ belonging to $G$.
Verify whether the following mapping is a homomorphism. If so, determine its kernel.$f(x)=x^3$, for all $x$ belonging to $G$.
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2 votes
0 answers
128
GATE CSE 1988 | Question: 13ib
Verify whether the following mapping is a homomorphism. If so, determine its kernel. $\overline{G}=G$
Verify whether the following mapping is a homomorphism. If so, determine its kernel.$\overline{G}=G$
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1 votes
0 answers
129
GATE CSE 1988 | Question: 13ia
Verify whether the following mapping is a homomorphism. If so, determine its kernel. $G$ is the group of non zero real numbers under multiplication.
Verify whether the following mapping is a homomorphism. If so, determine its kernel.$G$ is the group of non zero real numbers under multiplication.
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15 votes
2 answers
130
GATE CSE 1988 | Question: 2xviii
Show that if $G$ is a group such that $(a. b)^2 = a^2.b^2$ for all $a, b$ belonging to $G$, then $G$ is an abelian.
Show that if $G$ is a group such that $(a. b)^2 = a^2.b^2$ for all $a, b$ belonging to $G$, then $G$ is an abelian.
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15 votes
4 answers
131
GATE CSE 1988 | Question: 2xvi
Write the adjacency matrix representation of the graph given in below figure.
Write the adjacency matrix representation of the graph given in below figure.
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13 votes
3 answers
132
GATE CSE 1988 | Question: 2vii
Define the validity of a well-formed formula(wff)?
Define the validity of a well-formed formula(wff)?
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31 votes
5 answers
133
GATE CSE 1989 | Question: 14a
Symbolize the expression "Every mother loves her children" in predicate logic.
Symbolize the expression "Every mother loves her children" in predicate logic.
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25 votes
4 answers
134
GATE CSE 1989 | Question: 13c
Find the number of single valued functions from set $A$ to another set $B,$ given that the cardinalities of the sets $A$ and $B$ are $m$ and $n$ respectively.
Find the number of single valued functions from set $A$ to another set $B,$ given that the cardinalities of the sets $A$ and $B$ are $m$ and $n$ respectively.
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0 votes
0 answers
135
GATE CSE 1988 | Question: 2iv
Give one property of the field of real numbers which no longer holds when we compute using finite-precision floating point numbers.
Give one property of the field of real numbers which no longer holds when we compute using finite-precision floating point numbers.
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21 votes
6 answers
136
GATE CSE 1988 | Question: 1vii
The complement(s) of the element $'a'$ in the lattice shown in below figure is (are) ____
The complement(s) of the element $'a'$ in the lattice shown in below figure is (are) ____
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37 votes
5 answers
138
GATE CSE 1989 | Question: 4-i
How many substrings (of all lengths inclusive) can be formed from a character string of length $n$? Assume all characters to be distinct, prove your answer.
How many substrings (of all lengths inclusive) can be formed from a character string of length $n$? Assume all characters to be distinct, prove your answer.
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31 votes
4 answers
140
GATE CSE 1989 | Question: 3-vi
Which of the following graphs is/are planar?
Which of the following graphs is/are planar?
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