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12 votes
2 answers
9181
GATE CSE 1995 | Question: 2.13
A unit vector perpendicular to both the vectors $a=2i-3j+k$ and $b=i+j-2k$ is: $\frac{1}{\sqrt{3}} (i+j+k)$ $\frac{1}{3} (i+j-k)$ $\frac{1}{3} (i-j-k)$ $\frac{1}{\sqrt{3}} (i+j-k)$
A unit vector perpendicular to both the vectors $a=2i-3j+k$ and $b=i+j-2k$ is:$\frac{1}{\sqrt{3}} (i+j+k)$$\frac{1}{3} (i+j-k)$$\frac{1}{3} (i-j-k)$$\frac{1}{\sqrt{3}} (i...
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19 votes
3 answers
9182
GATE CSE 1995 | Question: 2.8
If the cube roots of unity are $1, \omega$ and $\omega^2$, then the roots of the following equation are $(x-1)^3 +8 =0$ $-1, 1 + 2\omega, 1 + 2\omega^2$ $1, 1 - 2\omega, 1 - 2\omega^2$ $-1, 1 - 2\omega, 1 - 2\omega^2$ $-1, 1 + 2\omega, -1 + 2\omega^2$
If the cube roots of unity are $1, \omega$ and $\omega^2$, then the roots of the following equation are $$(x-1)^3 +8 =0$$$-1, 1 + 2\omega, 1 + 2\omega^2$ $1, 1 - 2\omeg...
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33 votes
5 answers
9183
GATE CSE 1995 | Question: 1.25
The minimum number of edges in a connected cyclic graph on $n$ vertices is: $n-1$ $n$ $n+1$ None of the above
The minimum number of edges in a connected cyclic graph on $n$ vertices is:$n-1$$n$$n+1$None of the above
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23 votes
7 answers
9184
GATE CSE 1995 | Question: 1.24
The rank of the following $(n+1) \times (n+1)$ matrix, where $a$ ... $1$ $2$ $n$ Depends on the value of $a$
The rank of the following $(n+1) \times (n+1)$ matrix, where $a$ is a real number is $$ \begin{bmatrix} 1 & a & a^2 & \dots & a^n \\ 1 & a & a^2 & \dots & a^n \\ \vdots ...
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26 votes
3 answers
9185
GATE CSE 1995 | Question: 1.21
In the interval $[0, \pi]$ the equation $x=\cos x$ has No solution Exactly one solution Exactly two solutions An infinite number of solutions
In the interval $[0, \pi]$ the equation $x=\cos x$ has No solutionExactly one solutionExactly two solutionsAn infinite number of solutions
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24 votes
6 answers
9186
GATE CSE 1995 | Question: 1.20
The number of elements in the power set $P(S)$ of the set $S=\{\{\emptyset\}, 1, \{2, 3\}\}$ is: $2$ $4$ $8$ None of the above
The number of elements in the power set $P(S)$ of the set $S=\{\{\emptyset\}, 1, \{2, 3\}\}$ is:$2$$4$$8$None of the above
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28 votes
6 answers
9187
GATE CSE 1995 | Question: 1.19
Let $R$ be a symmetric and transitive relation on a set $A$. Then $R$ is reflexive and hence an equivalence relation $R$ is reflexive and hence a partial order $R$ is reflexive and hence not an equivalence relation None of the above
Let $R$ be a symmetric and transitive relation on a set $A$. Then$R$ is reflexive and hence an equivalence relation$R$ is reflexive and hence a partial order$R$ is reflex...
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3 votes
0 answers
9188
GATE CSE 1994 | Question: 16
Every element $a$ of some ring $(R, +, o)$ satisfies the equation $a\;o\;a=a$. Decide whether or not the ring is commutative.
Every element $a$ of some ring $(R, +, o)$ satisfies the equation $a\;o\;a=a$. Decide whether or not the ring is commutative.
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18 votes
2 answers
9189
GATE CSE 1994 | Question: 15
Use the patterns given to prove that $\sum\limits_{i=0}^{n-1} (2i+1) = n^2$ (You are not permitted to employ induction) Use the result obtained in (A) to prove that $\sum\limits_{i=1}^{n} i = \frac{n(n+1)}{2}$
Use the patterns given to prove that$\sum\limits_{i=0}^{n-1} (2i+1) = n^2$(You are not permitted to employ induction)Use the result obtained in (A) to prove that $\sum\li...
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22 votes
3 answers
9190
GATE CSE 1994 | Question: 3.13
Let $p$ and $q$ be propositions. Using only the Truth Table, decide whether $p \Longleftrightarrow q$ does not imply $p \to \lnot q$ is True or False.
Let $p$ and $q$ be propositions. Using only the Truth Table, decide whether $p \Longleftrightarrow q$ does not imply $p \to \lnot q$is True or False.
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17 votes
3 answers
9191
GATE CSE 1994 | Question: 3.12
Find the inverse of the matrix $\begin{bmatrix} 1 & 0 & 1 \\ -1 & 1 & 1 \\ 0 & 1 & 0 \end{bmatrix}$
Find the inverse of the matrix $\begin{bmatrix} 1 & 0 & 1 \\ -1 & 1 & 1 \\ 0 & 1 & 0 \end{bmatrix}$
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21 votes
5 answers
9192
GATE CSE 1994 | Question: 3.9
Every subset of a countable set is countable. State whether the above statement is true or false with reason.
Every subset of a countable set is countable.State whether the above statement is true or false with reason.
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17 votes
4 answers
9193
GATE CSE 1994 | Question: 2.9
The Hasse diagrams of all the lattices with up to four elements are ________ (write all the relevant Hasse diagrams)
The Hasse diagrams of all the lattices with up to four elements are ________ (write all the relevant Hasse diagrams)
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25 votes
2 answers
9194
GATE CSE 1994 | Question: 2.8
Let $A, B,$ and $C$ be independent events which occur with probabilities $0.8, 0.5,$ and $0.3$ respectively. The probability of occurrence of at least one of the event is _______
Let $A, B,$ and $C$ be independent events which occur with probabilities $0.8, 0.5,$ and $0.3$ respectively. The probability of occurrence of at least one of the event is...
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19 votes
3 answers
9196
GATE CSE 1994 | Question: 2.5
The number of edges in a regular graph of degree $d$ and $n$ vertices is ____________
The number of edges in a regular graph of degree $d$ and $n$ vertices is ____________
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31 votes
4 answers
9197
GATE CSE 1994 | Question: 2.4
The number of subsets $\left\{ 1,2, \dots, n\right\}$ with odd cardinality is ___________
The number of subsets $\left\{ 1,2, \dots, n\right\}$ with odd cardinality is ___________
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23 votes
3 answers
9198
GATE CSE 1994 | Question: 2.3
Amongst the properties $\left\{\text{reflexivity, symmetry, anti-symmetry, transitivity}\right\}$ the relation $R=\{(x, y) \in N^2|x \neq y\}$ satisfies _________
Amongst the properties $\left\{\text{reflexivity, symmetry, anti-symmetry, transitivity}\right\}$ the relation $R=\{(x, y) \in N^2|x \neq y\}$ satisfies _________
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39 votes
4 answers
9199
GATE CSE 1994 | Question: 2.2
On the set $N$ of non-negative integers, the binary operation ______ is associative and non-commutative.
On the set $N$ of non-negative integers, the binary operation ______ is associative and non-commutative.
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26 votes
5 answers
9200
GATE CSE 1994 | Question: 1.15
The number of substrings (of all lengths inclusive) that can be formed from a character string of length $n$ is $n$ $n^2$ $\frac{n(n-1)}{2}$ $\frac{n(n+1)}{2}$
The number of substrings (of all lengths inclusive) that can be formed from a character string of length $n$ is$n$$n^2$$\frac{n(n-1)}{2}$$\frac{n(n+1)}{2}$
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