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29 votes
6 answers
122
GATE CSE 2002 | Question: 2.17
The binary relation $S= \phi \text{(empty set)}$ on a set $A = \left \{ 1,2,3 \right \}$ is Neither reflexive nor symmetric Symmetric and reflexive Transitive and reflexive Transitive and symmetric
The binary relation $S= \phi \text{(empty set)}$ on a set $A = \left \{ 1,2,3 \right \}$ is Neither reflexive nor symmetricSymmetric and reflexiveTransitive and reflexive...
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38 votes
9 answers
124
GATE CSE 2001 | Question: 2.1
How many $4$-digit even numbers have all $4$ digits distinct? $2240$ $2296$ $2620$ $4536$
How many $4$-digit even numbers have all $4$ digits distinct?$2240$$2296$$2620$$4536$
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3 votes
2 answers
125
If X and Y are two sets, then X⋂(Y⋃X) C equals
If X and Y are two sets, then X⋂(Y⋃X) C equals (a) X (b) Y (c) ϕ (d) None of these My attempt: X = {1,2,3} Y = {3,4,5} (Y⋃X) = {1,2,3,4,5} X⋂(Y⋃X) = {1,2,3} But the given answer is C
If X and Y are two sets, then X⋂(Y⋃X) C equals(a) X (b) Y (c) ϕ (d) None of these My attempt:X = {1,2,3} Y = {3,4,5}(Y⋃X) = {1,2,3,4,5}X⋂(Y&#...
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37 votes
7 answers
126
GATE CSE 2004 | Question: 77
The minimum number of colours required to colour the following graph, such that no two adjacent vertices are assigned the same color, is $2$ $3$ $4$ $5$
The minimum number of colours required to colour the following graph, such that no two adjacent vertices are assigned the same color, is$2$$3$$4$$5$
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14 votes
5 answers
130
GATE 2019
Let U = {1, 2, ..., n} and A = {(x, X), x ∈ X and X ⊆ U}. Consider the following two statements for |A|. (i) |A| = n*$\small 2^{n-1}$ (ii) |A|= Sigma(k=1 to n) k.(nCk) Which of the following is correct? (a) (i) only (b) (ii) only (c) Both (i) and (ii) (d) None of the above
Let U = {1, 2, ..., n} and A = {(x, X), x ∈ X and X ⊆ U}. Consider the following twostatements for |A|.(i) |A| = n*$\small 2^{n-1}$(ii) |A|= Sigma(k=1 to n) k.(nCk) W...
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60 votes
6 answers
131
GATE CSE 2014 Set 1 | Question: 50
Let ܵ$S$ denote the set of all functions $f:\{0,1\}^4 \to \{0,1\}$. Denote by $N$ the number of functions from S to the set $\{0,1\}$. The value of $ \log_2 \log_2N $ is _______.
Let ܵ$S$ denote the set of all functions $f:\{0,1\}^4 \to \{0,1\}$. Denote by $N$ the number of functions from S to the set $\{0,1\}$. The value of $ \log_2 \log_2N $ is...
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38 votes
7 answers
135
GATE CSE 1999 | Question: 2.2
Two girls have picked $10$ roses, $15$ sunflowers and $15$ daffodils. What is the number of ways they can divide the flowers among themselves? $1638$ $2100$ $2640$ None of the above
Two girls have picked $10$ roses, $15$ sunflowers and $15$ daffodils. What is the number of ways they can divide the flowers among themselves?$1638$$2100$$2640$None of th...
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29 votes
4 answers
136
GATE CSE 2018 | Question: 19
Let $G$ be a finite group on $84$ elements. The size of a largest possible proper subgroup of $G$ is _____
Let $G$ be a finite group on $84$ elements. The size of a largest possible proper subgroup of $G$ is _____
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32 votes
5 answers
137
GATE CSE 2018 | Question: 18
The chromatic number of the following graph is _____
The chromatic number of the following graph is _____
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57 votes
10 answers
138
GATE CSE 2017 Set 2 | Question: 11
Let $p, q, r$ ... $(\neg p \wedge r) \vee (r \rightarrow (p \wedge q))$
Let $p, q, r$ denote the statements ”It is raining”, “It is cold”, and “It is pleasant”, respectively. Then the statement “It is not raining and it is pleas...
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1 votes
2 answers
140
UGC NET CSE | December 2006 | Part 2 | Question: 3
The number of edges in a complete graph with $N$ vertices is equal to : $N (N−1)$ $2N−1$ $N−1$ $N(N−1)/2$
The number of edges in a complete graph with $N$ vertices is equal to :$N (N−1)$$2N−1$$N−1$$N(N−1)/2$
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