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question_answer1)
If \[X=\{{{8}^{n}}-7n-1:n\in N\}\] and \[Y=\{49(n-1):n\in N\},\] then
A)
\[X\subseteq Y\] done
clear
B)
\[Y\subseteq X\] done
clear
C)
\[X=Y\] done
clear
D)
None of these done
clear
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question_answer2)
If \[{{N}_{a}}=\{an:n\in N\},\] then \[{{N}_{3}}\cap {{N}_{4}}=\]
A)
\[{{N}_{7}}\] done
clear
B)
\[{{N}_{12}}\] done
clear
C)
\[{{N}_{3}}\] done
clear
D)
\[{{N}_{4}}\] done
clear
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question_answer3)
Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in A U B [MNR 1987; Karnataka CET 1996]
A)
3 done
clear
B)
6 done
clear
C)
9 done
clear
D)
18 done
clear
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question_answer4)
If \[A=[(x,\,y):{{x}^{2}}+{{y}^{2}}=25]\] and B = \[[(x,\,y):{{x}^{2}}+9{{y}^{2}}=144]\], then \[A\cap B\] contains [AMU 1996; Pb. CET 2002]
A)
One point done
clear
B)
Three points done
clear
C)
Two points done
clear
D)
Four points done
clear
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question_answer5)
If \[A=[x:x\] is a multiple of 3] and \[B=[x:x\] is a multiple of 5], then A - B is (\[\bar{A}\] means complement of A) [AMU 1998]
A)
\[\bar{A}\cap B\] done
clear
B)
\[A\cap \bar{B}\] done
clear
C)
\[\bar{A}\cap \bar{B}\] done
clear
D)
\[\overline{A\cap B}\] done
clear
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question_answer6)
If \[A=\{x:{{x}^{2}}-5x+6=0\},\,B=\{2,\,4\},\,C=\{4,\,5\},\] then \[A\times (B\cap C)\] is [Kerala (Engg.) 2002]
A)
{(2, 4), (3, 4)} done
clear
B)
{(4, 2), (4, 3)} done
clear
C)
{(2, 4), (3, 4), (4, 4)} done
clear
D)
{(2,2), (3,3), (4,4), (5,5)} done
clear
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question_answer7)
In a college of 300 students, every student reads 5 newspaper and every newspaper is read by 60 students. The no. of newspaper is [IIT 1998]
A)
At least 30 done
clear
B)
At most 20 done
clear
C)
Exactly 25 done
clear
D)
None of these done
clear
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question_answer8)
Let A = {1, 2, 3, 4, 5}; B = {2, 3, 6, 7}. Then the number of elements in \[\left( A\text{ }~\times \text{ }B \right)\text{ }\cap \text{ }\left( B\text{ }\times \text{ }A \right)\] is
A)
18 done
clear
B)
6 done
clear
C)
4 done
clear
D)
0 done
clear
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question_answer9)
Let A = {1, 2, 3}, B = {1, 3, 5}. A relation \[R:A\to B\] is defined by R = {(1, 3), (1, 5), (2, 1)}. Then \[{{R}^{-1}}\] is defined by
A)
{(1,2), (3,1), (1,3), (1,5)} done
clear
B)
{(1, 2), (3, 1), (2, 1)} done
clear
C)
{(1, 2), (5, 1), (3, 1)} done
clear
D)
None of these done
clear
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question_answer10)
Let R be the relation on the set R of all real numbers defined by a R b iff \[|a-b|\le 1\]. Then R is [Roorkee 1998]
A)
Reflexive and Symmetric done
clear
B)
Symmetric only done
clear
C)
Transitive only done
clear
D)
Anti-symmetric only done
clear
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question_answer11)
With reference to a universal set, the inclusion of a subset in another, is relation, which is [Karnataka CET 1995]
A)
Symmetric only done
clear
B)
Equivalence relation done
clear
C)
Reflexive only done
clear
D)
None of these done
clear
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question_answer12)
Let R be a relation on the set N of natural numbers defined by nRm \[\Leftrightarrow \] n is a factor of m (i.e., n|m). Then R is
A)
Reflexive and symmetric done
clear
B)
Transitive and symmetric done
clear
C)
Equivalence done
clear
D)
Reflexive, transitive but not symmetric done
clear
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question_answer13)
Let R and S be two non-void relations on a set A. Which of the following statements is false
A)
R and S are transitive \[\Rightarrow \text{ }R\text{ }\cup \text{ }S\] is transitive done
clear
B)
R and S are transitive \[\Rightarrow \text{ }R\text{ }\cap \text{ }S\] is transitive done
clear
C)
R and S are symmetric \[\Rightarrow \text{ }R\text{ }\cup \text{ }S\] is symmetric done
clear
D)
R and S are reflexive \[\Rightarrow \text{ }R\text{ }\cap \text{ }S\] is reflexive done
clear
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question_answer14)
Let a relation R be defined by R = {(4, 5); (1, 4); (4, 6); (7, 6); (3, 7)} then \[{{R}^{-1}}oR\] is
A)
{(1, 1), (4, 4), (4, 7), (7, 4), (7, 7), (3, 3)} done
clear
B)
{(1, 1), (4, 4), (7, 7), (3, 3)} done
clear
C)
{(1, 5), (1, 6), (3, 6)} done
clear
D)
None of these done
clear
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question_answer15)
Let R be a relation on the set N be defined by {(x, y)| x, y
\[\overset{\hat{\ }}{\mathop{i}}\,\]
N, 2x + y = 41}. Then R is
A)
Reflexive done
clear
B)
Symmetric done
clear
C)
Transitive done
clear
D)
None of these done
clear
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