
If \[A=\{1,2,3,4,5\}\], then the number of proper subsets of A is
A)
31 done
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B)
38 done
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C)
48 done
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D)
54 done
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Which of the following is true?
A)
\[a\in \{\{a\},b\}\] done
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B)
\[\{b,c\}\subset \{a,\{b,c\}\}\] done
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C)
\[\{a,b\}\subset \{a,\{b,c\}\}\] done
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D)
None of these done
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Let S be a set of all distinct numbers of the form \[\frac{P}{Q}\], where \[p,q\in \{1,2,3,4,5,6\}.\] What is the cardinality of the set S?
A)
21 done
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B)
23 done
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C)
32 done
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D)
36 done
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Which of the following is a singleton set?
A)
\[\{x:\left x \right=5,x\in N\}\] done
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B)
\[\{x:\left x \right=6,x\in Z\}\] done
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C)
\[\{x:{{x}^{2}}+2x+1=0,x\in N\}\] done
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D)
\[\{x:{{x}^{2}}=7,x\in N\}\] done
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Let\[A=\{xx\le 9,x\in N\}\]. Let \[B=\{a,b,c\}\] be the subset of A where \[\left( a+b+c \right)\] is a multiple of 3. What is the largest possible number of subsets like B?
A)
12 done
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B)
21 done
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C)
27 done
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D)
30 done
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Two finite sets have m and n elements, the total number of subsets of the first set is 56 more than the total number of subsets of the second set. Then:
A)
\[m=3,n=6\] done
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B)
\[m=6,n=3\] done
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C)
\[m=5,n=6\] done
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D)
None of these done
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If P denotes the power set of A and A is the void set, then what is number of elements in \[P\{P\{P\{P(A)\}\}\}\]?
A)
0 done
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B)
1 done
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C)
4 done
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D)
16 done
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Which of the following sets is a finite set?
A)
\[A=\{x:x\in Z\,\,and\,\,{{x}^{2}}5x+6=0\}\] done
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B)
\[B=\{x:x\in Z\,\,and\,\,{{x}^{2}}\,is\,even\}\] done
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C)
\[D=\{x:x\in Z\,\,and\,\,x>10\}\] done
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D)
All of these done
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Let S = the set of all triangles, P= the set of all isosceles triangles, Q= the set of all equilateral triangles, R= the set of all right  angled triangles. What do the sets \[P\cap Q\] and \[RP\] represents respectively?
A)
The set of isosceles triangles; the set of nonisosceles right angled triangles done
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B)
The set of isosceles triangles; the set of right angled triangles done
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C)
The set of equilateral triangles; the set of right angled triangles done
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D)
The set of isosceles triangles; the set of equilateral triangles done
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If A, B, C are there sets, then what is \[A(BC)\]equal to?
A)
\[A(B\cap C)\] done
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B)
\[(AB)\cup C\] done
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C)
\[(AB)\cup (A\cap C)\] done
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D)
\[(AB)\cup (AC)\] done
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If A and B are two sets, then \[(AB)\cup (BA)\]\[\cup (A\cap B)\] is equal to
A)
Only A done
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B)
\[A\cup B\] done
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C)
\[(A\cup B')\] done
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D)
None of these done
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Each student in a class of 40, studies at least one of the subjects English, Mathematics and Economics. 16 study English, 22 Economics and 26 Mathematics, 5 study English and? Economics, 14 Mathematics and Economics and 2 study all the three subjects. The number of students who study English and Mathematics but not Economics is
A)
7 done
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B)
5 done
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C)
10 done
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D)
4 done
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If A and B are subsets of a set X, then what is \[\{A\cap (XB)\}\cup B\] equal to?
A)
\[A\cup B\] done
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B)
\[A\cap B\] done
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C)
A done
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D)
B done
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A survey of 500 television viewers produced the following information, 285 watch football, 195 watch hockey, 115 watch basketball, 45 watch football and basketball, 70 watch football and hockey, 50 watch hockey and basketball, 50 do not watch any of the three games. The number of viewers, who watch exactly one of the three games are
A)
325 done
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B)
310 done
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C)
405 done
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D)
372 done
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If \[A=\{4n+2n\] is a natural number} and \[B=\{3nn\] is a natural number,}, then what is \[(A\cap B)\] equal to?
A)
\[\{12{{n}^{2}}+6nn\] is a natural number} done
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B)
\[\{24n12n\] is a natural number} done
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C)
\[\{60n+30n\] is a natural number} done
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D)
\[\{12n6n\] is a natural number} done
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A dinner party is to be fixed for a group of 100 persons. In this party, 50 persons do not prefer fish, 60 prefer chicken and 10 do not prefer either chicken of fish. The number of persons who prefer both fish and chicken is.
A)
20 done
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B)
22 done
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C)
25 done
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D)
None of these done
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Which is the simplified representation of \[(A'\cap B'\cap C)\cup (B\cap C)\cup (A\cap C)\] where A, B, C are subsets of set X?
A)
A done
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B)
B done
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C)
C done
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D)
\[X\cap (A\cup B\cup C)\] done
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Which one of the following is correct?
A)
\[A\cup (BC)=A\cap (B\cap C')\] done
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B)
\[A(B\cup C)=(A\cap B')\cap C'\] done
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C)
\[A(B\cap C)=(A\cap B')\cap C\] done
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D)
\[A\cap (BC)=(A\cap B)\cap C\] done
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If F (n) denotes the set of all divisors of n except 1. What is the least value of y satisfying \[[F(20)\cap F(16)]\subseteq F(y)?\]
A)
1 done
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B)
2 done
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C)
4 done
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D)
8 done
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If \[\mu \] is the universal set and P is a subset of \[\mu \], then what is \[P\cap (P\mu )\cup (\mu P)\}\] equal to?
A)
\[\phi \] done
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B)
P? done
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C)
m done
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D)
P done
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Consider the following statements: For nonempty sets. A, B and C
1. \[A(BC)=(AB)\cup C\] 
2. \[A(B\cup C)=(AB)C\] 
Which of the statements given above is/are correct?
A)
1 only done
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B)
2 only done
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C)
Both 1 and 2 done
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D)
neither 1 nor 2 done
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In a group of 500 students, there are 475 students who can speak Hindi and 200 can speak Bengali. What is the number of students who can speak Hindi only?
A)
275 done
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B)
300 done
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C)
325 done
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D)
350 done
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Consider the following:
1. \[A\cup (B\cap C)=(A\cap B)\cup (A\cap C)\] 
2. \[A\cap (B\cup C)=(A\cup B)\cap (A\cup C)\] 
Which of the above is/are correct?
A)
1 only done
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B)
2 only done
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C)
Both 1 and 2 done
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D)
Neither 1 nor 2 done
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In a city 20 percent of the population travels by car, 50 percent travels by bus and 10 percent travels by both car and bus. Then person travelling by car or bus is
A)
80 percent done
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B)
40 percent done
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C)
60 percent done
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D)
70 percent done
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In a survey of 400 students in a school, 100 were listed as taking apple juice, 150 as taking orange juice and 75 were listed as taking both apple as well as orange juice. Then, which of the following is/are true?
I. 150 students were taking at least one juice. 
II. 225 students were taking neither apple juice nor orange juice. 
A)
Only I is true done
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B)
Only II is true done
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C)
Both I and II are true done
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D)
None of these done
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If A, B and C are three finite sets, then what is \[\left[ (A\cup B)\cap C \right]'\] equal to?
A)
\[A'\cup B'\cap C'\] done
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B)
\[A'\cap B'\cap C'\] done
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C)
\[A'\cap B'\cup C'\] done
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D)
\[A\cap B\cap C\] done
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A market research group conducted a survey of 2000 consumers and reported that 1720 consumers like product \[{{P}_{1}}\] and 1450 consumers like product \[{{P}_{2}}.\] What is the least number that must have liked both the products?
A)
1150 done
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B)
2000 done
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C)
1170 done
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D)
2500 done
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If n = 115, n = 326, n(A  B) = 47, then what in \[n(A\cup B)\] equal to?
A)
373 done
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B)
165 done
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C)
370 done
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D)
394 done
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If X and Y are two sets such that \[(X\cup Y)\] has 60 elements, X has 38 elements and Y has 42 elements, how many elements does \[(X\cap Y)\]have?
A)
11 done
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B)
20 done
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C)
13 done
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D)
None of these done
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Let A, B, C be finite sets. Suppose that \[n(A)=10,\]\[n(B)=15,\] \[n(C)=20,\] \[n(A\cap B)=8\] and \[n(B\cap C)=9.\] Then the possible value of \[n(A\cup B\cup C)\] is
A)
26 done
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B)
27 done
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C)
28 done
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D)
Any of the three values 26, 27, 28 is possible done
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A survey shows that 61%, 46% and 29% of the people watched ?3 idiots??, ?Raajneeti? and ?Avatar? respectively. 25% people watched exactly two of the three movies and 3% watches none. What percentage of people watched all the three movies?
A)
39% done
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B)
11% done
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C)
14% done
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D)
7% done
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In a class of 80 students numbered a to 80, all odd numbered students opt if Cricket, students whose numbers are divisible by 5 opt for football and those whose numbers are divisible by 7 opt for Hockey. The number of students who do not opt any of the three games, is
A)
13 done
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B)
24 done
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C)
28 done
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D)
52 done
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20 teachers of a school either teach mathematics or physics. 12 of them teach mathematics while 4 teach both the subjects. Then the number of teachers teaching physics only is
A)
12 done
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B)
8 done
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C)
16 done
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D)
None of these done
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In a B School there are 15 teachers who teach marketing or finance. Of these, 8 teach finance. How many teach marketing but not finance?
A)
15 done
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B)
20 done
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C)
11 done
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D)
None of these done
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The cardinality of the set \[P\left\{ P\left[ P(\phi ) \right] \right\}\] is
A)
0 done
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B)
1 done
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C)
2 done
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D)
4 done
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The number of elements in the set \[\{(a,b):2{{a}^{2}}+3{{b}^{2}}=35,a,b\in Z\}\], where Z is the set of all integers, is
A)
2 done
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B)
4 done
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C)
8 done
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D)
12 done
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Which of the following is/are true?
I. If A is a subset of the universal set U then its complement A? is also a subset of U. 
II. If \[U=\{1,2,3,....,10\}\] and \[A=\{1,3,5,7,9\}\]then \[{{(A')}^{'}}=A.\] 
A)
Only I is true done
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B)
Only II is true done
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C)
Both I and II are true done
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D)
None of these done
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For a set A, consider the following statements:
1. \[A\cup P(A)=P(A)\] 
2. \[\{A\}\cap P(A)=A\] 
3. \[P(A)\{A\}=P(A)\] 
where P denotes power set. Which of the statements given above is/are correct?
A)
1 only done
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B)
2 only done
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C)
3 only done
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D)
1, 2 and 3 done
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If A and B are two disjoint sets, then which one of the following is correct?
A)
\[AB=A(A\cap B)\] done
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B)
\[BA'=A\cap B\] done
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C)
\[A\cap B=(AB)\cap B\] done
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D)
All of these done
clear
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Let n denote the set of natural numbers and \[A=\{{{n}^{2}}:n\in N\}\] and \[B=\{{{n}^{3}}:n\in N\},\] which one of the following is incorrect?
A)
\[A\cup B=N\] done
clear
B)
The complement of \[(A\cup B)\] is an infinite set done
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C)
\[A\cap B\] Must be a finite set done
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D)
\[A\cap B\] Must be proper subset of \[\{{{m}^{6}}:m\in N\}\] done
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If the cardinality of a set A is 4 and that of a set B in 3, then what is the cardinality of the set A \[\Delta \] B?
A)
1 done
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B)
5 done
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C)
7 done
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D)
Cannot be determined as the sets A and B are not given done
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Let N be the set of nonnegative integers, I the set of integers, \[{{N}_{P}}\] the set of nonpositive integers, E the set of even integers and P the set of prime numbers. Then
A)
\[IN={{N}_{p}}\] done
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B)
\[N\cap {{N}_{p}}=\phi \] done
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C)
\[E\cap P=\phi \] done
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D)
\[N\Delta {{N}_{p}}=I\{0\}\] done
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Let A and B be two sets then \[(A\cup B)'\cup (A'\cap B)\] is equal to
A)
A? done
clear
B)
A done
clear
C)
B? done
clear
D)
None of these done
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What does the shaded portion of the Venn diagram given below represent?
A)
\[(P\cap Q)\cap (P\cap R)\] done
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B)
\[((P\cap Q)R)\cup ((P\cap R)Q)\] done
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C)
\[((P\cup Q)R)\cap ((P\cap R)Q)\] done
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D)
\[((P\cap Q)\cup R)\cap ((P\cup Q)R)\] done
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A, B, C and D are four sets such that \[A\cap B=C\cap D=\phi .\] Consider the following:
1. \[A\cup B\] and \[B\cup D\] are always disjoint. 
2. \[A\cap C\] and \[B\cap D\] are always disjoint. 
Which of the above statements is/are correct? 
A)
1 Only done
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B)
2 only done
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C)
Both 1 and 2 done
clear
D)
neither 1 nor 2s done
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Let A, B, C are three nonempty sets. If \[A\subset B\]and \[B\subset C,\]then which of the following is true?
A)
\[BA=CB\] done
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B)
\[A\cap B\cap C=B\] done
clear
C)
\[A\cup B=B\cap C\] done
clear
D)
\[A\cup B\cup C=A\] done
clear
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Let X and Y be two nonempty sets such that \[X\cap A=Y\cap A=\phi \] and \[X\cup A=Y\cup A\]for some nonempty set A. Then
A)
X is a proper subset of Y done
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B)
Y is a proper subset of X done
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C)
X = Y done
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D)
X and Y are disjoint sets done
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Which one of the following is correct?
A)
\[A\cup P(A)=P(A)(b)\] done
clear
B)
\[A\cap P(A)=A\] done
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C)
\[AP(A)=A\] done
clear
D)
\[P(A)\{A\}=P(A)\] Here P denotes the power set of a set A. done
clear
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If \[(AB)\cup (BA)=A\] for subsets A and B of the universal set U, then which one of the following is correct?
A)
B is proper nonempty subset of A done
clear
B)
A and B are nonempty disjoint sets done
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C)
\[B=\phi \] done
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D)
None of the above done
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What does the shaded region in the Venn diagram given below represent?
A)
\[C\cap (A'\cap B')\] done
clear
B)
\[C\cup (C'\cap A\cap B)\] done
clear
C)
\[C\cup (C\cap A)\cup (C\cap B)\] done
clear
D)
\[C\cup (A/B)\] done
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Let\[n(U)=700,n(A)=200,n(B)=300,n(A\cap B)=100\]then \[n(A'\cap B')\] is equal to
A)
400 done
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B)
600 done
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C)
300 done
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D)
None of these done
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There are 600 student in a school. If 400 of them can speak Telugu, 300 can speak Hindi, then the number of students who can speak both Telugu and Hindi is:
A)
100 done
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B)
200 done
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C)
300 done
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D)
400 done
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In a group of 50 people, two tests were conducted, one for diabetes and one for blood pressure. 30 people were diagnosed with diabetes and 40 people were diagnosed with high blood pressure. What is the minimum number of people who were having diabetes and high blood pressure?
A)
0 done
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B)
10 done
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C)
20 done
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D)
30 done
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Out of 32 persons, 30 invest in national savings certificates and 17 invest in shares. What is the number of persons who invest in both?
A)
13 done
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B)
15 done
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C)
17 done
clear
D)
19 done
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Which of the following is correct?
I. \[n(S\cup T)\] is maximum when n \[n(S\cap T)\] is least, 
II. If \[n(U)=1000,n(S)=720,n(T)=450,\] then least value of \[n(S\cap T)=170.\] 
A)
Only I is true done
clear
B)
Only II is true done
clear
C)
Both I and II are true done
clear
D)
Both I and II are false done
clear
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In a school, there are 20 teachers who teach mathematics of physics of these, 12 teach mathematics and 4 teach both math?s and physics then the number of teachers teaching only physics are
A)
4 done
clear
B)
8 done
clear
C)
12 done
clear
D)
16 done
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Given \[n(U)=20,n(A)=12,n(B)=9,n(A\cap B)=4,\]where U is the universal set, A and B are subsets of U, then \[n({{(A\cup B)}^{c}})=\]
A)
17 done
clear
B)
9 done
clear
C)
11 done
clear
D)
3 done
clear
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In a town of 10000 families, it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% families buy newspaper C, 5% buy A and B, 3% buy B and C and 4% buy A and C. if 2% families buy all of three newspapers, then the number of families which buy A only, is
A)
4400 done
clear
B)
3300 done
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C)
2000 done
clear
D)
500 done
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In a class of 30 pupils, 12 take needle work, 16 take physics and 18 take history. If all the 30 students take at least one subject and no one takes all three then the number of pupils taking 2 subjects is
A)
16 done
clear
B)
6 done
clear
C)
8 done
clear
D)
20 done
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Consider the following statements.
I. If \[{{A}_{n}}\]is the set of first n prime numbers, then \[\underset{n=2}{\overset{10}{\mathop{U}}}\,{{A}_{n}}\]is equal to {2, 3, 5, 7, 11, 13, 17, 19, 23, 29} 
II. If A and B are two sets such that \[n(A\cup B)=50,\]\[n(A)=28,\,\,n(B)=32,\] then \[n(A\cap B)=10.\] Which of these is correct? 
A)
Only I is true done
clear
B)
Only II is true done
clear
C)
Both are true done
clear
D)
Both are false done
clear
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