CBSE Questions for Class 11 Commerce Applied Mathematics Set Theory Quiz 6 - MCQExams.com

Suppose $$\displaystyle A_{1},A_{2}.....A_{30}$$ are thirty sets having 5 elements and $$\displaystyle B_{1},B_{2}....B_{n}$$ are n sets each with 3 elements. Let $$\displaystyle \bigcup_{i=1}^{30}Ai=\bigcup_{i=1}^{n}Bj=S$$ and each elements of S belongs to exactly 10 of the Ai's and exactly 9 of the Bj's. Then n is equal to 
  • 35
  • 45
  • 55
  • 65
S = {1, 2, 3, 5, 8, 13, 21, 34}. Find $$\displaystyle \sum max\left ( A \right )$$ where the sum is taken over all 28 two elements subsets A to S
  • 844
  • 480
  • 484
  • 488
Given n(A) = 11, n(B) = 13, n(C) = 16, $$\displaystyle n\left ( A\cap B \right )=3,n\left ( B\cap C \right )=6,n\left ( A\cap C \right )=5\: \: and\: \: n\left ( A\cap B\cap C \right )=2$$ then the value of $$\displaystyle n [ A\cup B \cup C ]=$$
  • $$24$$
  • $$27$$
  • $$25$$
  • $$28$$
In a group, if 60% of people drink tea and 70% drink coffee. What is the maximum possible percentage of people drinking either tea or coffee but not both?
  • $$100\%$$
  • $$70\%$$
  • $$30\%$$
  • $$10\%$$
If A and B are two disjoint sets and N is universal set, then $$\displaystyle A^{\circ}\cup \left [ \left ( A\cup B \right )\cap B^{\circ} \right ]$$ is 
  • $$\displaystyle \phi $$
  • $$A$$
  • $$B$$
  • $$N$$
If out of 150 students who read at least one newspaper The Times of India, The Hindustan Times and The Hindu. There are 65 who read The Times of India, 41 who read The Hindu and 50 who read The Hindustan Times. What is the maximum possible number of students who read all the three newspaper?
  • $$7$$
  • $$42$$
  • $$3$$
  • Cannot be determined
Find the number of students that had taken only mathematics
  • 2
  • 3
  • 4
  • 5
Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in $$A\cup B$$ ? 
  • $$9$$
  • $$6$$
  • $$3$$
  • $$18$$
How many subsets can be formed from the set $$\left \{p, q, r\right \}$$ is?
  • 6
  • 7
  • 8
  • 9
If $$A=\left \{1, 2, 3, .....9\right \}$$ and $$B=\left \{2, 3, 4, 5, 7, 8\right \}$$, then A-B is given by
  • $$\left \{1, 6, 7, 8\right \}$$
  • $$\left \{1, 6, 9\right \}$$
  • $$\left \{1, 9\right \}$$
  • $$\left \{6, 9\right \}$$
Let $$ S=\left\{1,2,3,.....40\right\} $$ and let $$A$$ be a subset of $$S$$ such that no two elements in $$A$$ have their sum divisible by $$5$$ What is the maximum number of elements possible in $$A$$?
  • $$10$$
  • $$13$$
  • $$17$$
  • $$20$$
Look at the set of numbers below.
Set : $$\left \{6, 12, 30, 48\right\}$$
Which statement about all the numbers in this set is NOT true?
  • They are all multiples of $$3$$
  • They are all even numbers
  • They are all factors of $$48$$
  • They are all divisible by $$2$$
Let $$A$$ and $$B$$ be two sets such that $$n(A)=16$$, $$n(B)=12$$, and $$n(A\cap B)=8$$. Then $$n(A\cup B)$$ equals
  • $$28$$
  • $$20$$
  • $$36$$
  • $$12$$
If A={a,b,c,d,e}, B={a,c,e,g} and C={b,d,e,g}  then which of the following is true?
  • $$\displaystyle C\subset \left ( A\cup B \right )$$
  • $$\displaystyle C\subset \left ( A\cap B \right )$$
  • $$\displaystyle A\cup B=A\cup C$$
  • Both(1) and (3)
Let $$A=\{1,2,3,4,5,6\}$$. How many subsets of $$A$$ can be formed with just two elements, one even and one odd?
  • $$6$$
  • $$8$$
  • $$9$$
  • $$10$$
In a class 60% of the students were boys and 30% of them had I class. If 50%of the students in the class had I class, find the fraction of the girls in the class who did not have a I class.
  • $$1/5$$
  • $$4/5$$
  • $$1/4$$
  • $$1/3$$
The sets $$\displaystyle S_{x}$$ are defined to be $$(x, x + 1, x + 2, x + 3, x + 4)$$ where $$x=1, 2, 3,.....80$$. How many of these sets contain $$6$$ or its multiple? 
  • $$65$$
  • $$66$$
  • $$59$$
  • $$60$$
If $$A=\{\dots,-6,-4,-2,0,2,4,6,\dots\}$$, then
  • $$10\notin A$$
  • $$-10\notin A$$
  • $$5\in A$$
  • $$50\in A$$
If $$\displaystyle Q=\left((x|x=\frac{1}{y}\:\ \text{wher} \ e\:y\in N\right)$$, then
  • $$0\notin Q$$
  • $$1\in Q$$
  • $$2\in Q$$
  • $$\displaystyle\frac{2}{3}\in Q$$
If the universal set is U = $$ \displaystyle \left \{ 1^{2},2^{2},3^{2},4^{2},5^{2},6^{2} \right \}  $$   What is the complement of the intersection of set A = $$ \displaystyle \left \{ 2^{2},4^{2},6^{2} \right \}  $$ and set B=$$ \displaystyle \left \{ 2^{2},3^{2},4^{2} \right \}  $$ ?  
  • $$ \displaystyle \left \{ 2^{2},4^{2} \right \} $$
  • $$ \displaystyle \left \{ 1^{2},5^{2} \right \} $$
  • $$ \displaystyle \left \{ 1^{2},5^{2},6 ^{2} \right \} $$
  • $$ \displaystyle \left \{ 1^{2},3^{2},5^{2},6^{2} \right \} $$
  • Answer required
Three sets $$A, B, C$$ are such that $$\displaystyle A=B\cap C$$ and $$\displaystyle B=C\cap A$$, then
  • $$\displaystyle A\subset B$$
  • $$\displaystyle A\supset B$$
  • $$\displaystyle A\equiv B$$
  • $$\displaystyle A\subset { B }^{ \prime }$$
P, Q and R are three sets and $$\xi = P\cup Q\cup R$$. Given that $$n(\xi) = 60, n (P\cap Q) = 5, n(Q\cap R) = 10, n(P) = 20$$ and $$n(Q) = 23$$, find $$n(P\cup R)$$
514849.jpg
  • $$37$$
  • $$38$$
  • $$45$$
  • $$52$$
If n is a member of both set A$$=\left\{\displaystyle\frac{4}{7}, 1, \frac{5}{2}, 4, \frac{1}{2}, 7\right\}$$ and set B$$=\left\{\displaystyle\frac{4}{7}, \frac{7}{4}, 4, 7\right\}$$, which of the following must be true?
I. n is an integer.
II. $$4n$$ is an integer.
III. $$n=4$$
  • None
  • II only
  • I and II only
  • I and III only
  • I, II, and III
If A is a finite set, let $$P(A)$$ denote the set all subsets of A and $$n(A)$$ denote the number of elements in A. If for two finite sets X and Y, $$n[P(X)] = n[P(Y)] + 15$$ then find $$n(X)$$ and $$n(Y)$$
  • $$n(X) = 4; n(Y) = 0$$
  • $$n(X) = 5; n(Y) = 0$$
  • $$n(X) = 6; n(Y) = 0$$
  • $$n(X) = 7; n(Y) = 0$$
If the universal set $$\{x\in W ,3<x≤12\} ,A=\{5,7,9\}$$, then $$A'=$$
  • $$\{3,6,8,10,11,12\}$$
  • $$\{4,6,8,10,11,12\}$$
  • $$\{6,8,10,11,12\}$$
  • None of the above
$$(P\cap Q)' \cup R$$
  • $$\left \{a, c, e, f, g, h, i, j\right \}$$
  • $$\left \{a, c, d, e, f, h, i, j\right \}$$
  • $$\left \{a, c, d, e, f, g, h, j\right \}$$
  • $$\left \{a, c, d, e, f, g, h, i, j\right \}$$
The number of subsets of the set $$\left \{ 10,11,12 \right \}$$ is
  • $$7$$
  • $$3$$
  • $$8$$
  • $$6$$
For any two sets $$A$$ and $$B$$, $$A-\left( A-B \right) $$ equals
  • $$B$$
  • $$A-B$$
  • $$A\cap B$$
  • $${ A }^{ C }\cap { B }^{ C }$$
If $$A$$ and $$B$$ are any two sets, then state the following statement is true/false 
$$A - (A - B) = A\cap B$$
  • True
  • False
In a class, $$20$$ opted for Physics, $$17$$ for Maths, $$5$$ for both and $$10$$ for other subjects. The class contains how many students?
  • $$35$$
  • $$42$$
  • $$52$$
  • $$60$$
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers