CBSE Questions for Class 11 Commerce Applied Mathematics Set Theory Quiz 8 - MCQExams.com

If $$A/B=\left\{ a,b \right\} ,B\setminus A=\left\{ c,d \right\} $$ and $$A\cap B=\left\{ e,f \right\} $$ then the set $$B$$ is equal to
  • $$\left\{ a,b,c,d \right\} $$
  • $$\left\{ e,f,c,d \right\} $$
  • $$\left\{ a,b,e,f \right\} $$
  • $$\left\{ c,d,a,e \right\} $$
  • $$\left\{ d,e,a,b \right\} $$
If $$a.N = \left\{ ax\thinspace :\thinspace x\in N \right\}$$ then $$3N\cap 7N=$$
  • $$21\ N$$
  • $$10\ N$$
  • $$4\ N$$
  • $$none$$
State whether the following statement is true or false.
Whole numbers $$\subseteq$$ natural numbers 
  • True
  • False
Let $$A$$ and $$B$$ be two events such that $$P\left( \overline { A\cup B }  \right) =\dfrac { 1 }{ 6 } ,$$ $$P\left( A\cap B \right) =\dfrac { 1 }{ 4 } $$ and $$P\left( \overline { A }  \right) =\dfrac { 1 }{ 4 } $$, where, $$\overline { A } $$ stands for complement of event $$A$$. Then, event $$A$$ and $$B$$ are
  • Mutually exclusive and independent
  • Independent but not equally likely
  • Equally likely but not independent
  • Equally likely and mutually exclusive
Let $$X$$ and $$Y$$ be two non-empty sets such that $$X\cap A=Y\cap A=\phi$$ and $$X\cup A=Y\cup A$$ for some non-empty set $$A$$. Then which of the following is true?
  • $$X$$ is a proper subset of $$Y$$
  • $$Y$$ is a proper subset of $$X$$
  • $$X=Y$$
  • $$X$$ and $$Y$$ are disjoint sets
  • $${ X }/{ A }=\phi $$
If $$X = \left \{1, 2, 3, ..., 10\right \}$$ and $$A = \left \{1, 2, 3, 4, 5\right \}$$. Then, the number of subsets $$B$$ of $$X$$ such that $$A - B = \left \{4\right \}$$ is
  • $$2^{5}$$
  • $$2^{4}$$
  • $$2^{5} - 1$$
  • $$1$$
  • $$2^{4} - 1$$
If the sets $$A$$ and $$B$$ are as follows:
$$A=\left\{ 1,2,3,4 \right\} ,B=\left\{ 3,4,5,6 \right\} $$, then
  • $$A-B=\left\{ 1,2 \right\} $$
  • $$B-A=\left\{ 5,6 \right\} $$
  • $$\left[ \left( A-B \right) -\left( B-A \right) \right] \cap A=\left\{ 1,2 \right\} $$
  • $$\left[ \left( A-B \right) -\left( B-A \right) \right] \cup A=\left\{ 3,4 \right\} $$
If $$n(A)=10,n(B)=6$$ and $$(C)=5$$ for three disjoint sets $$A,B,C$$ then $$n(A\cup B\cup C)$$ equals
  • $$21$$
  • $$11$$
  • $$1$$
  • $$9$$
The total number of subsets of {1, 2, 6, 7} are?
  • $$16$$
  • $$8$$
  • $$64$$
  • $$32$$
If U = {1, 3, 5, 7, 9, 11, 13}, then which of the following are subsets of U. 
B = {2, 4} 
A = {0}
C = {1, 9, 5, 13}
D = {5, 11, 1} 
E = {13, 7, 9, 11, 5, 3, 1} 
F = {2, 3, 4, 5} 
  • $$A$$ and $$B$$
  • $$C$$, $$D$$ and $$E$$
  • $$A$$ and $$D$$
  • only $$A$$
Let $$S = \left \{(a, b): a, b\epsilon Z, 0\leq a, b\leq 18\right \}$$. The number of elements $$(x, y)$$ in $$S$$ such that $$3x + 4y + 5$$ is divided by $$19$$ is
  • $$38$$
  • $$19$$
  • $$18$$
  • $$1$$
 State whether true or false. 
 Quadrilateral $$\subseteq$$ polygon 
  • True
  • False
If $$a, b, c, d$$ are four distinct numbers chosen from the set $$\left \{1, 2, 3, ..., 9\right \}$$, then the minimum value of $$\dfrac {a}{b} + \dfrac {c}{d}$$ is
  • $$\dfrac {3}{8}$$
  • $$\dfrac {1}{3}$$
  • $$\dfrac {13}{36}$$
  • $$\dfrac {25}{72}$$
Let $$A,B$$ and $$C$$ be three events such that $$P(A)=0.3,P(B)=0.4,P(C)=0.8,P(A\cup B)=0.08,\quad P(A\cap C)=0.28,P(A\cap B\cap C)=0.09$$. If $$P(A\cup B\cup C)\ge 0.75$$, then $$P(B\cap C)$$ satisfies
  • $$P(B\cap C)\le 0.23$$
  • $$P(B\cap C)\le 0.48\quad $$
  • $$0.23\le P(B\cap C)\le 0.48$$
  • $$0.23\le P(B\cap C)\ge 0.48$$
A set of $$n$$ numbers has the sum $$s$$. Each number of the set is increased by $$20$$, then multiplied by $$5$$, and then decreased by $$20$$. The sum of the numbers in the new set thus obtained is:
  • $$s+20n$$
  • $$5s+80n$$
  • $$s$$
  • $$5s$$
If $$A= \{x:x$$ is a multiple of $$2\}, \,\,B= \{x:x$$ is a multiple of $$5\}$$ and $$C = \{x:x$$ is a multiple of 10$$\}$$, then $$ A\cap (B\cap C)$$ is equal to 
  • $$A$$
  • $$B$$
  • $$C$$
  • $$\{x:x$$ is a multiple of $$100\}$$
If $$X=\left\{ { 4 }^{ n }-3n-1;n\in R \right\} $$ and $$Y=\left\{ 9\left( n-1 \right) ;n\in N \right\} $$, then $$X\cap Y=$$
  • $$X$$
  • $$Y$$
  • $$\phi $$
  • $$\left\{ 0 \right\} $$
In the equation $${ \left( x-m \right)  }^{ 2 }-{ \left( x-n \right)  }^{ 2 }={ \left( m-n \right)  }^{ 2 }$$, $$m$$ is a fixed positive number, and $$n$$ is a fixed negative number. The set of values $$x$$ satisfying the equation is:
  • $$x\ge 0$$
  • $$x\le n$$
  • $$x=0$$
  • the set of all real numbers
  • none of these
The number of binary operations on the set $$\{1, 2, 3\}$$ is _________.
  • $$3^9$$
  • $$9^3$$
  • $$27$$
  • $$3!$$
Choose the correct answers from the alternatives given.
Directions for questions $$71$$ to $$75$$ : Study the pie chart carefully to answer the questions that follow.
Percentage distribution of students in different courses.
What is the value of half of the difference between the number of students in MBA and MBBS?
The Total number of student = $$6500$$

901469_958955978534499c93e4691511a47474.png
  • $$800$$
  • $$1600$$
  • $$1300$$
  • $$650$$
The relation $$S=\{(3, 3), (4, 4)\}$$ on the set $$A=\{3, 4, 5\}$$ is __________.
  • Not reflexive but symmetric and transitive
  • Reflexive only
  • Symmetric only
  • An equivalence relation
If $$M = \left\{ {x:x \geqslant 7\,\,{\text{and}}\,x \in N} \right\}$$ for universal set of natural numbers, then $$M'$$ is
  • $$\left\{ {1,2,3,4,5} \right\}$$
  • $$\left\{ {1,2,3,4,5,6,7} \right\}$$
  • $$\left\{ {1,2,3,4,5,6} \right\}$$
  • $$\left\{ {0,1,2,3,4,5,6} \right\}$$
If $$X$$ and $$Y$$ are two sets, then $$X\cap \left( X\cup Y \right)$$ equals
  • $$X$$
  • $$Y$$
  • $$\phi$$
  • $$None\ of\ these$$
Let $$A=\left\{ \left( x,y \right) :y={ e }^{ x },x\in R \right\}$$
      $$B=\left\{ \left( x,y \right) :y={ e }^{ -x },x\in R \right\}$$. Then 
  • $$A\cap B=\phi$$
  • $$A\cap B\neq \phi$$
  • $$A\cup B={ R }^{ 2 }$$
  • $$none\ of\ these$$
If a relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B is
  • $$2^{mn}$$
  • $$2^{mn}-1$$
  • 2 mn
  • $$m^n$$
If $$X$$ and $$Y$$ are two sets, then $$X\cap \left( Y\cup X \right)'$$ equals
  • $$X$$
  • $$Y$$
  • $$\phi$$
  • $$None\ of\ these$$
If X = {$$4^n \,-\,3n\,-\,1\,:\,\epsilon N$$} and
 Y = {$$9(n\,-\,1) \,:\,\epsilon N$$}
then $$X\subset Y$$ 
  • True
  • False
Given : A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}
Find : $$(A \, \times \, B) \, \cap \, (B \, \times \, C)$$.
  • {4,4}
  • {3,4}
  • {3,4}, {3,3}
  • {3,3}
Let $$A=\left\{ x:x\ \in\ R,\left| x \right| <1 \right\}$$
$$B=\left\{ x:x\ \in\ R,\left| x-1 \right| \ge 1 \right\}$$
and $$A\cup B=R-D$$, then set $$D$$ is
  • $$\left\{ x:1 < x \le 2 \right\}$$
  • $$\left\{ x:1\le x<2 \right\}$$
  • $$\left\{ x:1\le x\le 2 \right\}$$
  • None of these
If X and Y are two sets such that n(X)=17, n(Y)=23 and n(X $$\cup$$ Y)=38, find n(X $$\cap$$ Y).
  • $$2$$
  • $$4$$
  • $$6$$
  • $$8$$
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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers