CBSE Questions for Class 11 Commerce Applied Mathematics Set Theory Quiz 9 - MCQExams.com

If sets $$A$$ and $$B$$ are define as
$$A=\left\{ \left( x,y \right) :y={ e }^{ x },x\in R \right\}$$
$$B=\left\{ \left( x,y \right) :y=x,x\in R \right\}$$, then 
  • $$B\subset A$$
  • $$A\subset B$$
  • $$A\cap B=\phi$$
  • $$A\cup B=A$$
Range of the function f(x) = cos (K sinx) is [-1, 1], then the positive integral value of K can be?
  • 1
  • 2
  • 5
  • 4
Suppose $${A_1},{A_2},...,{A_{30}}$$ are thirty sets each having 5 elements and $${B_1},{B_2},...,{B_n}$$ are $$n$$ sets each with 3 elements, let $$\bigcup\limits_{i = 1}^{30} {{A_i}}  = \bigcup\limits_{i = 1}^n {Bj}  = S$$ and each element of $$S$$ belongs to exactly 10 of the $${A_i}'s$$ and exactly 9 of the $$B,'s$$. Then $$n$$ is equal to 
  • $$15$$
  • $$3$$
  • $$45$$
  • $$35$$
Consider the word $$W=MISSISSIPPI$$.
If $$N$$ denotes the number of different selections of $$5$$ letters from the word $$W = MISSISSIPPI$$ then $$N$$ belongs to the set,
  • $$\{ 15,\ 16,\ 17,\ 18,\ 19\} $$
  • $$\{ 20,\ 21,\ 22,\ 23,\ 24\} $$
  • $$\{ 25,\ 26,\ 27,\ 28,\ 29\} $$
  • $$\{ 30,\ 31,\ 32,\ 33,\ 34\} $$
If $$X =\{1,2,3,4,5,6,7,8,9, 10\}$$ is the universal set and$$ A= \{1, 2, 3,4\}, B= \{2,4,6,8\}, C= \{3,4,5,6\}$$  verify the following.
(a) $$A \cup (B\cup C) = (A \cup B) \cup C$$
(b)$$A \cap (B\cup C) = (A \cap B) \cup (A \cap C)$$
(c) $$(A')' =A$$
  • Only a is true
  • Only b and c are true
  • Only a and b are true
  • All three a,b and c are true.
In certain town, $$25\%$$ families own a cell phone, $$15\%$$ families own a scooter and $$65\%$$ families own neither a cell phone nor a scooter. If $$1500$$ families own both a cell phone and a scooter, then the total number of families in the town is:
  • $$10000$$
  • $$20000$$
  • $$30000$$
  • $$50000$$
If $$A \subset B$$, then
  •  $$C - B \subset C - A$$.
  • $$A \cup B = A$$
  • $$A \cap B = B$$
  • None
If two sets $$A$$ and $$B$$ are having $$99$$ elements in common, then the number of ordered pairs common to each of the sets $$AxB$$ and $$BxA$$ are
  • $$2^{99}$$
  • $$99^{2}$$
  • $$100$$
  • $$18$$
The set of all $$x$$ for which $$1 + \log x < x$$ is
  • $$(1, \infty)$$
  • $$(0, 1)$$
  • $$(0, \infty)$$
  • None of these
If $$\alpha,\xi,\eta$$ are non-empty sets then:
  • $$(\alpha \times \beta)\cup (\xi \times \eta)=(\alpha \times \beta)\cap (\xi \times \eta)$$
  • $$(\alpha \times \beta)\cap (\xi \times \eta)=(\alpha \times \beta)\cap (\xi \times \eta)$$
  • $$(\alpha \cap \beta)\cup (\xi \cap \eta)=(\alpha \times \beta)\cup (\xi \times \eta)$$
  • $$(\alpha \cap \beta)= (\xi \cap \eta)=(\alpha \times \beta)\cup (\xi \times \eta)$$
$$S_1:(p\Rightarrow q) V ( q \Rightarrow p )$$ is a tautology.
$$S_2: ((p\Rightarrow q) V ( q \Rightarrow p))$$ is a fallacy
  • $$S_1$$ is true, $$S_2$$ is false
  • $$S_1$$ false
  • $$S_1$$ is false, $$S_2$$ is false
  • $$S_1$$ is true
$$If\,A = \left\{ {\left( {x,y} \right)\,\left| {{x^2} + {y^2} \le \left. 4 \right\}\,and} \right.} \right.$$
$$B = \left\{ {\left( {x,y} \right)\,\left| {{{(x - 3)}^2} + {y^2}} \right. \le \left. 4 \right\}} \right.\,and\,the$$
$$po{\mathop{\rm int}} \,P\left( {a,\frac{1}{2}} \right)\,belongs\,to\,the\,set\,B - A$$ then the set of possible real values of $$a$$ is
  • $$\left( {\frac{{1 + \sqrt {3} }}{4},\frac{{7 + \sqrt 7 }}{4}} \right)$$
  • $$\left( {\frac{{7 - \sqrt 7 }}{4},\frac{{1 + \sqrt 7 }}{4}} \right)$$
  • $$\left( {\frac{{1 - \sqrt {31} }}{4},\frac{{7 - \sqrt 7 }}{4}} \right)$$
  • none of these
In a selection process, a hundred candidate participate in Group Discussion sessions (GD) and Personal Interview (PI). The possibilities of a candidate's good performance in GD and in PI are independent of each other. It was found that $$20$$ candidates were good in GD and $$30$$ were good in PI. The number of candidates good in both GD and PI is expected to be about:
  • $$6$$
  • $$10$$
  • $$20$$
  • $$30$$
Let $$A\subset B$$ then $$A'\cap B'=$$
  • $$A'$$
  • $$B'$$
  • $$B$$
  • none of these
$$s = \{ x \in N:2 + {\log _2}\sqrt {x + 1}  > 1 - {\log _{1/2}}\sqrt {4 - {x^2}} \} $$ , then
  • $$S={ 1 }$$
  • $$S=Z$$
  • $$S=N$$
  • none of these
Let $$S=\{1,2,3,4,5,6,7\}$$ and let $$A=\{2,5,7\}$$ then $$A'$$ is
  • $$\{1,3,6\}$$
  • $$\{1,3,4,6\}$$
  • $$\{1,4,6\}$$
  • none of these
If AandB are subsects of the universal set X and n(X)=$$50,$$n(A)=$$35$$,n(B)=20 Find
$$n(A\bigcup {B)} $$
$$n(A\bigcap {B)} $$
$$n(A`\bigcap {B)} $$
$$n(A\bigcap {B`} )$$
  • $$ 45,10,10,25 $$
  • $$ 45,10,10,20 $$
  • $$ 40,10,10,25 $$
  • $$ 45,10,15,25 $$
For any two sets A and B, A' - B' is equal to
  • A -B
  • B - A
  • A - A'
  • A - B'
Let $$A=\{x:x\in R\  \&\ x^2+1=0\}$$ then $$A$$ is a null set.
  • True
  • False
$$|x|$$ represent number of elements in region X. Now the following conditions are given
$$|U|=14$$, $$|(A-B)^C|=12$$, $$|A\cup B|=9$$ and $$|A\Delta B|=7$$, where A and B are two subsets of the universal set U and $$A^C$$ represents complement of set A, then?
  • $$|A|=2$$
  • $$|B|=5$$
  • $$|A|=4$$
  • $$|B|=7$$
If $$A=\{4^n-3n-1:n\in N\}$$ and $$B=\{9(n-1): n\in N\}$$, then?
  • $$B\subset A$$
  • $$A\cup B = N$$
  • $$A\subset B$$
  • None of these
$$A \cup B= A \cap B$$ if : 
  • $$A\supset B$$
  • $$A=B$$
  • $$A\subset B$$
  • $$A \subseteq B$$
 Let $$N$$ be the set of non-negative integers, $$I$$ the set of integers,$$N_p$$ the set of non-positive integers, $$E$$ the set of even integers and $$P$$ the set of prime numbers. Then
  • $$I-N=N_p$$
  • $$N \cap {N_p} = \phi $$
  • $$E \cap P = \phi $$
  • $$N\Delta {N_p} = 1 - \{ 0\} $$
The set which begins with additive identity is 
  • W
  • N
  • Q
  • Z
If $$A$$ and $$B$$ are events such that
$$P(A\cup B)=\cfrac{3}{4},P(A\cap B)=\cfrac{1}{4},P(\overline { A } )=\cfrac{2}{3}$$, then $$P(\overline { A } \cap B)$$ is
  • $$\cfrac{5}{12}$$
  • $$\cfrac{3}{8}$$
  • $$\cfrac{5}{8}$$
  • $$\cfrac{1}{4}$$
If set 's' contains all the real values of x for which $$log_ {(2x+3)^{x^2}}<1$$ is true, then set 'S' contain:
  • $$(log_25,log_2 7)$$
  • $$[log_34,log_3 8]$$
  • $$\left(\dfrac{-3}{2},1\right)$$
  • $$(-1,0)$$
Events $$A$$ and $$C$$ are independent. If the probabilities relating $$A,B$$  and $$C$$ are $$P\left( A \right) = \dfrac{1}{5},\,\,P\left( B \right) = \dfrac{1}{6},$$ $$P\left( {A \cap C} \right) = \dfrac{1}{20},\,P\left( {B \cup C} \right) = \dfrac{3}{8}$$ then
  • events $$B$$ and $$C$$ are independent
  • events $$B$$ and $$C$$ are mutually exclusive
  • events $$B$$ and $$C$$ are neither independent nor mutually exclusive
  • events $$B$$ and $$C$$ are equiprobable
If $$A\ and\ B$$ are any two sets, then 
(i) $$ A\subset A\cup B$$
(ii) $$ A\cup A\subset B$$
both relation is ?
  • True
  • False
Let $$A=\left\{ 1,2,3,4 \right\} ,B=\left\{ 2,4,6 \right\} $$. Then the number of sets $$C$$ such that $$A\cap B\subseteq C\subseteq A\cup B$$ is
  • $$6$$
  • $$9$$
  • $$8$$
  • $$10$$
The set $$ \left( A\cup B\cup C \right) \cap \left( A\cap B'\cap C' \right) '\cap C'$$ is equal to 
  • $$ B\cap C'$$
  • $$ A\cap C'$$
  • $$ B\cap C$$
  • $$A\cap B\cap C'$$
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers