CBSE Questions for Class 11 Commerce Applied Mathematics Set Theory Quiz 7 - MCQExams.com

If $$A = \{ a, b, p, d\}  B = \{ p, d, e\}  C = \{p, e, f, g\}$$ then find 

$$A \times (B \cap C ) $$ is equal to 
  • $$ (A \times B) \cup (A \times C)$$
  • $$ (A \times B) \cap (A \times C)$$
  • $$ (A \times B) \cap (A \times C)\cap (B\times C)$$
  • none
In a class of 250 students, 175 take mathematics and 142 take science. How many take both mathematics

and science? (All take math and/or science.)
  • 67
  • 75
  • 33
  • 184
  • cannot be determined from information given
If X is a finite set. Let $$P(X)$$ denote the set of all subsets of X and let $$n(X)$$ denote the number of elements in X. If for two finite subsets $$A, B, n(P(A)) = n(P(B)) + 15$$ then $$n(B) = $$ ____, $$n(A) =$$ _____
  • $$n(A) = 4, n(B) = 0$$
  • $$n(A) = 5, n(B) = 0$$
  • $$n(A) = 4, n(B) = 2$$
  • $$n(A) = 6, n(B) = 0$$
If A and B are two sets, where A has more elements than B. Calculate the least possible value of n(A) + n(B), where n(A) is the number of elements in A and n(B) is the number of elements in B.
  • $$n(A)$$
  • $$n(B)$$
  • $$n(A+B)$$
  • None of these
Solve the following inequalities: $$\displaystyle\frac{1}{2-|x|}\geq 1$$.
  • $$x\epsilon (-8, -1]\cup [1,2)$$
  • $$x\epsilon (-2, -1]\cup [1,2)$$
  • $$x\epsilon (-2, -1]\cup [1,6)$$
  • $$x\epsilon (-2, 0]\cup [1,2)$$
Let $$S = \left \{(a, b, c)\epsilon N\times N\times N : a + b + c =a \leq b\leq c\right \}$$ and $$T = \left \{a, b, c)\epsilon N\times N\times N : a, b, c,\ are\ in\ A.P.\right \}$$, where $$N$$ is the set of all natural numbers. Then the number of elements in the set $$S\cap T$$ is
  • $$6$$
  • $$7$$
  • $$13$$
  • $$14$$
If $$A=\left \{ 5,\left \{ 5,6 \right \},7 \right \}$$, which of the following is correct? 
  • $$\left \{ 5,6 \right \}\in A$$
  • $$\left \{ 5 \right \}\in A$$
  • $$\left \{ 7 \right \}\in A$$
  • $$\left \{ 6 \right \}\in A$$
If $$X=\left \{ a,\left \{ b,c \right \},d \right \}$$, which of the following is a subset of $$X$$?
  • $$\left \{ a,b \right \}$$
  • $$\left \{ b,c \right \}$$
  • $$\left \{ c,d \right \}$$
  • $$\left \{ a,d \right \}$$
Which one of the following is a finite set?
  • $$\left \{ x:x\in Z,x< 5 \right \}$$
  • $$\left \{ x:x\in W,x\geq 5 \right \}$$
  • $$\left \{ x:x\in N,x> 10 \right \}$$
  • { $$x:x$$ is an even prime number }
Which one of the following is correct?
  • $$\left \{ x:x^{2}=-1,x\in Z \right \}=\phi$$
  • $$\phi=0$$
  • $$\phi=\left \{ 0 \right \}$$
  • $$\phi=\left \{ \phi \right \}$$
If $$n(A) = 20, n(B) = 30$$ and $$n(A \cup B)= 40$$, then $$n(A \cap B)$$ is equal to: 
  • $$50$$
  • $$10$$
  • $$40$$
  • $$70$$
For any three sets , A B and C, $$B\setminus (A \cup C)$$ is:
  • $$(A\setminus B)\cap (A\setminus C)$$
  • $$(B\setminus A)\cap (B \setminus C)$$
  • $$(B \setminus A)\cap (A\setminus C)$$
  • $$(A\setminus B)\cap (B \setminus C)$$
Let U = { $$x \in N : 1 \le x \le 10 $$ } be the universal set, $$N$$ being the set of natural numbers. If $$A = \{1, 2, 3, 4\}$$ and $$B = \{2, 3, 6, 10\} $$ then what is the complement of $$(A - B)$$ ?
  • $$\{6, 10\}$$
  • $$\{1, 4\}$$
  • $$\{2, 3, 5, 6, 7, 8, 9, 10\}$$
  • $$\{5, 6, 7, 8, 9, 10\}$$
Out of 500 first year students, 260 passed in the first semester and 21 0 passed in the second semester. If 170 did not pass in either semester, how many passed in both semesters ?
  • $$30$$
  • $$40$$
  • $$70$$
  • $$140$$
Which  one of the following is not true? 
  • $$A\setminus B=A\cap B'$$
  • $$A\setminus B=A\cap B$$
  • $$A\setminus B=(A\cup B)\cap B'$$
  • $$A\setminus B=(A\cup B)\setminus B$$
If A and B are finite sets and $$A \subset B$$, then
  • $$n(A \cap B) = \phi$$
  • $$n(A \cup B) = n(B)$$
  • $$n(A \cap B) = n (B)$$
  • $$n(A \cup B) = n (A)$$
The set $$(A\cup B\cup C) \cap (A\cap B'\cap C')\cap C'$$ is equal to?
  • $$B\cap C'$$
  • $$A\cap C$$
  • $$B' \cap C'$$
  • None of these
Let X be a set of $$5$$ elements. The number d of ordered pairs (A, B) of subsets of X such that $$A\neq \Phi, B\neq \Phi, A\cap B=\Phi$$ satisfies.
  • $$50\leq d \leq 100$$
  • $$101\leq d \leq 150$$
  • $$151 \leq d \leq 200$$
  • $$201 \leq d$$
If $$A = \left \{(x, y) : x^{2} + y^{2} \leq 1; x, y \epsilon R\right \}$$ and $$B = \left \{(x, y) : x^{2} + y^{2} \geq 4; x, y \epsilon R\right \}$$, then
  • $$A - B = \phi$$
  • $$B - A = \phi$$
  • $$A\cap B \neq \phi$$
  • $$A\cap B = \phi$$
Consider the following:
$$A\cup \left( B\cap C \right) =\left( A\cap B \right) \cup \left( A\cap C \right) $$
$$A\cap \left( B\cup C \right) =\left( A\cup B \right) \cap \left( A\cup C \right) $$
Which of the above is/are correct?
  • 1 only
  • 2 only
  • Both 1 and 2
  • Neither 1 nor 2
What is the percentage of persons who read only two papers ?
  • $$19\%$$
  • $$31\%$$
  • $$44\%$$
  • None of the above
A market research group conducted a survey of $$1000$$ consumers and reported that $$720$$ consumers like product A and $$420$$ consumers like product B. Then, the least number of consumers that must have liked both the products is.
  • $$140$$
  • $$180$$
  • $$210$$
  • $$190$$
$$ A={1 , 11 , 21 , 31 ,....... , 541 , 551}$$. B is a subset of A such that $$ x+y\neq552$$ , for any $$x , y \epsilon B.$$ The maximum number of elements in B is
  • $$26$$
  • $$30$$
  • $$29$$
  • $$28$$
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?
  • $$0$$
  • $$10$$
  • $$20$$
  • $$30$$
If $$A : \left \{x : x \text { is a multiple of } 3\right \}$$ and $$B = \left \{x : x \text { is a multiple of } 4\right \}$$ and $$C = \left \{x : x \text { is a multiple of } 12\right \}$$, then which one of the following is a null set?
  • $$(A / B) \cup C$$
  • $$(A / B) / C$$
  • $$(A \cap B)\cap C$$
  • $$(A \cap B)/ C$$
In a city, three daily newspapers A, B, C are published, $$42\%$$ read A; $$51\%$$ read B; $$68\%$$ read C; $$30\%$$ read A and B; $$28\%$$ read B and C; $$36\%$$ read A and C; $$8\%$$ do not read any of the three newspapers.
What is the percentage of persons who read only one paper ?
  • $$38\%$$
  • $$48\%$$
  • $$51\%$$
  • None of the above.
If $$a\mathbb{N}=(an:n\in \mathbb{N})$$ and $$b\mathbb{N}\cap c\mathbb{N}=d\mathbb{N}$$, where $$a,b,c\in \mathbb{N}$$ and $$b,c$$ are coprime, then
  • $$b=cd$$
  • $$c=bd$$
  • $$d=bc$$
  • None of these
A college awarded $$38$$ medals in football, $$15$$ in basketball and $$20$$ in cricket. If these medals went to a total of $$58$$ men and only three men got medals in all the three sports. Then the number of students who received medals in exactly two of the three sports, is
  • $$18$$
  • $$15$$
  • $$9$$
  • $$6$$
If $$S$$ is a set with $$10$$ elements and $$A = \left \{(x, y) : x, y\epsilon S, x\neq y\right \}$$, then number of elements in $$A$$ is
  • $$100$$
  • $$90$$
  • $$50$$
  • $$45$$
If $$A=\left\{ a,b,c \right\} ,$$ $$B=\left\{ b,c,d \right\} $$ and $$C=\left\{ a,d,c \right\} $$, then $$\left( A-B \right) \times \left( B\cap C \right) $$ is equal to
  • $$\left\{ \left( a,c \right) ,\left( a,d \right) \right\} $$
  • $$\left\{ \left( a,b \right) ,\left( c,d \right) \right\} $$
  • $$\left\{ \left( c,a \right) ,\left( d,a \right) \right\} $$
  • $$\left\{ \left( a,c \right) ,\left( a,d \right) ,\left( b,d \right) \right\} $$
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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers