CBSE Questions for Class 11 Engineering Maths Sets Quiz 8 - MCQExams.com

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
If $$A=\begin{Bmatrix}x\in R : x^2+6x-7<0\end{Bmatrix}$$ and $$B=\begin{Bmatrix}x\in R : x^2+9x+14<0\end{Bmatrix}$$, then which of the following is/are correct?
$$(A\cap B)=(-2, 1)$$
$$(A \setminus B)=(-7, -2)$$
Select the correct answer using the code given below :
  • 1 only
  • 2 only
  • Both 1 and 2
  • Neither 1 nor 2
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.
  • $$140$$
  • $$180$$
  • $$210$$
  • $$190$$
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?
  • $$0$$
  • $$10$$
  • $$20$$
  • $$30$$
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
  • $$\left\{ \left( a,c \right) ,\left( a,d \right) \right\} $$
  • $$\left\{ \left( a,b \right) ,\left( c,d \right) \right\} $$
  • $$\left\{ \left( c,a \right) ,\left( d,a \right) \right\} $$
  • $$\left\{ \left( a,c \right) ,\left( a,d \right) ,\left( b,d \right) \right\} $$
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
  • $$\left\{ a,b,c,d \right\} $$
  • $$\left\{ e,f,c,d \right\} $$
  • $$\left\{ a,b,e,f \right\} $$
  • $$\left\{ c,d,a,e \right\} $$
  • $$\left\{ d,e,a,b \right\} $$
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
The relation R defined on set A = {1, 2, 3, 4, 5} is defined by R = $${(x, y): |x^2 - y^2| > 4}$$. Which of the following could be the range of relation R?
  • {4, 5}
  • {3, 4, 5 }
  • {1, 2, 3, 4, 5 }
  • {1, 2}
$$ A={1 , 11 , 21 , 31 ,....... , 541 , 551}$$. 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
  • $$26$$
  • $$30$$
  • $$29$$
  • $$28$$
State whether the following statement is true or false.
Whole numbers $$\subseteq$$ natural numbers 
  • True
  • False
If $$a.N = \left\{ ax\thinspace :\thinspace x\in N \right\}$$ then $$3N\cap 7N=$$
  • $$21\ N$$
  • $$10\ N$$
  • $$4\ N$$
  • $$none$$
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
  • $$P(B\cap C)\le 0.23$$
  • $$P(B\cap C)\le 0.48\quad $$
  • $$0.23\le P(B\cap C)\le 0.48$$
  • $$0.23\le P(B\cap C)\ge 0.48$$
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