MCQExams
0:0:1
CBSE
JEE
NTSE
NEET
Practice
Homework
×
CBSE Questions for Class 11 Engineering Maths Sets Quiz 11 - MCQExams.com
CBSE
Class 11 Engineering Maths
Sets
Quiz 11
If $$A=\left\{1, 2, 3, 4\right\}$$, then the number of subsets of $$A$$ that contain the element $$2$$ but not $$3$$, is
Report Question
0%
$$16$$
0%
$$4$$
0%
$$8$$
0%
$$24$$
Explanation
The subsets are be $$\left\{1, 2, 4\right\},\left\{1, 2\right\}, \left\{2, 4\right\}, \left\{2\right\}$$
Number of subsets of $$A$$ that contain the element $$2$$ but not $$3$$ is $$4$$
Let $$p$$ and $$q$$ be two statements. amongst the following, the statement is equivalent to $$p\rightarrow q$$ is
Report Question
0%
$$\displaystyle p\wedge \sim q$$
0%
$$\displaystyle \sim p\vee q$$
0%
$$\displaystyle \sim p\wedge q$$
0%
$$\displaystyle p\vee \sim q$$
Explanation
$$ \begin{array}{l} \text { Given, } \quad P \longrightarrow q \\ \text { ne trinow that, } \rightarrow \text { - if then } \\ \Rightarrow \text { if } P \text { then } q \end{array} $$
$$ \begin{array}{lll} p & q & p \rightarrow q \\ 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{array} $$
$$ \begin{array}{c} \Rightarrow \text { Evaluating option } A(p \wedge \sim q) \\ P \text { iq } p \wedge \sim q \\ 111 & 1 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \\ 1 & 0 & 0 \\ \text { Incorrect assumption } \end{array} $$
$$ \begin{array}{c} \Rightarrow \text { Eualuating } B(\sim p \wedge q) \\ \sim p \quad q \quad \sim p \wedge q \\ 0 \\ 0 \\ 1 \\ 1 \quad 0 \\ \text { Incorrect assumption } \end{array} $$
$$ \begin{array}{rlrl} \Rightarrow \text { Evaluating } & c(\sim p \vee q) \\ & \sim p & q & \sim p v q \\ & 0 & 1 & & \\ 0 & 0 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & 1 \\ & \text { correct assumption } \end{array} $$
If $$A=\left\{ 1,3,5,7,9,11,13,15,17 \right\} ,B=\left\{ 2,4,....,18 \right\} $$ and N is the universal set, then $$A'\cup \left( \left( A\cup B \right) \cap B' \right) $$
Report Question
0%
A
0%
N
0%
B
0%
R
Explanation
$$A=\left\{1,3,5,7,9,11,13,15,17\right\}$$
$${A}^{\prime}=N-A=N-\left\{1,3,5,7,9,11,13,15,17\right\}=\left\{2,4,6,8,10,12,14,16,18\right\}$$
$$A\cup B=\left\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18\right\}$$
$${B}^{\prime}=N-B=N-\left\{2,4,6,8,10,12,14,16,18\right\}=\left\{1,3,5,7,9,11,13,15,17\right\}$$
$$\left(A\cup B\right)\cap {B}^{\prime}$$
$$=\left\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18\right\}\cap\left\{1,3,5,7,9,11,13,15,17\right\}$$
$$=\left\{1,3,5,7,9,11,13,15,17\right\}$$
$${A}^{\prime}\cup \left(\left(A\cup B\right)\cap {B}^{\prime}\right)$$
$$=\left\{2,4,6,8,10,12,14,16,18\right\}\cup\left\{1,3,5,7,9,11,13,15,17\right\}$$
$$=\left\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18\right\}=N$$
Number of functions from Set-A containing $$5$$ elements to a set-$$B$$ containing $$4$$ elements is
Report Question
0%
$${5}^{4}$$
0%
$${4}^{5}$$
0%
$$4!$$
0%
$$5!$$
If $$A=\left\{ 1,2,4 \right\} ,B=\left\{ 2,4,5 \right\} $$ and $$C=\left\{ 2,5 \right\} $$, then $$\left( A-B \right) \times \left( B-C \right) =$$
Report Question
0%
$$\left\{ \left( 1,2 \right) ,\left( 1,5 \right) ,\left( 2,5 \right) \right\} $$
0%
$$\left\{ \left\{ 1,4 \right\} \right\} $$
0%
$$\left( 1,4 \right) $$
0%
$$\left\{ \left( 1,2 \right) \right\} $$
Explanation
$$A=\left\{1,2,4\right\}$$ and $$B=\left\{2,4,5\right\}$$
$$A-B=\left\{1,2,4\right\}-\left\{2,4,5\right\}=\left\{1\right\}$$
$$B=\left\{2,4,5\right\}$$ and $$C=\left\{2,5\right\}$$
$$B-C=\left\{2,4,5\right\}-\left\{2,5\right\}=\left\{4\right\}$$
$$\left(A-B\right)\times\left(B-C\right)=\left\{1\right\}\times \left\{4\right\}=\left(1,4\right)$$
{$$x \epsilon R : \dfrac{14x}{x+1} - \dfrac{9x-30}{x-4} <0$$ } is equal to
Report Question
0%
$$(-1, 4)$$
0%
$$(1, 4) \cup (5, 7)$$
0%
$$(1, 7)$$
0%
$$(-1, 1) \cup (4, 6)$$
Explanation
Given,
$$\dfrac{14x}{x+1}-\dfrac{9x-30}{x-4}<\:0$$
$$\dfrac{5x^2-35x+30}{\left(x+1\right)\left(x-4\right)}<0$$
$$\dfrac{(x-1)(x-6)}{\left(x+1\right)\left(x-4\right)}<0$$
For $$(x-1),(x-6)$$ and $$(x+1),(x-4)$$ we get,
$$-1<x<1\quad \mathrm{or}\quad \:4<x<6$$
$$\begin{bmatrix}\mathrm{Solution:}\:&\:-1<x<1\quad \mathrm{or}\quad \:4<x<6\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-1,\:1\right)\cup \left(4,\:6\right)\end{bmatrix}$$
$$A = \{ a , e , i , o , u \} , B = \{ a , i , u \}$$, then $$B - A.$$
Report Question
0%
$$\{ e , o \}$$
0%
$$\{ a , i , u \}$$
0%
$$\{ o \}$$
0%
$$\{ \}$$
If $$a * b = 2 ^ { a b }$$ on $$N \cup \{ 0 \}$$ then $$*$$ is
Report Question
0%
commutative
0%
associate
0%
$$(a) \& (b)$$ both
0%
none of these
The number of finctions ffrom the set A = { 0,1,2 } into the set B ={ 0,1,2,3,4,5,6,7} such that $$ f ( i ) \leq f ( i ) $$ for $$ i < j \text { and, } i , j , \in A $$
Report Question
0%
$$
^ { 8 } C _ { 3 }
$$
0%
$$
^ { 8 } C _ { 3 } + 2 \left( ^ { 8 } C _ { 2 } \right)
$$
0%
$$
^ { 10 } C _ { 3 }
$$
0%
None of these
If $$A = \{ 2,3,4,5,7 \} , B = \{ 7,8,9 \}$$, then find $$n ( A \cup B ).$$
Report Question
0%
$$1$$
0%
$$3$$
0%
$$5$$
0%
$$7$$
Explanation
$$A=\left \{ 2,3,4,5,7 \right \}$$
$$n(A)=5$$
$$B=\left \{ 7,8,9 \right \}$$
$$n(B)= 3$$
$$n(A \cap B)=1$$
$$\therefore (A\cup B)=n(A)+n(B)-n(A\cap B)$$
$$(A\cup B)=5+3-1=7$$
If $$I$$ is the set of isosceles triangle and $$E$$ is the equilateral triangles then _____________.
Report Question
0%
$$I\subset E$$
0%
$$E \subset I$$
0%
$$E=I$$
0%
None of these
Explanation
Given,
$$I$$ is the set of isosceles triangle and $$E$$ is the equilateral triangles.
We know that every equilateral triangle is an isosceles triangle but the converse is not true.
Hence $$E\subset I$$.
If $$A=\left\{x|x\in N\quad and\quad x < 6\dfrac{1}{4}\right\}$$ and $$B=\left\{x|x\in N\quad and\quad x^2\leq 5\right\}$$. Then the number of subsets of set $$A\times (A\cap B)$$ which contains exactly $$3$$ elements is?
Report Question
0%
$$126$$
0%
$$220$$
0%
$$280$$
0%
$$144$$
Let $$A, B$$ and $$C$$ be sets such that $$\phi = A\cap B \subseteq C$$. Then which of the following statements is not true?
Report Question
0%
If $$(A - C) \subseteq B$$, then $$A\subseteq B$$
0%
$$(C \cup A)\cap (C\cup B) = C$$
0%
If $$(A - B)\subseteq C$$, then $$A\subseteq C$$
0%
$$B\cap C \neq \phi$$
Explanation
for $$A = C, A - C = \phi$$
$$\Rightarrow \phi \subseteq B$$
But $$A\not {\subseteq} B$$
$$\Rightarrow$$ option $$1$$ is NOT true
Let $$x\epsilon (C \cup A)\cap (C\cup B)$$
$$\Rightarrow x\epsilon (C\cup A)$$ and $$x \epsilon (C\cup B)$$
$$\Rightarrow (x \epsilon C$$ or $$x \epsilon A)$$ and $$(x\epsilon C$$ or $$x \epsilon B)$$
$$\Rightarrow x \epsilon C$$ or $$x \epsilon (A\cap B)$$
$$\Rightarrow x \epsilon C$$ or $$x\epsilon C$$ (as $$A\cup B\subseteq C)$$
$$\Rightarrow x \epsilon C$$
$$\Rightarrow (C \cup A)\cap (C\cup B)\subseteq C....(1)$$
Now $$x \epsilon C\Rightarrow x \epsilon (C\cup A)$$ and $$x \epsilon (C \cup B)$$
$$\Rightarrow x\epsilon (C\cup A)\cap (C\cup B)$$
$$\Rightarrow C\subseteq (C\cup A)\cap (C \cup B) .....(2)$$
$$\Rightarrow$$ from (1) and (2)
$$C = (C\cup A)\cap (C\cup B)$$
$$\Rightarrow$$ option 2 is true
Let $$x \epsilon A$$ and $$x \not {\epsilon} B$$
$$\Rightarrow x \epsilon (A - B)$$
$$\Rightarrow x \epsilon C$$ (as $$A - B \subseteq C)$$
Let $$x \epsilon A$$ and $$x \epsilon B$$
$$\Rightarrow x \epsilon (A\cap B)$$
$$\Rightarrow x \epsilon C$$ (as $$A\cap B\subseteq C)$$
Hence $$x \epsilon A \Rightarrow x \epsilon C$$
$$\Rightarrow A \subseteq C$$
$$\Rightarrow$$ Option 3 is true
as $$C\supseteq (A\cap B)$$
$$\Rightarrow B\cap C\supseteq (A\cap B)$$
as $$A\cap B\neq \phi$$
$$\Rightarrow B\cap C \neq \phi$$
$$\Rightarrow$$ Option 4 is true.
State whether the following statement is true or false. Give reason to support your answer.
Every subset of a finite set is finite.
Report Question
0%
True
0%
False
If $$u=\{2, 3, 5, 7, 9\}$$ is the universal set and $$A=\{3, 7\}, B=\{2, 5, 7, 9\}$$, then find the following statement is true/false.
$$(A\cap B)'=A'\cap B'$$.
Report Question
0%
True
0%
False
Explanation
The given sets are:
$$u=\left\{2,3,5,7,9 \right\}\ A=\left\{3,7 \right\}\ B=\left\{2,5,7,9 \right\}$$
$$A\cap B=\left\{7 \right\}$$
$$(A\cap B)'=u-(A\cap B)=\left\{2,3,5,9 \right\}$$
$$A'=u-A=\left\{2,5,9 \right\}$$
$$B'=u-B=\left\{3 \right\}$$
$$A' \cap B'=\phi$$
$$\Rightarrow \ \boxed {(A\cap B)' \neq A' \cap B'}$$
State whether the following statement is true or false. If the statement is false, re-write the given statement correctly.
If $$A=\{1, 2\}, B=\{3, 4\}$$, then $$A\times (B\cap \phi)=\phi$$.
Report Question
0%
True
0%
False
State whether the following statement is true or false. If the statement is false, re-write the given statement correctly.
If $$P=\{m, n\}$$ and $$Q=\{n, m\}$$, then $$P\times Q=\{(m, n), (n, m)\}$$.
Report Question
0%
True
0%
False
State whether the following statement is true or false. If the statement is false, re-write the given statement correctly.
If A and B are non-empty sets, then $$A\times B$$ is a non-empty set of ordered pairs $$(x, y)$$ such that $$x\in B$$ and $$y\in A$$.
Report Question
0%
True
0%
False
Mark the correct alternative of the following.
The number of subsets of a set containing n elements is?
Report Question
0%
n
0%
$$2^n-1$$
0%
$$n^2$$
0%
$$2^n$$
Examine whether the following statements are true or false:
$$a\in \left\{\{a\}\, b \right\}$$
Report Question
0%
True
0%
False
If $$A=\left\{3, \left\{ 4, 5\right\}, 6\right\}$$, then the statement is true or false
$$\left\{ 3\right\} \subseteq A$$
Report Question
0%
True
0%
False
Explanation
$$A=\{3,\{4,5\},6\}$$
We have to find out if $$\{3\}$$ is subset of $$A$$ or not.
Since, $$3$$ is present in elements of $$A$$, then $$\{3\}\subseteq \{A\}$$
$$\therefore$$ Given statement is true.
Examine whether the following statements are true or false:
$$\left\{b, c\right\}\subset \left\{a, \left\{b, c\right\}\right\}$$
Report Question
0%
True
0%
False
For any set $$A$$, if $$A\subseteq \phi \Leftrightarrow A=\phi$$.
Report Question
0%
True
0%
False
Explanation
True
Possible sunsets of $$\phi={\phi}$$
$$A\subseteq \phi$$
$$\rightarrow A=\phi$$
Examine whether the following statements are true or false:
$$(a,e) \subset$$ ($$x : x$$ is a vowel in the English alphabet)
Report Question
0%
True
0%
False
Explanation
True, $$a,e$$ are two vowels of the English alphabet.
Examine whether the following statements are true or false:
($$x : x$$ is an even natural number less than $$6$$ ) $$\subset $$ ($$x: x$$ is a natural number which divide $$36$$.
Report Question
0%
True
0%
False
Explanation
True. ($$x : x$$ is an even natural number less than $$6$$ )= $$(2,4)$$
($$x : x$$ is a natural number which divides $$36$$ )= $$(1,2,3,4,6,9,12,18,36)$$.
Examine whether the following statements are true or false:
$$(a)\subset (a,b,c)$$
Report Question
0%
True
0%
False
Explanation
True. Each element of $$(a)$$ is also an element of $$(a, b, c)$$.
Examine whether the following statements are true or false:
$$(a,b)\not{\subset}(b,c,a)$$
Report Question
0%
True
0%
False
Explanation
False. Each element of $$(a,b)$$ is also an element of $$(b,c,a)$$.
In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
If $$x A$$ and $$A B$$, then $$x B$$
Report Question
0%
True
0%
False
Explanation
False
Let, $$A = \left \{ 3, 5, 7 \right \}$$ and $$B = \left \{ 3, 4, 6 \right \}$$
Now, $$5\in A$$ and $$A ⊄ B$$
However, $$5\notin B$$
In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
If $$A B$$ and $$B C$$, then $$A C$$
Report Question
0%
True
0%
False
Explanation
False
Let $$A = \left \{ 2 \right \}$$
$$B = \left \{ 0,2 \right \}$$
And, $$C = \left \{ 1,\left \{ 0,2 \right \},3 \right \}$$
As, $$A ⊂ B$$
$$B ∈ C$$
$$\Rightarrow A ∉ C$$
Choose the correct answer from the given four options
Which of the following collection doesn't form a set
Report Question
0%
Collection of 5 odd prime numbers
0%
Collection of 3 most intelligent students of your class
0%
Collection of 4 vowels of the English alphabet
0%
Collection of first 6 months of a year
Explanation
Collection of 5 odd prime number. Collection of 4 vowels of English alphabet and collection of first 6 months of a year, all are sets but a collection of 3 most intelligent students of your class is not a set, because intelligence is not well defined.(b)
0:0:1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
0
Answered
0
Not Answered
0
Not Visited
Correct : 0
Incorrect : 0
Report Question
×
What's an issue?
Question is wrong
Answer is wrong
Other Reason
Want to elaborate a bit more? (optional)
Practice Class 11 Engineering Maths Quiz Questions and Answers
<
>
Support mcqexams.com by disabling your adblocker.
×
Please disable the adBlock and continue.
Thank you.
Reload page
