MCQ Questions for Class 11 Engineering Maths Sets Quiz 11

$A=\left\{1, 2, 3, 4\right\}$ , then the number of subsets of

$A$ that contain the element

$2$ but not

$3$ , is

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

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

$\begin{array}{l} \text { Given, } \quad P \longrightarrow q \\ \text { ne trinow that, } \rightarrow \text { - if then } \\ \Rightarrow \text { if } P \text { then } q \end{array}$

$\begin{array}{lll} p & q & p \rightarrow q \\ 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{array}$

$\begin{array}{c} \Rightarrow \text { Evaluating option } A(p \wedge \sim q) \\ P \text { iq } p \wedge \sim q \\ 111 & 1 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \\ 1 & 0 & 0 \\ \text { Incorrect assumption } \end{array}$

$\begin{array}{c} \Rightarrow \text { Eualuating } B(\sim p \wedge q) \\ \sim p \quad q \quad \sim p \wedge q \\ 0 \\ 0 \\ 1 \\ 1 \quad 0 \\ \text { Incorrect assumption } \end{array}$

$\begin{array}{rlrl} \Rightarrow \text { Evaluating } & c(\sim p \vee q) \\ & \sim p & q & \sim p v q \\ & 0 & 1 & & \\ 0 & 0 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & 1 \\ & \text { correct assumption } \end{array}$

$A=\left\{ 1,3,5,7,9,11,13,15,17 \right\} ,B=\left\{ 2,4,....,18 \right\}$ and N is the universal set, then

$A'\cup \left( \left( A\cup B \right) \cap B' \right)$

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

0%
${5}^{4}$
0%
${4}^{5}$
0%
$4!$
0%
$5!$

$A=\left\{ 1,2,4 \right\} ,B=\left\{ 2,4,5 \right\}$ and

$C=\left\{ 2,5 \right\}$ , then

$\left( A-B \right) \times \left( B-C \right) =$

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

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

$B - A.$

0%
$\{ e , o \}$
0%
$\{ a , i , u \}$
0%
$\{ o \}$
0%
$\{ \}$

$a * b = 2 ^ { a b }$ on

$N \cup \{ 0 \}$ then

$*$ is

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

$i < j \text { and, } i , j , \in A$

0%
$^ { 8 } C _ { 3 }$
0%
$^ { 8 } C _ { 3 } + 2 \left( ^ { 8 } C _ { 2 } \right)$
0%
$^ { 10 } C _ { 3 }$
0%
None of these

$A = \{ 2,3,4,5,7 \} , B = \{ 7,8,9 \}$ , then find

$n ( A \cup B ).$

0%
$1$
0%
$3$
0%
$5$
0%
$7$

Explanation

$A=\left \{ 2,3,4,5,7 \right \}$

$n(A)=5$

$B=\left \{ 7,8,9 \right \}$

$n(B)= 3$

$n(A \cap B)=1$

$\therefore (A\cup B)=n(A)+n(B)-n(A\cap B)$

$(A\cup B)=5+3-1=7$

$I$ is the set of isosceles triangle and

$E$ is the equilateral triangles then _____________.

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

$E\subset I$ .

$A=\left\{x|x\in N\quad and\quad x < 6\dfrac{1}{4}\right\}$ 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?

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?

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.
1247200_1615075_ans_005ea1b2d1a44e42b1b0826402402ee1.png

State whether the following statement is true or false. Give reason to support your answer.
Every subset of a finite set is finite.

0%
True
0%
False

$u=\{2, 3, 5, 7, 9\}$ is the universal set and

$A=\{3, 7\}, B=\{2, 5, 7, 9\}$ , then find the following statement is true/false.

$(A\cap B)'=A'\cap B'$ .

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

$A\times (B\cap \phi)=\phi$ .

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

$P\times Q=\{(m, n), (n, m)\}$ .

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

$y\in A$ .

0%
True
0%
False

Mark the correct alternative of the following.
The number of subsets of a set containing n elements is?

0%
n
0%
$2^n-1$
0%
$n^2$
0%
$2^n$

Examine whether the following statements are true or false:

$a\in \left\{\{a\}\, b \right\}$

0%
True
0%
False

$A=\left\{3, \left\{ 4, 5\right\}, 6\right\}$ , then the statement is true or false

$\left\{ 3\right\} \subseteq A$

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:

$\left\{b, c\right\}\subset \left\{a, \left\{b, c\right\}\right\}$

0%
True
0%
False

For any set

$A$ , if

$A\subseteq \phi \Leftrightarrow A=\phi$ .

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)

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

$36$ .

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:

$(a)\subset (a,b,c)$

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:

$(a,b)\not{\subset}(b,c,a)$

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

$x B$

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

$A C$

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

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

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

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Practice Class 11 Engineering Maths Quiz Questions and Answers

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

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Practice Class 11 Engineering Maths Quiz Questions and Answers

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