Set Theory Test 27

Result

Set Theory Test 27

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Let $$Q$$ be a non empty subset of $$N$$ and $$q$$ is a statement as given below :
$$q:$$ There exists an even number $$a \in Q$$ Negation of the statement $$q$$ will be :

A
There is no even number in the set $$Q$$

B
Every $$a \in Q$$ is an odd number.

C
$$(a)$$ and $$(b)$$ both

D
None of these

Solution

Let $$Q$$ be a non empty subset of $$N$$ and $$q.$$ There exists even number $$a\in Q$$ negation of statement $$q.$$ There does not exist a even number in set Q.
Hence, the answer is there is no even number in the set $$Q.$$
Question 2
1 / -0

Let $$A$$ and $$B$$ be two sets. $$A \cap B = \{1, 2\}, A \cup B = \{1, 2, 3, 4, 5\}$$ and if $$n_1$$ is the maximum number of function from $$A$$ to $$B$$ and $$n_2$$ is the minimum number of function form $$A$$ to $$B$$ then $$n_1 - n_2$$ equals

A
$$32$$

B
$$56$$

C
$$64$$

D
$$81$$

Solution
Question 3
1 / -0

In a battle $$70$$% of the combatants lost one eye, $$80$$% an ear, $$75$$% an arm, $$85$$% a leg, $$x$$% lost all the four limbs the minimum value of $$x$$ is

A
$$10$$

B
$$12$$

C
$$15$$

D
$$5$$

Solution

$$70\%$$ of the combatants lost one eye, $$80\%$$ an ear, $$75\%$$ an arm and $$85\%$$ a leg.
Now,
$$\Rightarrow$$ The combatants who lost one eye and one ear $$=(70+80-100)\%$$
$$=50\%$$

$$\Rightarrow$$ The combatants who lost one eye, one ear and one erm $$=(50+75-100)\%$$
$$=25\%$$

$$\Rightarrow$$ The combatants who lost one eye, one ear one arm and one leg $$=(25-85-100)\%$$
$$=10\%$$
$$\therefore$$ Combatant who lost all the four limbs $$=10\%$$
$$\therefore$$ $$x=10\%$$
Question 4
1 / -0

The value of set $$(A\cup B\cup C)\cap(A\cap B^1\cap C^1)^1\cap C^1$$ is equal to

A
$$B\cap C^1$$

B
$$A\cap C$$

C
$$B\cap C^1$$

D
$$A\cap C^1$$

Solution
Question 5
1 / -0

Two sets A and B are defined as follows
$$A=\left\{ \left( x,y \right) :y={ e }^{ 2x },x\in R \right\} $$ and
$$B=\left\{ \left( x,y \right) :y={ x }^{ 2 },x\in R \right\} $$, then

A
$$A\subset B$$

B
$$B\subset A$$

C
$$A\bigcup B$$

D
$$A\cap B=\phi $$

Solution

$$\begin{array}{l} A=\left\{ { \left( { x,\, y } \right) \, :\, y={ e^{ 2x } },\, x\in R } \right\} \, and \\ B=\left\{ { \left( { x,\, y } \right) \, :\, y={ x^{ 2 } },\, x\in R } \right\} \\ then, \\ A=\left( { { e^{ \circ } },\, { e^{ 1 } },\, { e^{ 2 } },....,\, { e^{ \infty } } } \right) \\ =\left( { 1,\, { e^{ 1 } },\, { e^{ 2 } },....... } \right) \\ and, \\ B=\left( { 0,\, 1,\, 4,\, ..... } \right) \\ \therefore A\subset B \\ Hence,\, the\, option\, A\, is\, the\, correct\, answer. \end{array}$$
Question 6
1 / -0

If $$A=\left\{1,2,3,4\right\}; B=\left\{2,4,6,8\right\}; C=\left\{3,4,5,8\right\}$$ then $$A\cap B\cap C=$$

A
$$\phi$$

B
$${4}$$

C
$$\mu$$

D
$${2,4}$$

Solution

$$\begin{matrix} A=\left\{ { 1,2,3,4 } \right\} \\ B=\left\{ { 2,4,6,8 } \right\} \\ C=\left\{ { 3,4,5,8 } \right\} \\ A\cap B\cap C=\left\{ { 4 } \right\} . \\ \end{matrix}$$
Question 7
1 / -0

If n(A)=3, n(B)=4, then $$n(A\times B\times C)=36 find \,n(C)$$ is equal to :

A
3

B
12

C
108

D
none of these

Solution

$$n(A)=3$$
$$n(B)=4$$
$$n(A\times B\times C)=36$$
$$n(3\times 4\times C)=36$$
$$n(12\times C)=36$$
$$\therefore n(C)=3$$
So, $$n(A\times B\times C)=36$$
$$n(3\times 4\times 3)=36$$. H.P.
Question 8
1 / -0

In a group of 800 people, 550 can speak Hindi and 450 can speak English. How many can speak both Hindi and English ?

A
$$100$$

B
$$150$$

C
$$200$$

D
None of these

Solution

Let H denote the set of people speaking Hindi and E denote the set of people speaking English. We are given :
$$n(H)=550, n(E)=450, n(H\cup E)=800$$
Now,
$$n(H\cup E)=n(H)+n(E)-n(H\cap E)$$
$$n(H \cap E)=550+450-800=200$$
Hence, 200 persons can speak both Hindi and English.
Question 9
1 / -0

If A= {1, 2, 5} and B= {3, 4, 5, 9}, then $$A \bigcup B$$ is equal to :

A
$$\{1, 2, 5, 9\}$$

B
$$\{1, 2, 3, 4, 9\}$$

C
$$\{1, 2, 3, 4, 5, 9\}$$

D
None of these

Solution

$$A=\left\{ 1,2,5 \right\} \quad B=\left\{ 3,4,5,9 \right\} $$
$$A\cup B=\left\{ 1,2,3,4,5,9 \right\} $$
Option C.
Question 10
1 / -0

If P(S) denotes the set of all subsets of a given set S, then the number of one to one function from the set s={1,2,3} to the set of P(S) is

A
336

B
8

C
36

D
320

Solution

$$\begin{array}{l} Given \\ P\left( s \right) =\left\{ { 1,\, 2,\, 3 } \right\} \\ P\left( s \right) =all\, subset\, of\, 5 \\ =\left\{ { \phi ,\left\{ 1 \right\} ,\left\{ 3 \right\} ,\left\{ { 1,2 } \right\} ,\left\{ { 2,3 } \right\} ,\left\{ { 3,1 } \right\} ,\left\{ { 1,2,3 } \right\} } \right\} \\ No.\, of\, element\, of\, 5=0\left( 5 \right) =3 \\ similarly \\ O\left( { p\left( s \right) } \right) =8 \\ Total\, no.\, of\, one-one\, function \\ =\frac { { n! } }{ { \left( { n-m } \right) ! } } \, ,\, where\, n=o\left( { p\left( s \right) } \right) \, and\, m=o\left( 5 \right) \\ =\frac { { 8! } }{ { \left( { 8-3 } \right) ! } } =\frac { { 8! } }{ { 5! } } \\ =336\, \, \\ No.\, of\, one-one\, function\, is\, 336 \\ Hence,\, \, option\, \, A\, \, is\, correct, \end{array}$$

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Set Theory Test 27

Result

Set Theory Test 27

Score

-

Rank

-

SHARING IS CARING

Question 1

There is no even number in the set $$Q$$

Every $$a \in Q$$ is an odd number.

$$(a)$$ and $$(b)$$ both

None of these

Solution

Question 2

$$32$$

$$56$$

$$64$$

$$81$$

Solution

Question 3

$$10$$

$$12$$

$$15$$

$$5$$

Solution

Question 4

$$B\cap C^1$$

$$A\cap C$$

$$B\cap C^1$$

$$A\cap C^1$$

Solution

Question 5

$$A\subset B$$

$$B\subset A$$

$$A\bigcup B$$

$$A\cap B=\phi $$

Solution

Question 6

$$\phi$$

$${4}$$

$$\mu$$

$${2,4}$$

Solution

Question 7

3

12

108

none of these

Solution

Question 8

$$100$$

$$150$$

$$200$$

None of these

Solution

Question 9

$$\{1, 2, 5, 9\}$$

$$\{1, 2, 3, 4, 9\}$$

$$\{1, 2, 3, 4, 5, 9\}$$

None of these

Solution

Question 10

336

8

36

320

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.