Sets Test

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Sets Test - 18

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Weekly Quiz Competition

Question 1
1 / -0

Let $$A = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$$. Then the number of subsets of $$A$$ containing exactly two elements is

A
$$20$$

B
$$40$$

C
$$45$$

D
$$90$$

Solution

Number of elements in $$A= 10$$
Number of subsets of $$A$$ containing exactly two elements
$$=$$ Number of ways we can select $$ 2 $$ elements from $$10$$ elements
$${}^{ 10 }{ C }_{2}=\dfrac { 10\times 9 }{ 2 } =45$$
$$\therefore$$ Number of subsets of $$A$$ containing exactly two elements $$=45$$
Question 2
1 / -0

In a class of $$60$$ students, $$45$$ students like music, $$50$$ students like dancing, $$5$$ students like neither. Then the number of students in the class who like both music and dancing is

A
$$35$$

B
$$40$$

C
$$50$$

D
$$55$$

Solution

Total number of students in class $$=60$$
Students who like music $$=X+Y=45$$
Students who like dancing $$=Y+Z=50$$
Students who like nothing $$=5$$
Students who like both music and dancing $$=Y$$
We know that $$X+Y+Z+5=60$$
$$\Rightarrow 45+Z+5=60$$
$$\Rightarrow Z=10$$
$$\Rightarrow Y=40$$
Hence, $$40$$ students like both music and dancing.
Question 3
1 / -0

Let $$A_1, A_2$$ and $$A_3$$ be subsets of a set $$X$$. Which one of the following is correct?

A
$$A_1\cup{A_2}\cup{A_3}$$ is the largest subset of $$X$$ containing elements of each of $$A_1, A_2$$ and $$A_3$$

B
$$A_1\cup{A_2}\cup{A_3}$$ is the smallest subset of $$X$$ containing either $$A_1$$ or $$A_2\cup{A_3}$$ but not both

C
The smallest subset of $$X$$ containing $$A_1\cup{A_2}$$ and $$A_3$$ equals the smallest subset of $$X$$ containing both $$A_1$$ and $$A_2\cup{A_3}$$ only if $$A_2=A_3$$

D
None of these

Solution

Since union of subsets is the smallest subset containing all the elements of the subsets.
Hence, option (A) is correct.
Question 4
1 / -0

Statements:
I. Some Politicians are social workers.
II. All Doctors are social workers.
Conclusions:
I. Some Doctors are Politicians.
II. Some social workers are Doctors as well as Politicians.

A
Both conclusion (I) and (II) follow

B
Only conclusion (II) follow

C
Neither conclusion (I) nor (II) follow

D
Only conclusion (I) follow

Solution

R.E.F image
Thus, option $$(3)$$ is correct.
Question 5
1 / -0

How many rural uneducated people are employed?

A
$$10$$

B
$$6$$

C
$$12$$

D
$$14$$

Solution

Rural uneducated people has been represented by $$'10'$$.
Question 6
1 / -0

From among the given alternatives select the one in which the set of numbers is most like the set of numbers given in the question.
Given set $$:$$ $$(7, 15, 31)$$

A
$$7, 13, 28$$

B
$$5, 13, 28$$

C
$$9, 13, 26$$

D
$$5, 13, 29$$

Solution

Let us find the Relation between the numbers of the set $$(7 , 15 , 31)$$.
$$(7)\times 2 +1 = (15)$$
$$(15)\times 2 +1 = (31)$$

Options $$A,B,C$$ are not of similar type of above set

This similar type of relation is shown by option D $$(7 , 15 , 31)$$.
$$(5)\times 2 +3 = (13)$$
$$(13)\times 2 +3 = (29)$$

Hence, option D is correct.
Question 7
1 / -0

If $$A=\left\{ 2,4\left\{ 5,6 \right\} ,8 \right\} $$, then which one of the following statements is not correct?

A
$$\left\{ 5,6 \right\} \subseteq A$$

B
$$\left\{ 5,6 \right\} \in A$$

C
$$\left\{ 2,4,8 \right\} \subseteq A$$

D
$$2,4,8\in A\quad $$

Solution

$$\left\{ 5,6 \right\} $$ is not the subset but is an element of $$A$$, $$\therefore$$ a is false.
Question 8
1 / -0

For two sets $$A$$ and $$B$$, $$ A\cap \left( A\cup B \right)=$$

A
$$A$$

B
$$B$$

C
$$ \phi$$

D
$$None\ of\ these$$

Solution

$$\left( A\cap A \right) \cup \left( A\cap B \right) =A\cup \left( A\cap B \right) =A$$
$$\because A\cap B\subset A$$
Question 9
1 / -0

If $$A=\left\{a,b,c\right\},B=\left\{c,d,e\right\},C\left\{a,d,f\right\},$$ then $$A\times \left( B\cup C \right)$$ is

A
$$\left\{(a,d),(a,e),(a,c)\right\}$$

B
$$\left\{(a,d),(b,d),(c,d)\right\}$$

C
$$\left\{(d,a),(d,b),(d,c)\right\}$$

D
$$none\ of\ these$$

Solution

$$(d)$$.
$$A\times \left( B\cup C \right) =\{ a,b,c\} \times \{ a,c,d,e,f\}$$
The above set will consist of $$15$$ ordered pairs and not $$3$$.
Question 10
1 / -0

$$A$$ and $$B$$ are two sets having $$3$$ and $$5$$ elements respectively and having $$2$$ elements in common. Then the number of elements in $$A\times B$$ is

A
$$6$$

B
$$36$$

C
$$15$$

D
$$None\ of\ these$$

Solution

Total ordered pairs $$= n(A) \times n(B) = 3\times 5 = 15$$

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Re-Attempt Weekly Quiz Competition

Sets Test - 18

Result

Sets Test - 18

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SHARING IS CARING

Question 1

$$20$$

$$40$$

$$45$$

$$90$$

Solution

Question 2

$$35$$

$$40$$

$$50$$

$$55$$

Solution

Question 3

$$A_1\cup{A_2}\cup{A_3}$$ is the largest subset of $$X$$ containing elements of each of $$A_1, A_2$$ and $$A_3$$

$$A_1\cup{A_2}\cup{A_3}$$ is the smallest subset of $$X$$ containing either $$A_1$$ or $$A_2\cup{A_3}$$ but not both

The smallest subset of $$X$$ containing $$A_1\cup{A_2}$$ and $$A_3$$ equals the smallest subset of $$X$$ containing both $$A_1$$ and $$A_2\cup{A_3}$$ only if $$A_2=A_3$$

None of these

Solution

Question 4

Both conclusion (I) and (II) follow

Only conclusion (II) follow

Neither conclusion (I) nor (II) follow

Only conclusion (I) follow

Solution

Question 5

$$10$$

$$6$$

$$12$$

$$14$$

Solution

Question 6

$$7, 13, 28$$

$$5, 13, 28$$

$$9, 13, 26$$

$$5, 13, 29$$

Solution

Question 7

$$\left\{ 5,6 \right\} \subseteq A$$

$$\left\{ 5,6 \right\} \in A$$

$$\left\{ 2,4,8 \right\} \subseteq A$$

$$2,4,8\in A\quad $$

Solution

Question 8

$$A$$

$$B$$

$$ \phi$$

$$None\ of\ these$$

Solution

Question 9

$$\left\{(a,d),(a,e),(a,c)\right\}$$

$$\left\{(a,d),(b,d),(c,d)\right\}$$

$$\left\{(d,a),(d,b),(d,c)\right\}$$

$$none\ of\ these$$

Solution

Question 10

$$6$$

$$36$$

$$15$$

$$None\ of\ these$$

Solution

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