Set Theory Test 29

Result

Set Theory Test 29

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Weekly Quiz Competition

Question 1
1 / -0

{$$x \epsilon R : \dfrac{14x}{x+1} - \dfrac{9x-30}{x-4} <0$$ } is equal to

A
$$(-1, 4)$$

B
$$(1, 4) \cup (5, 7)$$

C
$$(1, 7)$$

D
$$(-1, 1) \cup (4, 6)$$

Solution

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,

$$-1<x<1\quad \mathrm{or}\quad \:4<x<6$$

$$\begin{bmatrix}\mathrm{Solution:}\:&\:-1<x<1\quad \mathrm{or}\quad \:4<x<6\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-1,\:1\right)\cup \left(4,\:6\right)\end{bmatrix}$$
Question 2
1 / -0

If $$a * b = 2 ^ { a b }$$ on $$N \cup \{ 0 \}$$ then $$*$$ is

A
commutative

B
associate

C
$$(a) \& (b)$$ both

D
none of these

Solution
Question 3
1 / -0

If $$A = \{ 2,3,4,5,7 \} , B = \{ 7,8,9 \}$$, then find $$n ( A \cup B ).$$

A
$$1$$

B
$$3$$

C
$$5$$

D
$$7$$

Solution

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

$$n(A)=5$$

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

$$n(B)= 3$$

$$n(A \cap B)=1$$

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

$$(A\cup B)=5+3-1=7$$
Question 4
1 / -0

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?

A
$$126$$

B
$$220$$

C
$$280$$

D
$$144$$

Solution
Question 5
1 / -0

If $$I$$ is the set of isosceles triangle and $$E$$ is the equilateral triangles then _____________.

A
$$I\subset E$$

B
$$E \subset I$$

C
$$E=I$$

D
None of these

Solution

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 $$E\subset I$$.
Question 6
1 / -0

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

A
n

B
$$2^n-1$$

C
$$n^2$$

D
$$2^n$$

Solution
Question 7
1 / -0

In a flight 50 people speak Hindi, 20 speak English and 10 speak both English and Hindi. The number of people who speak atleast one of the two languages is

A
$$40$$

B
$$50$$

C
$$20$$

D
$$60$$

Solution

Let $$H$$ = People who speak Hindi

$$ E$$ = People who speak English

According to the questions,
$$n(H)=50,n(E)=20,n(H\cap E)=10$$

$$\therefore$$ Number of people who speak at least two language = $$n(H\cup E)$$

$$=n(H)+n(E)-n(H\cap E)$$

$$=50+20-10=60$$
Question 8
1 / -0

Choose the correct answer from the given four options
Which of the following collection doesn't form a set

A
Collection of 5 odd prime numbers

B
Collection of 3 most intelligent students of your class

C
Collection of 4 vowels of the English alphabet

D
Collection of first 6 months of a year

Solution

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)
Question 9
1 / -0

Find the correct option for the given question.
Which of the following collections is a set?

A
Colours of the rainbow

B
Tall trees in the school campus

C
Rich people in the village

D
Easy examples in the book

Solution

Since, the colors of the rainbow are well defined such as Violet, Indigo, Blue, Green, Yellow, Orange and Red.
So, the collection of colors of the rainbow is a set.
Question 10
1 / -0

Which of the following statements is true (if N, W and I are sets of Natural, Whole and Integer numbers respectively ?

A
$$N\, \subset \, W\, \subset \, I$$

B
$$I\, \subset \, N\, \subset \, W$$

C
$$W\, \subset \, N\, \subset \, I$$

D
$$I\, \subset \, W\, \subset \, N$$

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Set Theory Test 29

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Set Theory Test 29

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SHARING IS CARING

Question 1

$$(-1, 4)$$

$$(1, 4) \cup (5, 7)$$

$$(1, 7)$$

$$(-1, 1) \cup (4, 6)$$

Solution

Question 2

commutative

associate

$$(a) \& (b)$$ both

none of these

Solution

Question 3

$$1$$

$$3$$

$$5$$

$$7$$

Solution

Question 4

$$126$$

$$220$$

$$280$$

$$144$$

Solution

Question 5

$$I\subset E$$

$$E \subset I$$

$$E=I$$

None of these

Solution

Question 6

n

$$2^n-1$$

$$n^2$$

$$2^n$$

Solution

Question 7

$$40$$

$$50$$

$$20$$

$$60$$

Solution

Question 8

Collection of 5 odd prime numbers

Collection of 3 most intelligent students of your class

Collection of 4 vowels of the English alphabet

Collection of first 6 months of a year

Solution

Question 9

Colours of the rainbow

Tall trees in the school campus

Rich people in the village

Easy examples in the book

Solution

Question 10

$$N\, \subset \, W\, \subset \, I$$

$$I\, \subset \, N\, \subset \, W$$

$$W\, \subset \, N\, \subset \, I$$

$$I\, \subset \, W\, \subset \, N$$

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