Definition of Sets

Q. Three sets $A,B$, and $C$ are defined as,

$\begin{array}{cc}A& =\{x:x\text{is a whole number less than equal to 10}\}\\ & \\ B& =\{x:x\text{is a letter in the word "ARITHMETIC"}\}\\ & \\ C& =\{x:x\text{is a prime number less than 30}\}\end{array}$

With respect to the cardinality of these sets, choose the correct option.

1. $n\left(A\right)\ne n\left(B\right)\ne n\left(C\right)$
2. $n\left(A\right)=n\left(C\right)\ne n\left(B\right)$
3. $n\left(B\right)=n\left(C\right)\ne n\left(A\right)$
4. $n\left(A\right)=n\left(B\right)=n\left(C\right)$

Q.

Which of the following collection is not a set?

1. The vowels in the English alphabet

2. All natural numbers which divide 42

3. Names of 10 most renowned actors

4. Names of rivers in India

Q.

Janhavi types 480 words in 15 minutes. How many words would she type in 5 minutes?

1. 150

2. 170

3. 160

4. 140

Q. The number of elements in the set {x : x is a letter of the word 'MISSISSIPPI'}, is ____ .

1. 4

Q. If X = { 1, 3, 5, 7}, then n(X) = _________.

1. 1
2. 2
3. 4
4. 3

Q. Choose the subset of the set {b, a, l, i}.

1. {b, a, l}
2. {b, a, d}
3. {b, a, d}
4. {b, a, e}

Q.

The sets

$A=\{x:x\in N\text{and}13>2x+1\}$ and

$B=\{y:y\in Z\text{and}-30\le y<-25\}$ are ___ sets.

1. equal
2. equivalent
3. joint
4. null

Q. Sets having at least one element in common are called joint or overlapping sets.

1. True
2. False

Q.

Which of the below is a mapping?

1. 

2. 

3. 

4. None of the these

Q. If X = { 1, 3, 5, 7}, then n(X) = _________.

1. 4
2. 3
3. 1
4. 2

Q. The set Z = { ..........., -1, 0, 1, 2, ........}, this form of represention of a set is called _________________.

1. Set-Builder form
2. Rule method
3. Roster form
4. Tabular form

Q.

The sets

$A=\{x:x\in N\text{and}13>2x+1\}$ and

$B=\{y:y\in Z\text{and}-30\le y<-25\}$ are ___ sets.

1. nan
2. equivalent
3. equal
4. joint

Q. $A=\{x:x\in Nandx\le 8\}$
This form of representation of set is called __________.

1. Set -Builder form
2. Rule Method
3. Roster form
4. Tabular method

Q. What is the additive identity for a number x?

1. -x
2. 1
3. 0
4. x

Q. Question 9
A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:
$$\begin{array}{cccccccc}2.6& 3.0& 3.7& 3.2& 2.2& 4.1& 3.5& 4.5\\ 3.5& 2.3& 3.2& 3.4& 3.8& 3.2& 4.6& 3.7\\ 2.5& 4.4& 3.4& 3.3& 2.9& 3.0& 4.3& 2.8\\ 3.5& 3.2& 3.9& 3.2& 3.2& 3.1& 3.7& 3.4\\ 4.6& 3.8& 3.2& 2.6& 3.5& 4.2& 2.9& 3.6\end{array}$$
Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the intervals 2−2.5.

Q. By which smallest number the given numbers below should be divided, so that the result becomes a perfect square
396

Q.

In how many ways can the letters of the word INSURANCE be arranged so that vowels are occupied at even places?

Q. Choose the subset of the set {b, a, l, i}.

1. {b, a, e}
2. {b, a, l}
3. {b, a, d}
4. {b, a, d}

Q.

doesnt the definition of sets have the word non-repeated also?

such that- A set is a collection of well-defined and non-repeated objects?

Q. Sets having at least one element in common are called joint or overlapping sets.

1. False
2. True

Q. You have been studying abroad for three years and are planning to go home to your country for the vacations. You wish to write a letter to your parents, informing them about your plans. Which line would best fit the context of the letter?

1. I am sorry to say that....
2. I am really happy to tell you both that...
3. I am pleased to inform you both that...
4. It is an honor to announce that...

Q.

Write the given set in Set builder form.

$B=\left\{Allmonthsoftheyear\right\}$.

Q. If X = { 1, 3, 5, 7}, then n(X) = _________.

1. 3
2. 1
3. 2
4. 4

Q.

If 1/3 of a mans property is $2million , then find the value of 2/5 of his property.

Q. Sets having at least one element in common are called joint or overlapping sets.

1. False
2. True

Q.

All equal sets are ___ .

1. Joint

2. Equivalent

3. Singleton

4. Null

Q. Identify the infinite sets among the following.

1. Rational numbers
2. Stars in the sky
3. Points in a plane
4. Days in an year
5. Circles in a plane
6. Natural numbers
7. Points in a circle
8. People in a city

Q. (i) Every point on the numbeer line is of the form v/m, where m is a natural number.

Q. If X = { 1, 3, 5, 7}, then n(X) = _________.

1. 2
2. 3
3. 4
4. 1

Q.

Which of the following collection is not a set?

1. Names of rivers in India

2. All natural numbers which divide 42

3. Names of 10 most renowned actors

4. The vowels in the English alphabet