Finite and Infinite Set

Q.

Which of the following are correct?

1. If a set is said to be finite, then the number of elements in that set is always a natural number.

2. A set which does not contain any element is called an empty set.

3. A set which is empty or consists of a definite number of elements is called finite set, otherwise, the set is called infinite set.

4. Set of integers is a finite set.

Q.

One or more options are correct:

Which of the following is/are infinite set?

1. The set of all lines parallel to Y-axis

2. Set of all atoms in solar system

3. Set of letters in English alphabet

4. Set of circles passing through (0, 0)

Q.

Which of the following is a finite set?

1. Set of all 4 digit prime number

2. Set of all positive integers which are multiple of 5

3. The set of positive integers greater than 100.

4. Set of points on a line.

Q. If $f\left(x\right)+2f\left(\frac{1}{x}\right)=3x,x\ne 0andS=xϵR:f\left(x\right)=f(-x)$; then S

1. is an empty set
2. contains exactly one element
3. contains exactly two elements
4. contains more than two elements

Q. Which of the following is an infinite set?

1. {x : x is an odd prime number more than 100}
2. {(x, y) : x and y are integers and a solution of the equation 2x + 3y = 12}
3. {x: x is a point common to two non-parallel lines in xy plane}
4. {(x, y) : x and y are a natural number and solution of equation 3x+4y=25}

Q. Which of the following is an infinite set?

1. The set of human beings on the earth
2. The set of water drops in a glass of water
3. The set of trees in a forest
4. The set of all prime numbers

Q. Which of the following is a finite set?

1. $N$
2. $Z$
3. $R$
4. $W-N$

Q. The most appropriate option for the following sets
$A$ is set of letters of the word 'NARAYANA'
$B$ is the set of letters of the word 'ARANYA'

1. $A$ and $B$ are equivalent sets
2. $A$ and $B$ are equal sets
3. $A$ and $B$ are similar sets
4. $n\left(A\right)>n\left(B\right)$

Q. Which of the following is a finite set ?

1. $A=\{x:x\in N\text{and}x\text{is a prime number}\}$
2. $B=\{x:x\text{is a real number between}1\text{and}10\}$
3. $C=\{x:x\text{is a perfect square number between}0\text{and}99\}$
4. $D=\{x:x\text{is an integer less than}20\}$

Q. The correct options among the following is/are

1. $A=\{x,x\in N\text{and}{x}^2\le 4\}$, then $n\left(A\right)=2$
2. $B=\{x,x\in Z\text{and}|x|\le 3\}$, then $-2\in B$
3. $C=\{x,x\in R\text{and}|x|\ge -2\}$, then $-4\in C$
4. $D=\{x,\text{where}x\text{is a prime number less than}9\}$, then $1\in D$