Finite and Infinite Set

Q.

Let $\left[x\right]$ denotes the greatest integer $\le x.\mathrm{If}f\left(x\right)=\left[x\right]$ and $g\left(x\right)=\left|x\right|$, then the value of $f\left(g\left(\frac{8}{5}\right)\right)-g\left(f\left(\frac{-8}{5}\right)\right)$ is

1. $2$

2. $-2$

3. $1$

4. $0$

5. $-1$

Q.

For any complex number $Z$, the minimum value of $\left|Z\right|+|Z-1|$ is

1. $0$

2. $1$

3. $2$

4. $-1$

Q. Q.4 In a farm, there are few chicken and goats only. If their head counts and leg counts are 10 and 28 respectively then the number of chicken among them is

Q.

State whether each of the following sets is a finite set or an infinite set:

(i) The set of multiples of 8.

(ii) The set of integers less than 10.

(iii) The set of whole numbers less than 12.

(iv)$\{x:x=3n-2,n\in W,n\le 8\}$ (v) $\{x:x=3n-2,n\in Z,n\le 8\}$ (vi)$\{x:x=\frac{n-2}{n+1},n\in W\}$

Q. Which of the following statement represents a finite set?

1. Set of positive integers greater than 100
2. Set of rational numbers between 1 and 2
3. Set of points common to any 2 parallel lines
4. Set of points on a line

Q. A set with unlimited or uncountable number of elements is called:

1. infinite set
2. empty set
3. singleton set
4. finite set

Q. The set $B=\{x:x=3n+1,nϵN\text{and}n\le 20\}$ is _________.

1. an infinite set
2. a finite set
3. singleton set
4. a null set

Q.

The GCD of $1080$ and $675$ is

1. $145$

2. $135$

3. $225$

4. $125$

Q. The set $B=\{x:x=3n+1,nϵN\text{and}n\le 20\}$ is _________.

1. a finite set
2. a null set
3. an infinite set
4. singleton set

Q.

State whether the following statements are true or false:

(a) The set of all even natural numbers is a infinite set.

(b) Every non-empty subset of has the smallest element.

(c) Every integer can be identified with a rational number.

(d) For each rational number, one can find the next rational number.

(e)There is no largest rational number.

(f) Every integer is either even or odd.

(g) Between any two rational numbers, there is an integer.

Q.

Which of the following is a finite set?

1. Set of points on a line.
2. Set of points common to any 2 parallel lines.
3. The set of positive integers greater than 1.
4. The set of positive integers greater than 100.

Q. If $U=1,2,3,4,5,6,7,A=1,2,3,4,5$, and $B=1,3,5,7$, then $A^{\prime }–B^{\prime }$ is equal to:

1. $\{3,4,6\}$
2. $\{4,6\}$
3. $\left\{7\right\}$
4. $\{1,3,5\}$

Q. A set with unlimited or uncountable number of elements is called:

1. singleton set
2. finite set
3. empty set
4. infinite set

Q. How many types of sets are there

Q.

Two sets are called equal sets if both the sets have $\_\_\_\_\_$elements.

1. identical

2. some common

3. no common

4. equal number of

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. The set of positive integers greater than 100 is a finite set.

1. True
2. False

Q. A set with unlimited or uncountable number of elements is called:

1. infinite set
2. singleton set
3. empty set
4. finite set

Q.

Which of the following is a finite set?

1. Set of points common to any 2 parallel lines.
2. The set of positive integers greater than 1.
3. The set of positive integers greater than 100.
4. Set of points on a line.

Q. The set $B=\{x:x=3n+1,nϵN\text{and}n\le 20\}$ is _________.

1. a null set
2. singleton set
3. a finite set
4. an infinite set