Mathematics ยท Quantitative Aptitude

Real Number System

277 Questions

The real number system encompasses rational and irrational numbers, forming the basis of arithmetic and number theory. It is a key area in the quantitative aptitude and mathematics sections of school level and competitive exams. Practice these questions to master the properties and identification of different types of numbers.

Identifying irrational numbersOrdering rational numbersProperties of square rootsPerfect number propertiesRational and irrational products

Real Number System Questions

Multiple choice

The set of all irrational numbers is:

  1. Open.

  2. Closed.

  3. Both open and closed.

  4. Neither open nor closed.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The set of all irrational numbers is neither open nor closed because it contains some of its boundary points but not all of them.

Multiple choice

Which of the following is a finite field?

  1. The set of rational numbers

  2. The set of real numbers

  3. The set of complex numbers

  4. The set of integers modulo 7
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A finite field is a field with a finite number of elements. The set of integers modulo 7 is a finite field with 7 elements.

Multiple choice

Which of the following sets is an open set in the real numbers?

  1. The set of all rational numbers

  2. The set of all irrational numbers

  3. The set of all numbers greater than 0

  4. The set of all numbers less than 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

An open set in the real numbers is a set that contains an open interval around each of its points. The set of all numbers greater than 0 is an open set because for any number in the set, we can find an open interval around that number that is entirely contained in the set.

Multiple choice

Which of the following sets is a closed set in the real numbers?

  1. The set of all rational numbers

  2. The set of all irrational numbers

  3. The set of all numbers greater than or equal to 0

  4. The set of all numbers less than or equal to 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A closed set in the real numbers is a set that contains all of its limit points. The set of all numbers greater than or equal to 0 is a closed set because all of its limit points are also in the set.

Multiple choice

Is zero a rational number?

  1. Yes

  2. No
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Zero is a rational number because it can be expressed as a fraction of two integers. For example, 0/1 is a rational number.

Multiple choice

Is zero an irrational number?

  1. Yes

  2. No
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Zero is not an irrational number because it is a rational number. Irrational numbers are numbers that cannot be expressed as a fraction of two integers.

Multiple choice

Which of the following sets is uncountable?

  1. The set of all rational numbers

  2. The set of all irrational numbers

  3. The set of all real numbers

  4. The set of all complex numbers
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The set of all irrational numbers is uncountable because it cannot be put into a one-to-one correspondence with the set of natural numbers.