Introduction to Real Numbers:
Real numbers are a fundamental concept in mathematics. They include rational numbers, such as fractions and integers, as well as irrational numbers, such as square roots and pi. Real numbers can be represented on a number line and have various properties and operations associated with them.

Multiple Choice Questions (MCQ) on Real Numbers:
1. Which of the following is a real number?
a) 3/4
b) √2
c) -5
d) All of the above

2. Which of the following is not a real number?
a) √-1
b) 5
c) 0
d) -2/3

3. Which of the following is an irrational number?
a) 0.5
b) -3
c) π
d) 2/3

4. The set of real numbers is denoted by:
a) R
b) Q
c) Z
d) N

5. Which of the following is not a property of real numbers?
a) Closure property
b) Associative property
c) Identity property
d) Commutative property

Solutions:
1. d) All of the above
- All the options given in the question are real numbers. Rational numbers like 3/4 and -5 can be expressed as fractions or integers, while the square root of 2 (√2) is an irrational number.

2. a) √-1
- The square root of a negative number is not a real number. It is an imaginary number denoted by 'i'.

3. c) π (pi)
- π is an irrational number that represents the ratio of a circle's circumference to its diameter. It is a non-repeating and non-terminating decimal.

4. a) R
- The set of real numbers is denoted by the letter 'R'.

5. d) Commutative property
- The commutative property states that changing the order of numbers does not affect the result. This property does not hold true for subtraction and division of real numbers.

Conclusion:
Real numbers are an essential component of mathematics, encompassing both rational and irrational numbers. MCQs on real numbers help test the understanding of these concepts. By practicing these questions, students can strengthen their knowledge and problem-solving skills related to real numbers.

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