Real Numbers - MCQ with Solution, Class 10 Mathematics

Real numbers are an essential concept in mathematics that includes rational and irrational numbers. Understanding real numbers is crucial for various mathematical operations and applications. Here are some multiple-choice questions (MCQs) with solutions related to real numbers for Class 10 Mathematics.

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

Solution:
The correct answer is c) √2.

Explanation:
- Real numbers consist of rational and irrational numbers.
- Option a) 0 is a real number because it is a rational number (0/1).
- Option b) -5 is a real number because it is a rational number (-5/1).
- Option c) √2 is an irrational number because it cannot be expressed as a fraction and its decimal representation goes on forever without repeating.
- Option d) 2/3 is a real number because it is a rational number.

Question 2: Which of the following is not a rational number?
a) 0.25
b) -2/5
c) √3
d) 1/2

Solution:
The correct answer is c) √3.

Explanation:
- Rational numbers can be expressed as fractions (p/q) where q is not equal to 0.
- Option a) 0.25 can be expressed as 1/4, so it is a rational number.
- Option b) -2/5 is a rational number since it can be expressed as a fraction.
- Option c) √3 is an irrational number because it cannot be expressed as a fraction.
- Option d) 1/2 is a rational number.

Question 3: The sum of a rational number and an irrational number is always:
a) Rational
b) Irrational
c) Integer
d) Real

Solution:
The correct answer is b) Irrational.

Explanation:
- When we add a rational number and an irrational number, the result is always an irrational number.
- This is because the sum of a rational and an irrational number cannot be expressed as a fraction, and its decimal representation goes on forever without repeating.

Question 4: Which of the following is a terminating decimal?
a) 0.123456
b) 0.333...
c) 0.625
d) 0.272727...

Solution:
The correct answer is c) 0.625.

Explanation:
- A terminating decimal is a decimal number that ends after a finite number of digits.
- Option a) 0.123456 is a non-terminating decimal because it goes on forever without repeating.
- Option b) 0.333... is a non-terminating decimal because it represents a repeating decimal.
- Option c) 0.625 is a terminating decimal since it ends after three digits.
- Option d) 0.272727... is a repeating decimal.

Question 5: Which of the following is an irrational number?
a) 0.5
b) -3
c) π (pi)
d) 2/3

Before answering any question study yours.. First go and Study about real numbers