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Real Numbers Practice Questions

Class 10 · Mathematics · 2599 free MCQs with instant results and detailed explanations.

2599
Total
876
Easy
1220
Medium
503
Hard

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Topics in Real Numbers

Euclid's Division Lemma 504
Irrational Numbers 752
Rational Numbers and Decimals 772
Fundamental Theorem of Arithmetic 561

Sample Questions from Real Numbers

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
Which of the following is a rational number?
A. 0.75
B. √2
C. π
D. e
Show Answer & Explanation
Correct Answer: A
0.75 can be expressed as the fraction 3/4, making it a rational number. The others are not expressible as fractions.
Q2
Easy
What is the decimal representation of the rational number 5/8?
A. 0.625
B. 0.75
C. 0.5
D. 0.8
Show Answer & Explanation
Correct Answer: A
Dividing 5 by 8 gives 0.625. This is the correct decimal representation of the fraction.
Q3
Easy
Which of the following sets contains only irrational numbers?
A. {√3, √5, 4}
B. {π, √7, -2.5}
C. {2, -√2, √8}
D. {√2, √11, √13}
Show Answer & Explanation
Correct Answer: D
Option D contains only square roots of prime numbers, which are irrational. The other options contain rational numbers.
Q4
Medium
Which of the following is a rational number?
A. √2
B. 1/3
C. π
D. √3
Show Answer & Explanation
Correct Answer: B
A rational number can be expressed as a fraction of two integers. 1/3 fits this definition.
Q5
Medium
Which of the following numbers is irrational?
A. 7.5
B. 0.333...
C. √5
D. 8
Show Answer & Explanation
Correct Answer: C
An irrational number cannot be expressed as a fraction of two integers. √5 is an example of an irrational number.
Q6
Medium
If the number 12 is expressed in the form of p/q, where p and q are integers with no common factors, what is the simplest form?
A. 12/1
B. 3/1
C. 4/1
D. 2/1
Show Answer & Explanation
Correct Answer: A
The simplest form of 12 expressed as p/q is 12/1, where 12 and 1 have no common factors other than 1.
Q7
Medium
Which of the following represents a non-terminating but repeating decimal?
A. 1/2
B. 1/3
C. 1/4
D. 1/5
Show Answer & Explanation
Correct Answer: B
1/3 equals 0.333..., which is non-terminating and repeating, while the others terminate.
Q8
Hard
If the square root of a number is a rational number, which of the following statements is true about the number?
A. It must be a perfect square.
B. It can be any integer.
C. It is always negative.
D. It is an irrational number.
Show Answer & Explanation
Correct Answer: A
The square root of a number is rational only if the number is a perfect square, as non-perfect squares yield irrational roots.
Q9
Hard
Which of the following sets of numbers is closed under the operation of multiplication?
A. All integers
B. All rational numbers
C. All natural numbers
D. All whole numbers
Show Answer & Explanation
Correct Answer: A
The set of all integers is closed under multiplication because the product of any two integers is always an integer.
Q10
Hard
Using Euclid's Division Lemma, if a = 20 and b = 6, what is the value of q and r in the equation a = bq + r?
A. q=3, r=2
B. q=2, r=8
C. q=4, r=0
D. q=1, r=14
Show Answer & Explanation
Correct Answer: A
When dividing 20 by 6, the quotient is 3 and the remainder is 2, hence 20 = 6*3 + 2.

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Real Numbers — Class 10 Mathematics Practice Questions Online

This page contains 2599 practice MCQs for the chapter Real Numbers in Class 10 Mathematics. The questions are organized by difficulty — 876 easy, 1220 medium, 503 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 4 topics, giving you comprehensive coverage of the entire chapter.