NCERT Class 10 Mathematics Chapter 1 Real Numbers MCQ

NCERT Class 10 Maths Chapter 1 MCQs of Real Numbers help students strengthen their understanding of real numbers, including Euclid’s Division Lemma, prime factorization, HCF and LCM. NCERT Mathematics 10th Class multiple-choice questions improve problem-solving skills by testing conceptual clarity and logical reasoning. Practicing MCQs enhances speed and accuracy, preparing students for board exams and competitive tests. They also highlight common mistakes, ensuring better retention of mathematical principles. Regular MCQ practice builds confidence and sharpens analytical thinking in number theory.
Class 10 Maths Chapter 1 NCERT Solutions
Class 10 Multiple Choice Questions
Class 10 Mathematics MCQ

Class 10 Maths Chapter 1 MCQs with Answers for Real Numbers

In NCERT Class 10 Maths Chapter 1 MCQs with answers, students encounter problems related to rational and irrational numbers, divisibility rules and properties of real numbers. One of the fundamental concepts tested in multiple-choice questions is how numbers can be categorized. Rational numbers are those that can be written in fraction form, while irrational numbers have non-repeating, non-terminating decimal expansions. A typical MCQ ask students to determine whether a number like the square root of two is rational or not. Another important topic is the closure property, where operations like addition and multiplication are tested to check if they remain within the set of real numbers. Grade 10th Math MCQs strengthen a student’s understanding of how numbers behave under different mathematical operations.

Q1. The exponent of 5 in the prime factorisation of 3750, is

[A]. 6

[B]. 5

[C]. 4

[D]. 3

Q2. The LCM of two numbers is 1200. Which of the following cannot be their HCF?

[A]. 200

[B]. 400

[C]. 500

[D]. 600

Real Numbers with Class 10 MCQs PDF Application

Students looking for structured practice often refer to Real Numbers NCERT Class 10 Math MCQs PDF, which contains a variety of questions on Euclid’s Division Lemma, prime factorization and number relationships. Euclid’s Division Lemma is widely used to determine the Highest Common Factor (HCF) of two numbers by repeatedly dividing them until the remainder is zero. This process is required in simplifying fractions and solving problems involving divisibility. Prime factorization plays a key role in LCM and HCF calculations, where numbers are broken down into their smallest prime components. Many MCQs test the ability to express composite numbers uniquely as products of primes. Understanding these principles is necessary for advanced mathematical applications and helps in solving real-world problems efficiently.

Q3. If n = 2³ x 3⁴ x 5⁴ x 7, then the number of consecutive zeros in n, where n is a natural number, is

[A]. 2

[B]. 3

[C]. 5

[D]. 8

Q4. The total number of factors of a prime number is

[A]. 0

[B]. 1

[C]. 2

[D]. 3

Class 10 Maths Chapter 1 MCQ for Fundamental Theorem of Arithmetic

When solving Class 10 Maths Chapter 1 multiple choice questions, students must apply the Fundamental Theorem of Arithmetic, which states that every composite number has a unique prime factorization. This concept is useful in various mathematical computations, such as finding the least common multiple (LCM) and highest common factor (HCF). Many MCQs focus on determining whether a number is prime or composite by checking its divisibility. Another common question type involves proving the irrationality of numbers by assuming the opposite and deriving a contradiction. Students may be asked to analyze the properties of numbers, such as determining if the sum of two irrational numbers is always irrational. These multiple-choice questions help students develop logical reasoning and problem-solving skills.

Q5. The HCF of 95 and 152, is

[A]. 1

[B]. 19

[C]. 57

[D]. None of these.

Q6. The smallest irrational number by which √18 should be multiplies so as to get a rational number is

[A]. 2

[B]. √2

[C]. 2√2

[D]. 3√2

MCQs for Class 10 Maths Chapter 1 with LCM, HCF and Factorization

Practicing important MCQs for Class 10 Maths Solutions Chapter 1 helps students build a strong foundation in number theory, particularly in understanding LCM, HCF and factorization techniques. One frequently tested concept is finding the largest number that exactly divides two or more numbers, which involves using the HCF method. Determining the smallest common multiple of two numbers is done using LCM calculations. Factorization techniques, including the division method and prime factorization, are commonly used to break numbers into their simplest components. Many MCQs also require students to understand the relationship between HCF and LCM, particularly the fact that their product is equal to the product of the two numbers. Solving such MCQs strengthens analytical skills and mathematical accuracy.

Q7. The sum of the exponents of the prime factors in the prime factorisation of 196, is

[A]. 1

[B]. 2

[C]. 3

[D]. 4

Q8. The decimal expansion of π is

[A]. Terminating

[B]. Non-terminating

[C]. Non- terminating but repeating

[D]. Non- terminating non-repeating

Class 10 Maths Chapter 1 MCQs with Detailed Solutions

Using Class 10 Maths Chapter 1 MCQs with detailed solutions helps students analyze their mistakes and improve accuracy. Detailed solutions provide step-by-step explanations, allowing learners to understand the logic behind each answer. A common mistake students make while solving MCQs on real numbers is incorrectly assuming that all square roots are irrational. Another frequent error occurs when determining the prime factorization of a number, where missing or misidentifying prime factors can lead to incorrect answers. Detailed solutions also help students recognize patterns in number theory, such as how terminating and non-terminating decimals relate to rational numbers or irrational numbers. By reviewing solutions systematically, students improve their problem-solving approach and enhance their ability to tackle complex mathematical questions with confidence.

Q9. The HCF of two numbers is 18 and their product is 12960. Their LCM will be

[A]. 400

[B]. 620

[C]. 720

[D]. 900

Q10. If HCF (26, 169) = 13, then LCM (26, 169) =

[A]. 13

[B]. 226

[C]. 52

[D]. 338

What are some important MCQs for Class 10 Maths Chapter 1?

Important MCQs for Class 10 Maths Chapter 1 focus on key concepts like Euclid’s Division Lemma, the Fundamental Theorem of Arithmetic, prime factorization and rational irrational numbers. Many questions test a student’s ability to determine the Highest Common Factor (HCF) and Least Common Multiple (LCM) using different methods. Another frequently asked MCQ type involves proving whether a given number is rational or irrational based on its decimal representation. Students are also required to analyze number properties, such as the closure of real numbers under subtraction and multiplication. Practicing a variety of MCQs helps in building a strong mathematical foundation for board exams and competitive tests.

Why is practicing Real Numbers Class 10 MCQs PDF important?

Practicing Real Numbers Class 10 MCQs PDF is essential for the fundamental principles of number theory. These MCQs cover a wide range of topics, including Euclid’s Division Lemma, which helps in finding the HCF of numbers systematically, and the prime factorization method, which plays a crucial role in determining the LCM of given numbers. These PDFs often include questions on rational and irrational numbers, helping students understand the concept of terminating and non-terminating decimals. Solving MCQs from a well-structured PDF allows students to test their knowledge, identify weak areas and improve their speed and accuracy in mathematical problem-solving.

How do Class 10 Maths Chapter 1 MCQs solutions help in problem-solving?

Using NCERT Class 10 Maths Chapter 1 MCQs with detailed solutions provides a step-by-step approach to solving mathematical problems efficiently. Detailed solutions break down the problem into logical steps, allowing students to understand the reasoning behind each answer. Many common mistakes in number theory arise from miscalculations in prime factorization or incorrect assumptions about the nature of rational and irrational numbers. Reviewing MCQs with complete solutions helps in recognizing patterns, improving logical reasoning, and avoiding errors. These solutions enhance conceptual clarity, which is essential for tackling higher-level mathematics in board exams and entrance tests. Regular practice ensures better problem-solving skills and higher accuracy.

NCERT MCQ Solutions for Class 10 Maths Chapter 1 Real Numbers