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Practice Class 10 Maths Chapter 1 Real Numbers MCQ Questions with Answers based on NCERT syllabus. Learn irrational numbers, decimal expansion, prime factorization, Euclid Division Lemma, HCF and LCM with detailed solutions for CBSE and state board exams.
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Introduction:
This Class 10 Maths Chapter 1 Real Numbers MCQ set is designed according to the NCERT syllabus. These questions help students strengthen concepts related to irrational numbers, decimal expansions, prime factorization, and Euclid’s Division Algorithm. Detailed solutions are provided for better understanding and exam preparation.
Q1. Which of the following is an irrational number?
A) $$\frac{7}{8}$$
B) $$0.125$$
C) $$\sqrt{5}$$
D) $$0.75$$
Answer: $$\sqrt{5}$$
Solution:
An irrational number cannot be expressed in the form:
$$\frac{p}{q}$$
where $$q \ne 0$$.
$$\sqrt{5}$$ is irrational because its decimal expansion is non-terminating and non-recurring.
Therefore, the correct answer is:
$$\sqrt{5}$$
————————————————–
Q2. The prime factorization of $$84$$ is:
A) $$2 \times 2 \times 3 \times 7$$
B) $$2 \times 3 \times 7$$
C) $$2 \times 2 \times 7$$
D) $$3 \times 4 \times 7$$
Answer:
$$2 \times 2 \times 3 \times 7$$
Solution:
Prime factorization of $$84$$:
$$84 = 2 \times 42$$
$$42 = 2 \times 21$$
$$21 = 3 \times 7$$
Therefore:
$$84 = 2 \times 2 \times 3 \times 7$$
Hence, the correct answer is:
$$2 \times 2 \times 3 \times 7$$
————————————————–
Q3. The decimal expansion of
$$\frac{13}{25}$$
is:
A) $$0.52$$
B) $$0.25$$
C) $$0.13$$
D) $$0.75$$
Answer:
$$0.52$$
Solution:
Multiply numerator and denominator by $$4$$:
$$\frac{13}{25} = \frac{52}{100}$$
Therefore:
$$\frac{13}{25}=0.52$$
Hence, the correct answer is:
$$0.52$$
————————————————–
Q4. If the HCF of two numbers is $$5$$ and their LCM is $$60$$, then the product of the numbers is:
A) $$65$$
B) $$300$$
C) $$55$$
D) $$600$$
Answer:
$$300$$
Solution:
Using the formula:
$$HCF \times LCM = Product\ of\ two\ numbers$$
Substituting the values:
$$5 \times 60 = 300$$
Therefore, the product of the two numbers is:
$$300$$
Hence, the correct answer is:
$$300$$
————————————————–
Q5. In Euclid’s Division Lemma:
$$a = bq + r$$
the value of $$r$$ is called:
A) Dividend
B) Divisor
C) Quotient
D) Remainder
Answer:
Remainder
Solution:
According to Euclid’s Division Lemma:
$$a = bq + r$$
where:
$$a$$ = Dividend
$$b$$ = Divisor
$$q$$ = Quotient
$$r$$ = Remainder
Therefore, the correct answer is:
Remainder
————————————————–
Important Concepts:
$$a = bq + r$$
where
$$0 \le r < b$$
Prime factorization means expressing a number as a product of prime numbers.
An irrational number cannot be expressed in the form:
$$\frac{p}{q}$$
where $$q \ne 0$$.
————————————————–
FAQs:
Q. What is an irrational number?
Answer:
A number that cannot be written in the form:
$$\frac{p}{q}$$
is called an irrational number.
Q. What is prime factorization?
Answer:
Expressing a number as a product of prime numbers is called prime factorization.
Q. What is the relationship between HCF and LCM?
Answer:
$$HCF \times LCM = Product\ of\ two\ numbers$$
————————————————–
Conclusion:
These Class 10 Maths Chapter 1 Real Numbers MCQs with answers and solutions help students understand important concepts such as irrational numbers, prime factorization, decimal expansion, and Euclid’s Division Lemma. Regular practice of these questions can improve confidence and board exam performance.
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