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This Class 10 Maths Chapter 1 MCQ practice set is based on the NCERT syllabus and important board exam concepts.
These multiple choice questions cover real numbers, Euclid’s division lemma, irrational numbers, prime numbers, HCF, and LCM. Step-by-step solutions are included to help students understand each concept clearly. These questions are useful for CBSE and state board exam preparation.
Do You Know
Q1. According to Euclid’s Division Lemma:
$$Dividend = Divisor \times Quotient + Remainder$$
The remainder is always:
A) Negative
B) Greater than divisor
C) Less than divisor
D) Equal to divisor
Answer: Less than divisor
Solution:
According to Euclid’s Division Lemma:
$$a = bq + r$$
where:
$$0 \le r < b$$
This means the remainder is always less than the divisor.
Therefore, the correct answer is:
Less than divisor
Q2. Which of the following is an irrational number?
A) $$\frac{3}{5}$$
B) $$0.25$$
C) $$\sqrt{2}$$
D) $$0.333\ldots$$
Answer: $$\sqrt{2}$$
Solution:
An irrational number cannot be written in the form:
$$\frac{p}{q}$$
and its decimal expansion is non-terminating and non-recurring.
$$\sqrt{2}$$ is an irrational number.
But:
$$\frac{3}{5} = 0.6$$
and
$$0.333\ldots = \frac{1}{3}$$
are rational numbers.
Therefore, the correct answer is:
$$\sqrt{2}$$
Q3. The product of HCF and LCM of two numbers is equal to:
A) Sum of numbers
B) Difference of numbers
C) Product of numbers
D) Square of numbers
Answer: Product of numbers
Solution:
For any two numbers:
$$HCF \times LCM = Product\ of\ the\ numbers$$
Example:
For $$6$$ and $$8$$
$$HCF = 2$$
$$LCM = 24$$
$$2 \times 24 = 48$$
and
$$6 \times 8 = 48$$
Therefore, the correct answer is:
Product of numbers
Q4. Which of the following numbers has a terminating decimal expansion?
A) $$\frac{1}{3}$$
B) $$\frac{2}{7}$$
C) $$\frac{5}{8}$$
D) $$\frac{4}{9}$$
Answer: $$\frac{5}{8}$$
Solution:
A rational number has a terminating decimal expansion if the denominator contains only factors:
$$2$$ and/or $$5$$
For:
$$\frac{5}{8}$$
$$8 = 2^3$$
So its decimal expansion terminates.
$$\frac{5}{8} = 0.625$$
Therefore, the correct answer is:
$$\frac{5}{8}$$
Q5. The decimal expansion of:
$$\frac{7}{11}$$
is:
A) Terminating
B) Non-terminating recurring
C) Irrational
D) Whole number
Answer: Non-terminating recurring
Solution:
Dividing:
$$7 \div 11$$
we get:
$$0.636363\ldots$$
The digits repeat continuously.
So the decimal expansion is:
non-terminating recurring.
Therefore, the correct answer is:
Non-terminating recurring
Important Formula and Concept Section:
$$a = bq + r$$
where:
$$0 \le r < b$$
and
$$HCF \times LCM = Product\ of\ two\ numbers$$
A rational number can have:
– terminating decimal expansion
or
– non-terminating recurring decimal expansion
FAQs:
Q. What is Euclid’s Division Lemma?
Answer:
$$a = bq + r$$
where:
$$0 \le r < b$$
Q. What is an irrational number?
Answer:
An irrational number cannot be written in the form:
$$\frac{p}{q}$$
Q. Which numbers have terminating decimal expansion?
Answer:
Numbers whose denominators contain only factors:
$$2$$ and/or $$5$$
Conclusion:
These Class 10 Maths Chapter 1 MCQ questions with detailed solutions are useful for board exam preparation. Practice these Real Numbers questions regularly to improve understanding of irrational numbers, decimal expansions, HCF, LCM, and Euclid’s Division Lemma.
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