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This Class 10 Maths Chapter 1 MCQ quiz is based on the NCERT syllabus and covers important concepts of Real Numbers.
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These multiple choice questions are useful for CBSE and state board students preparing for board exams. Detailed step-by-step solutions are provided to help students understand the concepts easily. Practice these questions regularly to improve problem-solving skills and exam preparation.
Q1. The HCF of $$12$$ and $$18$$ is:
A) $$2$$
B) $$3$$
C) $$6$$
D) $$9$$
Answer: $$6$$
Solution:
Factors of $$12$$ are:
$$1, 2, 3, 4, 6, 12$$
Factors of $$18$$ are:
$$1, 2, 3, 6, 9, 18$$
The greatest common factor is:
$$6$$
Therefore, the correct answer is:
$$6$$
Q2. The LCM of $$8$$ and $$12$$ is:
A) $$12$$
B) $$24$$
C) $$36$$
D) $$48$$
Answer: $$24$$
Solution:
Prime factorization of $$8$$:
$$8 = 2 \times 2 \times 2$$
Prime factorization of $$12$$:
$$12 = 2 \times 2 \times 3$$
Taking highest powers:
$$LCM = 2^3 \times 3$$
$$= 8 \times 3$$
$$= 24$$
Therefore, the correct answer is:
$$24$$
Q3. Which of the following is a prime number?
A) $$9$$
B) $$15$$
C) $$17$$
D) $$21$$
Answer: $$17$$
Solution:
A prime number has only two factors:
$$1$$ and itself.
Checking the options:
$$9 = 3 \times 3$$
$$15 = 3 \times 5$$
$$21 = 3 \times 7$$
But $$17$$ has no factors other than:
$$1$$ and $$17$$
Therefore, the correct answer is:
$$17$$
Q4. The decimal expansion of a rational number is:
A) Always terminating
B) Always non-terminating
C) Either terminating or non-terminating recurring
D) Never recurring
Answer: Either terminating or non-terminating recurring
Solution:
A rational number can have:
– terminating decimal expansion
or
– non-terminating recurring decimal expansion
Example:
$$\frac{1}{2} = 0.5$$
Example:
$$\frac{1}{3} = 0.333\ldots$$
Therefore, the correct answer is:
Either terminating or non-terminating recurring
Q5. The HCF of two coprime numbers is:
A) $$0$$
B) $$1$$
C) $$2$$
D) $$The number itself$$
Answer: $$1$$
Solution:
Coprime numbers have only one common factor.
That common factor is:
$$1$$
Example:
$$8$$ and $$15$$
Their HCF is:
$$1$$
Therefore, the correct answer is:
$$1$$
Important Formula and Concept Section:
$$HCF \times LCM = Product\ of\ two\ numbers$$
A rational number can have:
– terminating decimal expansion
or
– non-terminating recurring decimal expansion
FAQs:
Q. What is the HCF of two coprime numbers?
Answer:
$$1$$
Q. What is a prime number?
Answer:
A prime number has exactly two factors:
$$1$$ and itself.
Q. What is the LCM of $$8$$ and $$12$$?
Answer:
$$24$$
Conclusion:
These Class 10 Maths Chapter 1 MCQ questions with answers are useful for students preparing for school exams and board exams. Regular practice of Real Numbers MCQs can improve understanding of HCF, LCM, prime numbers, and rational numbers.
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