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Rajasthan Board Class 10 (RBSE) Real Numbers — practice questions

Explore 30 free Real Numbers questions in Rajasthan Board Class 10 (RBSE) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Real Numbers questions and exercises with answers

Showing questions 1–30 of 30.

Euclid's division lemma states that for positive integers a and b, there exist unique q and r such that:Read the answer and worked solution →For any two positive integers, HCF × LCM equals:Read the answer and worked solution →The number √2 is:Read the answer and worked solution →A rational number p/q (in lowest terms) has a terminating decimal expansion if the prime factors of q are:Read the answer and worked solution →The HCF of 6 and 20 is:Read the answer and worked solution →The LCM of 6 and 20 is:Read the answer and worked solution →The product of the HCF and LCM of 6 and 20 is:Read the answer and worked solution →The decimal expansion of 1/3 is:Read the answer and worked solution →The decimal expansion of 7/8 is:Read the answer and worked solution →The number of prime numbers is:Read the answer and worked solution →The prime factorisation of 156 is:Read the answer and worked solution →The sum √3 + √5 is:Read the answer and worked solution →The Fundamental Theorem of Arithmetic states that every composite number can be expressed as:Read the answer and worked solution →Which of the following numbers is prime?Read the answer and worked solution →The prime factorisation of 360 is:Read the answer and worked solution →The Fundamental Theorem of Arithmetic guarantees that:Read the answer and worked solution →Find the HCF of 24 and 36.Read the answer and worked solution →Find the LCM of 12 and 18.Read the answer and worked solution →If HCF(a, b) = 9 and a · b = 1620, find LCM(a, b).Read the answer and worked solution →Two bells ring at intervals of 9 and 15 minutes. They ring together at noon. When do they ring together again?Read the answer and worked solution →Which of the following is an irrational number?Read the answer and worked solution →Will the decimal expansion of 13/125 terminate?Read the answer and worked solution →The decimal expansion of 1/6 is:Read the answer and worked solution →Which of the following will have a terminating decimal expansion?Read the answer and worked solution →Numbers that fill the number line completely (every point on the line corresponds to such a number) are called:Read the answer and worked solution →If p is prime and p divides a², then p divides a. This step is used to prove which number irrational in your syllabus?Read the answer and worked solution →Key in the numberRead the answer and worked solution →Prime or composite?Read the answer and worked solution →True or false: real numbersRead the answer and worked solution →Which one does NOT belong?Read the answer and worked solution →

Worked practice questions

Euclid's division lemma states that for positive integers a and b, there exist unique q and r such that:

  1. a = bq, with no remainder
  2. a = bq + r, where 0 ≤ r < b
  3. a = bq + r, where r > b
  4. a = b + qr
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Correct answer: B. a = bq + r, where 0 ≤ r < b

Euclid's division lemma: a = bq + r with 0 ≤ r < b, and q, r unique.

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For any two positive integers, HCF × LCM equals:

  1. the difference of the numbers
  2. the larger number
  3. the sum of the two numbers
  4. the product of the two numbers
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Correct answer: D. the product of the two numbers

For two positive integers, HCF × LCM = product of the numbers.

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The number √2 is:

  1. a natural number
  2. an integer
  3. irrational
  4. rational
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Correct answer: C. irrational

√2 cannot be written as p/q, so it is irrational.

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More Mathematics topics

SequencesBinomial TheoremGeometryProbability & StatisticsSequences and SeriesVectors & 3D GeometryProbabilityCorrelation and Regression