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Real Numbers — Practice Quiz

Telangana Board · Class 10 · Mathematics

Try a 4-question quiz on Real Numbers for Telangana Board Class 10 Mathematics: tap an answer to check it and see why.

43 questions28 flashcards10 formulas & key relations5 concepts

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Quick Quiz: Real Numbers

0/4

Tap an answer to check it instantly. No sign-up needed for these 4.

1

Using Euclid's division algorithm, find the HCF of 56 and 72.

2

Express 0.375 as a fraction in its simplest form.

3

Find the LCM of 12, 18, and 24 using prime factorization.

4

If 2ˣ = 32, find the value of x.

43 Questions·
multiple choicemultiple correct

Sample Questions

1multiple correct

Which of the following numbers will have terminating decimal expansion?

Show answer

7/16, 13/125, 17/20

For terminating decimals, denominator must have only factors 2 and 5. 16 = 2⁴ ✓, 125 = 5³ ✓, 20 = 2² × 5 ✓. But 18 = 2 × 3² (has factor 3) ✗, 30 = 2 × 3 × 5 (has factor 3) ✗.

2multiple choice

Prove that √3 is irrational by contradiction method.

Show answer

Assume √3 is rational, then 3 divides both numerator and denominator

Assume √3 = p/q where p,q are coprime. Then 3q² = p², so 3 divides p². By theorem, 3 divides p. Let p = 3k, then 3q² = 9k², so q² = 3k², meaning 3 divides q. This contradicts p,q being coprime.

3multiple choice

Express 2310 as a product of prime factors.

Show answer

2 × 3 × 5 × 7 × 11

2310 ÷ 2 = 1155, 1155 ÷ 3 = 385, 385 ÷ 5 = 77, 77 ÷ 7 = 11, 11 ÷ 11 = 1. So 2310 = 2 × 3 × 5 × 7 × 11.

4multiple correct

Which of the following are properties of logarithms?

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log_a(xy) = log_a(x) + log_a(y), log_a(x/y) = log_a(x) - log_a(y), log_a(x^n) = n × log_a(x), log_a(a) = 1

These are the fundamental properties: product rule, quotient rule, power rule, and log of base equals 1. The option log_a(x + y) = log_a(x) × log_a(y) is incorrect.

+39 more questions on Real Numbers (Telangana Board Class 10 Mathematics)

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Frequently Asked Questions

What are the important topics in Real Numbers for Telangana Board Class 10 Mathematics?
Key topics in Real Numbers include Division Algorithm and Euclid's Algorithm, Prime Factorisation, HCF and LCM, Decimal Expansions of Rational Numbers, Irrational Numbers and Proofs. Study these first, then practise questions on each for the Telangana Board Class 10 board exam.
How many practice questions are there for Real Numbers?
There are 43 questions on Real Numbers. Try the 4-question sample quiz on this page first; each answer shows an explanation when you tap it.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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