Real Numbers
31 solved questions from Class 10 Mathematics, each with the full working. Tap any question to see the step-by-step solution.
- 1 Find the HCF and the LCM of 306 and 657, and verify that HCF × LCM = product of the two numbers. medium 3 marks Relationship between HCF and LCM
- 2 Prove that √5 is an irrational number. medium 3 marks Proving irrationality by contradiction
- 3 Without performing long division, state whether 13/3125 has a terminating or a non-terminating repeating decimal expansion. Write the expansion if it terminates. easy 2 marks Condition for a terminating decimal expansion
- 4 Check whether 6^n can end with the digit 0 for any natural number n. medium 2 marks Fundamental Theorem of Arithmetic
- 5 Explain why 7 × 11 × 13 + 13 is a composite number. easy 2 marks Composite numbers and factorisation
- 6 Three bells toll at intervals of 9, 12 and 15 minutes respectively. If they all toll together at 8:00 a.m., at what time will they next toll together? medium 3 marks Using the LCM for repeating events
- 7 Express the repeating decimal 0.123 as a fraction in lowest terms. medium 2 marks Converting repeating decimals to fractions
- 8 What is the smallest integer that must be added to 245 so that the resulting number is a perfect square? medium 2 marks Nearest perfect square
- 9 Find the HCF and LCM of 84 and 126 using prime factorisation, and verify that HCF × LCM equals the product of the two numbers. easy 2 marks HCF and LCM via prime factorisation
- 10 Which of the following numbers is a rational number? easy MCQ 1 mark Definition of rational numbers
- 11 Prove that √27 is an irrational number using prime factorisation and the method of contradiction. medium 3 marks Irrationality proof by contradiction
- 12 Find the HCF and LCM of 84 and 150 using prime factorisation, and verify that HCF × LCM equals the product 84 × 150. medium 2 marks Prime factorisation for HCF and LCM
- 13 Express the repeating decimal 0.47 as a fraction in its lowest terms. easy 1 mark Conversion of repeating decimal to fraction
- 14 What is the smallest integer that must be added to 1729 so that the resulting number is a perfect square? State the integer and the perfect square obtained. hard 3 marks Completing to the next perfect square
- 15 Find the HCF of 24 and 36 using prime factorisation. medium MCQ Prime Factorisation and HCF
- 16 Express 140 as a product of its prime factors. medium MCQ Prime Factorisation
- 17 Is √2 a rational or irrational number? medium MCQ Irrational Numbers
- 18 What is the LCM of 12 and 15? medium MCQ LCM Calculation
- 19 Find the value of 5³ × 5² using exponent laws. medium MCQ Exponents and Powers
- 20 What is the multiplicative inverse of -4/5? medium MCQ Rational Numbers
- 21 Evaluate (-1)^100. medium MCQ Exponents
- 22 Is zero (0) a positive or negative integer? medium MCQ Integers
- 23 Simplify: 3/4 + 5/6. medium MCQ Fractions Addition
- 24 What is the predecessor of 10,000? medium MCQ Predecessor and Successor
- 25 What is the domain, range, or fundamental theorem introduced in 'Real Numbers' (Class 10 Mathematics)? medium MCQ Functions & Theorems
- 26 What is the derivative or integral formula associated with 'Real Numbers'? medium MCQ Calculus & Formulae
- 27 How do you find the solution set or optimum value in 'Real Numbers'? medium MCQ Problem Solving & Optimization
- 28 Express the repeating decimal 0.61 as a fraction in lowest terms. easy MCQ 1 mark Repeating decimal to fraction
- 29 Determine the domain and the range of the function f(x)=√(5 - x^2). medium 2 marks Domain and range of radical function
- 30 Find the smallest integer that must be added to 2037 so that the resulting number is a perfect square. State the integer and the perfect square. medium 2 marks Nearest perfect square
- 31 Which integer must be added to 1500 so that the resulting number is a perfect square? State the integer and the resulting perfect square. easy MCQ 2 marks Nearest perfect square above a number