Below are the most important / top questions from Class 10 Mathematics (JCERT / NCERT) – Chapter 1: Real Numbers. These questions are frequently asked in board exams and school tests.
Class 10 Maths – Real Numbers (Top Questions)
1. Very Important Questions (Long Answer – 4/5 Marks)
Use Euclid’s Division Algorithm to find the HCF of: (a) 135 and 225 (b) 867 and 255 (c) 196 and 38220 Prove that √5 is irrational. Prove that √2 is irrational. Prove that √7 is irrational. Show that every composite number can be expressed as a product of primes.
2. Important Questions (3 Marks)
Find the HCF and LCM of 306 and 657 using prime factorization, and verify: \text{HCF} \times \text{LCM} = \text{Product of the numbers} Find the HCF using Euclid’s Division Lemma of: 135 and 225 56 and 72 Explain why 17 × 11 × 5 × 3 is a composite number.
3. Short Answer Questions (2 Marks)
Write the Euclid’s Division Lemma. Is √13 a rational or irrational number? Justify. Find the LCM of 15 and 20. Write the fundamental theorem of arithmetic.
4. Objective / 1-Mark Questions
Is 1 a prime number? Write the prime factorization of 60. Write whether √9 is rational or irrational. How many prime factors does 36 have?
5. HOTS / Board-Oriented Questions
Prove that the square of any odd integer is of the form 4m + 1. Prove that 6n² + 4n is always even. Prove that any prime number greater than 3 is of the form 6n ± 1.