Question Bank
Real Numbers encompass all rational and irrational numbers, forming a complete and continuous number line essential for various mathematical concepts.
Must Practice Questions of chapter Real Numbers
How can you represent real numbers on a number line?
Discuss the properties of real numbers and how they are classified.
How can you determine if a number is irrational or rational?
Explain the concept of irrational numbers and provide examples.
What is the Fundamental Theorem of Arithmetic and why is it important in the study of real numbers?
Explain the process of finding the square root of a number.
Discuss the concept of real numbers.
How can you represent irrational numbers on a number line?
Differentiate between rational and irrational numbers.
Explain the concept of rational numbers.
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What is the Fundamental Theorem of Arithmetic?
Explain the concept of prime numbers.
Define composite numbers and provide examples.
How can you determine if a number is irrational?
Discuss the properties of irrational numbers.
Find the HCF and LCM of 6, 72 and 120, using the prime factorisation method.
Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429
Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. (i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54
Find the LCM and HCF of the following integers by applying the prime factorisation method. (i) 12, 15 and 21 (ii) 17, 23 and 29 (iii) 8, 9 and 25
Given that HCF (306, 657) = 9, find LCM (306, 657).
Check whether 6n can end with the digit 0 for any natural number n
Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers
There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?
Prove that sqrt of 3 is irrational.
Show that 5– sqrt of 3 is irrational.
Show that 3*(sqrt of 2) is irrational.
Prove that sqrt of 5 is irrational.
Prove that 3 + 2*sqrt of 5 is irrational.
Prove that the following are irrationals : (i) 1/sqrt 2 (ii) 7 *sqrt 5 (iii) 6 + sqrt 2
