Real Numbers-Class 10

1) Which of the following statements is true?

2) The product of a non-zero rational number and an irrational number is always:

3) The HCF of two numbers is 15 and their LCM is 300. If one number is 60, then the other number is:

4) If a = 7q + 3, then the possible values of the remainder are:

5) The Fundamental Theorem of Arithmetic states that every composite number can be uniquely expressed as a product of

6) Which of the following is an irrational number?

7) The smallest composite number is:

8) Substituting p = 2k in p^2 = 2q^2, we get 4k^2 = 2q^2, which simplifies to:

9) The LCM of two or more numbers is the product of the greatest power of each prime factor involved in the numbers. This statement is part of:

10) The prime factorization of 360 is:

11) The fact that both p and q are divisible by 2 contradicts our initial assumption that p and q are:

12) The sum of two rational numbers is always:

13) The HCF of 12 and 18 is:

14) The LCM of 12 and 18 is:

15) In the expression a = bq + r, 'a' is the:

16) To find the HCF of 867 and 255 using Euclid's Division Algorithm, the first step is:

17) If the prime factorization of a number is 2 * 3^2 * 7, then the number is:

18) Euclid's Division Lemma is a technique to find the:

19) Three bells toll at intervals of 9, 12, and 15 minutes respectively. If they start tolling together, after what time will they next toll together?

20) The number of prime factors in the prime factorization of 360 (counting multiplicities) is: