1. REAL NUMBERS 1. Using fundamental theorem on arithmetic, find the HCF of 945 and 1155. 2. State Euclid’s division lemma. 3. Using Euclid’s division lemma find the HCF of 324 and 594. 4. Find the LCM of (3465, 5460) using prime factorisation method. 5. Find the number which when divided by 117 gives 41 as quotient and 23 as remainder. 6. LCM (480, 672) = 3360. Find HCF (480, 672). 7. Prove that

is irrational.

8. Without actual division find whether the rational number

is a terminating or non-terminating

repeating decimal. – 9. Express 0.3 as a fraction in the simplest form. 10. Write the prime factorisation of 275. 11. If a divides b and b divides a what can you say about a and b ? 12. Prove that 17 × 41 × 43 × 61 + 43 is a composite number. 13. Will 6n end with the digit zero, for any natural number n ? Justify your answer. 14. Find the greatest number which when divides 245 and 1029 leaves remainder 5 in each case ? 15. Write the condition to be satisfied by q so that the rational number p/q is a terminating decimal. 16. Find the missing numbers. 2 2 2

17

17. Show that any positive odd integer is of the form 6q + 1, 6q + 3 or 6q + 5 where q is same integer. 18. Find the maximum number of boxes into which 1134 apples and 1215 oranges be distributed so that each box contains the same number of apples and oranges. 19. In a school, the duration of a period in junior section is 40 minutes and in senior section is 60 minutes. If the first bell for each section rings at 9 a.m, when will the two bells ring together again ? 20. Prove that 4n cannot end with the digit 0 for any x ∈ N. 21. Write the condition to be satisfied by q so that a rational number expansion. 22. Express 0.254 as a rational number in the form -1-

has a terminating decimal

where a and b are coprime.

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