Chapter: 01- Real numbers Test paper – 01 FM: 30 Time: 45 min
1 mark questions
1. 3.24636363... is:
(a) a terminating decimal number (b) a non-terminating repeating decimal number
(c) a rational number (d) both (b) and (c)
2. For some integer q, every odd integer is of the form :
(a) 2q (b) 2q + 1 (c) q (d) q + 1
3. If the HCF of 85 and 153 is expressible in the form 85m – 153, then the value of m is :
(a) 1 (b) 4 (c) 3 (d) 2
4. If two integers a and b are written as a = x3y2 and b = xy4; x, y are prime numbers, then H.C.F. (a, b) is :
(a) x3y3 (b) x2y2 (c) xy (d) xy2
5. If least prime factor of a is 3 and least prime factor of b is 7, the least prime factor of (a + b) is:
(a) 2 (b) 3 (c) 5 (d) 11
2 marks questions
6. Show that every positive even integer is of the from 2m, and that every positive odd integer is of the form 2m + 1, where m is some integer.
7. Show that any positive odd integer is of the form 6m + 1, or 6m + 3, or 6m + 5, where m is some integer.
8. Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.
9. Show that any positive integer is of the form 3q or 3q + 1 or 3q + 2 for some integer q.
10. Show that 5-√3 is irrational.
3 marks questions
11. Check whether 6n can end with the digit 0, for any natural number n.
12. Prove that one of every three consecutive positive integers is divisible by 3.
13. Prove that n2−n is divisible by 2 for every positive integer n.
14. Use Euclid division lemma to show that cube of any positive integer is either of the form 9m, 9m + 1, or 9m + 8
If d is the HCF of 45 and 27, find x & y satisfying d=27x +45y. (Ans d=9, x=2, y= -1 )
15. Prove that if x and y are both odd positive integers, then x2 + y2 is even but not divisible by 4
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