# Number System

**English**

**Math**>

**Rationals numbers**

**15 - 16**

**Number System**

**1. The decimal expansion of 22/7 is**

**(a) Terminating**

**(b) Non-terminating and repeating**

**(c) Non-terminating and Non-repeating**

**(d) None of the above**

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**2. For some integer n, the odd integer is represented in the form of:**

**(a) n**

**(b) n + 1**

**(c) 2n + 1**

**(d) 2n**

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**3. HCF of 26 and 91 is:**

**(a) 15**

**(b) 13**

**(c) 19**

**(d) 11**

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**4. Which of the following is not irrational?**

**(a) (3 + √7)**

**(b) (3 – √7)**

**(c) (3 + √7) (3 – √7)**

**(d) 3√7**

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**5. The addition of a rational number and an irrational number is equal to:**

**(a) rational number**

**(b) Irrational number**

**(c) Both**

**(d) None of the above**

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**6. The multiplication of two irrational numbers is:**

**(a) irrational number**

**(b) rational number**

**(c) Maybe rational or irrational**

**(d) None**

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**7. If set A = {1, 2, 3, 4, 5,…} is given, then it represents:**

**(a) Whole numbers**

**(b) Rational Numbers**

**(c) Complex numbers**

**(d) Natural numbers**

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**8. If p and q are integers and is represented in the form of p/q, then it is a:**

**(a) Rational number**

**(b) Whole number**

**(c) Natural number**

**(d) Even number**

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**9. The largest number that divides 70 and 125, which leaves the remainders 5 and 8, is:**

**(a) 65**

**(b) 15**

**(c) 13**

**(d) 25**

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**10. The least number that is divisible by all the numbers from 1 to 5 is:**

**(a) 60**

**(b) 70**

**(c) 80**

**(d) 90**

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**11. The sum or difference of two irrational numbers is always**

**(a) rational**

**(b) irrational**

**(c) rational or irrational**

**(d) not determined**

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**12. The decimal expansion of the rational number 23/(2² . 5) will terminate after**

**(a) one decimal place **

**(b) two decimal places**

**(c) three decimal places **

**(d) more than 3 decimal places**

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**13. Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy**

**(a) 0 ≤ r < b **

**(b) 0 < r ≤ b**

**(c) 1 < r < b**

**(d) 0 < r < b**

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**14. For some integer m, every even integer is of the form**

**(a) m **

**(b) m + 1**

**(c) 2m **

**(d) 2m + 1**

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**15. Using Euclid’s division algorithm, the HCF of 231 and 396 is**

**(a) 32**

**(b) 21**

**(c) 13**

**(d) 33**

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**16. If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is**

**(a) 1**

**(b) 2**

**(c) 9**

**(d) 4**

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**17. The prime factorisation of 96 is**

**(a) 25 × 3**

**(b) 26**

**(c) 24 × 3**

**(d) 24 × 32**

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**18. n² – 1 is divisible by 8, if n is**

**(a) an integer **

**(b) a natural number**

**(c) an odd integer **

**(d) an even integer**

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**19. For any two positive integers a and b, HCF (a, b) × LCM (a, b) = **

**(a) 1**

**(b) (a × b)/2**

**(c) a/b**

**(d) a × b**

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**20. The values of the remainder r, when a positive integer a is divided by 3 are**

**(a) 0, 1, 2**

**(b) Only 1**

**(c) Only 0 or 1**

**(d) 1, 2**

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