# Number System

Language: English
Subject: Math > Rationals numbers
Age: 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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