Unit 2: The Number System

1. Which of the following is a natural number (N)?

A) -1
B) 0
C) 3
D) 1/2

Explanation: Natural numbers are counting numbers starting from 1 (1, 2, 3...). 3 is the only one in this set.

2. Which number is an integer but NOT a natural number?

A) 5
B) 0
C) 1
D) 7

Explanation: Integers include negative whole numbers, zero, and positive whole numbers. 0 is an integer but not a natural number.

3. Which of these is a prime number?

A) 15
B) 21
C) 17
D) 1

Explanation: A prime number has only two factors (1 and itself). 17 is prime; 1 is neither prime nor composite.

4. The smallest prime number is:

A) 0
B) 1
C) 2
D) 3

Explanation: 2 is the first and only even prime number.

5. What is the greatest common factor (GCF) of 18 and 24?

A) 2
B) 6
C) 12
D) 24

Explanation: Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. The largest common one is 6.

6. Which pair is relatively prime?

A) 8 and 12
B) 9 and 15
C) 14 and 25
D) 6 and 21

Explanation: Relatively prime numbers have a GCF of 1. 14 and 25 have no common factors other than 1.

7. The prime factorization of 60 is:

A) 2² × 3 × 5
B) 2 × 30
C) 3 × 20
D) 5 × 12

Explanation: 60 = 2 × 30 = 2 × 2 × 15 = 2 × 2 × 3 × 5, which is 2² × 3 × 5.

8. LCM of 4 and 10 is:

A) 20
B) 40
C) 10
D) 14

Explanation: Multiples of 4: 4, 8, 12, 16, 20... Multiples of 10: 10, 20... The smallest common multiple is 20.

9. Which decimal is terminating?

A) 1/3
B) 1/8
C) 2/7
D) 1/11

Explanation: 1/8 = 0.125, which ends. Others are repeating decimals.

10. 0.75 as a fraction is:

A) 3/4
B) 2/3
C) 7/10
D) 75/1000

Explanation: 0.75 = 75/100 = 3/4 when simplified.

11. 0.333... equals:

A) 1/2
B) 1/3
C) 2/3
D) 3/10

Explanation: This is a repeating decimal equal to 1/3.

12. Which number is irrational?

A) 22/7
B) √2
C) 0.5
D) 3

Explanation: Irrational numbers cannot be written as simple fractions. √2 has a non-terminating, non-repeating decimal form.

13. √49 equals:

A) 7
B) -7
C) both 7 and -7
D) neither

Explanation: The principal square root of 49 is 7.

14. Which is a perfect square?

A) 81
B) 82
C) 80
D) 85

Explanation: 81 is 9 × 9.

15. 5 × √4 equals:

A) 10
B) 20
C) 5√2
D) 5

Explanation: √4 = 2, so 5 × 2 = 10.

16. The number of prime numbers less than 10 is:

A) 2
B) 3
C) 4
D) 5

Explanation: The prime numbers are 2, 3, 5, and 7. There are 4 of them.

17. Which of these is an odd composite number?

A) 9
B) 11
C) 13
D) 17

Explanation: 9 is odd and composite (3 × 3). 11, 13, and 17 are prime.

18. 0 is classified as:

A) Natural number
B) Integer but not natural
C) Rational only
D) Irrational

Explanation: 0 is a whole number and an integer, but natural numbers start from 1.

19. 100 written as product of primes is:

A) 2² × 5²
B) 2³ × 5
C) 10 × 10
D) 2 × 50

Explanation: 100 = 2 × 50 = 2 × 2 × 25 = 2 × 2 × 5 × 5 = 2² × 5².

20. The GCF of 14 and 35 is:

A) 1
B) 7
C) 14
D) 35

Explanation: Both numbers are divisible by 7 (14 = 7 × 2, 35 = 7 × 5).

21. 3/4 as a decimal is:

A) 0.75
B) 0.25
C) 0.7
D) 0.57

Explanation: Dividing 3 by 4 gives exactly 0.75.

22. Convert 0.125 to a fraction:

A) 1/8
B) 1/6
C) 2/15
D) 3/25

Explanation: 0.125 = 125/1000 = 1/8.

23. Which fraction has a terminating decimal expansion?

A) 1/8
B) 1/7
C) 1/3
D) 1/11

Explanation: Fractions with denominators having only prime factors of 2 and 5 (like 8 = 2³) terminate.

24. 0.090909... equals:

A) 1/11
B) 1/9
C) 1/10
D) 1/12

Explanation: This is 9/99, which simplifies to 1/11.

25. Which is largest: 0.6, 3/5, or 0.59?

A) 0.6 and 3/5 are equal and largest
B) 0.59
C) 3/5 only
D) 0.6 only

Explanation: 3/5 = 0.6, which is greater than 0.59.

26. 0.875 as a fraction is:

A) 7/8
B) 3/4
C) 7/9
D) 5/6

Explanation: 0.875 = 875/1000 = 7/8.

27. Which fraction is closest to 0.3?

A) 1/3
B) 2/7
C) 3/10
D) 1/4

Explanation: 3/10 is exactly 0.3.

28. 0.272727... equals which fraction?

A) 3/11
B) 27/99
C) Both 3/11 and 27/99
D) 1/4

Explanation: 0.2727... = 27/99, which simplifies to 3/11.

29. Simplify: √50

A) 5√2
B) 25√2
C) √25 + √2
D) 10√5

Explanation: √50 = √(25 × 2) = 5√2.

30. √(18) + √(8) simplified gives:

A) 5√2
B) √26
C) 5√10
D) 6√2

Explanation: √18 = 3√2 and √8 = 2√2. 3√2 + 2√2 = 5√2.

31. 2√5 × √5 equals:

A) 10
B) 5
C) 2√25
D) 25

Explanation: √5 × √5 = 5, so 2 × 5 = 10.

32. Which of the following is false?

A) Every terminating decimal is rational
B) Every repeating decimal is rational
C) Every irrational number is real
D) Every real number is irrational

Explanation: Real numbers include both rational and irrational numbers.

33. If |x| = x, then x is:

A) Negative
B) Zero only
C) Positive
D) Non-negative

Explanation: The absolute value of any non-negative number is itself.

34. Which expression is always non-negative?

A) x
B) x²
C) x³
D) -x

Explanation: Any real number squared is zero or positive.

35. Which number lies between 1.4 and 1.5?

A) √1.9
B) √2
C) √2.1
D) √2.3

Explanation: 1.4² = 1.96 and 1.5² = 2.25. √2.1 lies between them.

36. 3√6 + 4√6 is equal to:

A) 6√6
B) 7√6
C) 4√12
D) 7√12

Explanation: (3 + 4)√6 = 7√6.

37. Rationalising the denominator of 1/(√7 - 2) gives:

A) (√7 + 2)/3
B) (√7 - 2)/3
C) (√7 + 2)/5
D) (√7 + 2)/45

Explanation: Multiplying by (√7 + 2) gives (√7 + 2)/(7 - 4) = (√7 + 2)/3.

38. Scientific notation for 5,400 is:

A) 54 × 10²
B) 5.4 × 10³
C) 0.54 × 10⁴
D) 5.4 × 10⁻³

Explanation: Move the decimal 3 places to the left to get 5.4 × 10³.

39. Significant figures in 0.0045 are:

A) 2
B) 4
C) 5
D) 1

Explanation: Leading zeros are not significant. Only 4 and 5 count.

40. The sum of a rational and irrational number is always:

A) Rational
B) Irrational
C) Zero
D) Whole

Explanation: Adding a rational to an irrational always results in an irrational number.

UNIT 2: THE NUMBER SYSTEM