Integers
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Integers (Z) – Definition, Properties, Examples & 20 Solved MCQs for Competitive Exams

⭐ Integers (Z) – Detailed Description

Integers, denoted by Z, are the set of numbers that include:

  • All positive whole numbers (1, 2, 3…)
  • All negative whole numbers (–1, –2, –3…)
  • Zero (0)

Set Representation

  • Z={,5,4,3,2,1,0,1,2,3,4,5,}

Key Features of Integers

  1. Include positive, negative numbers & zero
  2. No fractions or decimals
  3. Extend infinitely in both directions
  4. Zero is neither positive nor negative
  5. All natural numbers & whole numbers are part of integers
  6. Useful in temperature, altitude, banking (profit/loss), and real-life comparisons
  7. Closed under addition, subtraction, and multiplication

Classification of Integers

  • Positive Integers: +1, +2, +3 …
  • Negative Integers: –1, –2, –3 …
  • Zero: Neutral integer

5 Examples of Integers (with explanation)

  • –5: A negative integer; lies left of zero on number line.
  • 0: Neither positive nor negative; central integer.
  • 12: A positive integer and also a natural and whole number.
  • –19: A negative whole number.
  • 7: A positive integer commonly used in counting and mathematics.

MCQ's For Exam

Q.1. Which of the following is an integer?

  1. -3
  2. 1/2
  3. 0.7
  4. √2

1) –3

📝Explanation: Integers include negatives, zero & positive whole numbers only.

Q.2. The smallest integer is:

  1. Does not exist
  2. –1
  3. -1000
  4. 0

1) Does not exist

📝 Description: Integers extend infinitely to the left.

Q.3. Which of the following is NOT an integer?

  1. –7
  2. 0
  3. 12
  4. 4.5

4) 4.5

📝 Description: Decimals are not integers.

Q.4. Zero is:

  1. Positive
  2. Negative
  3. Both
  4. Neither positive nor negative

4) Neither positive nor negative

📝 Description: 0 is always neither positive nor negative.

Q.5. Which of the following represents the set of integers?

  1. N
  2. W
  3. Z
  4. Q

3) Z

📝 Description: By convention, Z represents the set of natural numbers.

Q.6. Add: 5 + (–3)

  1. 8
  2. –8
  3. 2
  4.  –2

3) 2

📝 Description: Simple: 5 – 3 = 2

Q.7. Subtract: –10 – (–4)

  1. –6
  2. –14
  3. 14
  4. 6

1) -6

📝 Description: –10 – (–4), = –10 + 4 = –6

Q.8. Which integer is greater: –2 or –5?

  1. –2
  2. –5
  3. Both equal
  4. None

1) -2

📝 Description: –2 lies to the right of –5 on number line.

Q.9. The opposite of –9 is:

  1. 9
  2. –9
  3. 0
  4. –1

1) 9

📝 Description: Opposite of -9 is +9

Q.10. Which of the following integers is smallest?

  1. –3
  2. –7
  3. –1
  4. –2

2) –7

📝 Description: The further left on number line → smaller value.

Q.11. Find: (–4) × 6

  1. –24
  2. 24
  3. –10
  4. 10

1) -24

📝 Description: Negative × Positive = Negative.

Q.12. Find: (–3) × (–5)

  1. –15
  2. 0
  3. 15
  4. 30

3) 15

📝 Description: Negative × Negative = Positive.

Q.13. Add: –7 + –8

  1. –15
  2. 15
  3. –1
  4. 1

1) –15

📝 Description: Add numbers & keep negative sign.

Q.14. Which integer lies between –3 and 1?

  1. –4
  2. 2
  3. 0
  4. 5

3) 0

📝 Description: Integer range: –2, –1, 0 → 0 is correct option.

Q.15. Value of |–12| is:

  1. –12
  2. 12
  3. 0
  4. –1

2) 12

📝 Description: Absolute value = positive magnitude.

Q.16. Solve: (–6) ÷ (–3)

  1. –2
  2. 2
  3. 3
  4. –3

2) 2

📝 Description: Negative ÷ Negative = Positive.

Q.17. Find the sum of all integers from –3 to 3.

  1. –3
  2. 3
  3. 0
  4. 1

3) 0

📝 Description: Numbers: –3, –2, –1, 0, 1, 2, 3

Pairs cancel: (–3+3)=0, (–2+2)=0, (–1+1)=0.

Sum = 0

Q.18. Which statement is TRUE?

  1. Every whole number is an integer
  2. Every integer is a whole number
  3. Integers exclude zero
  4. Integers include fractions

1) Every whole number is an integer

📝 Description: All other options are false statement, so every whole number is an integer.

Q.19. Arrange in ascending order: –7, 0, 5, –2

  1. –2, –7, 0, 5
  2. –7, –2, 0, 5
  3. 5, 0, –2, –7
  4. –7, 0, –2, 5

2) –7, –2, 0, 5

📝 Description: Order → –7, –2, 0, 5

Q.20. The sum of two negative integers is always:

  1. Positive
  2. Negative
  3. Zero
  4. Depends on numbers

2) Negative

📝 Description: –5 + –7 = –12 (always negative).

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