FSc Part 1 Maths chapter 1: Number systems MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

20 exam-style questions on Number systems, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

20 questions · 2 topics · 10 per test

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What chapter 1 covers

Ten Number systems questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. The number π is

  1. A
    rational, because π = 22/7
  2. B
    irrational, because its decimal expansion is non-terminating and non-recurring
  3. C
    rational, because it is the ratio of circumference to diameter
  4. D
    irrational, because its decimal expansion recurs
Show answer

Answer: B. π cannot be written as p/q with integers p, q; its decimal never ends and never repeats. 22/7 is an approximation, and circumference and diameter are not both integers.

2. The product (2 + 3i)(1 − i) is

  1. A
    5 − i
  2. B
    −1 + i
  3. C
    5 + i
  4. D
    2 − 3i
Show answer

Answer: C. (2 + 3i)(1 − i) = 2 − 2i + 3i − 3i2 = 2 + i + 3 = 5 + i. Taking i2 = +1 gives the slip −1 + i.

3. Which of the following is an irrational number?

  1. A
    √7
  2. B
    √16
  3. C
    0.333... (3 recurring)
  4. D
    22/7
Show answer

Answer: A. 7 is not a perfect square, so √7 has a non-terminating, non-recurring decimal. 22/7 is only a rational approximation of π, and a recurring decimal is always rational.

4. If (x + 2y) + (2x − y)i = 5 + 5i, where x and y are real, then

  1. A
    x = 3, y = 1
  2. B
    x = 1, y = 2
  3. C
    x = 2, y = 3
  4. D
    x = 3, y = −1
Show answer

Answer: A. Equate real and imaginary parts: x + 2y = 5 and 2x − y = 5. From the second, y = 2x − 5; then x + 4x − 10 = 5 gives x = 3 and y = 1. Check: 3 + 2 = 5, 6 − 1 = 5.

5. Which set is NOT closed under subtraction?

  1. A
    natural numbers
  2. B
    integers
  3. C
    rational numbers
  4. D
    real numbers
Show answer

Answer: A. For example 2 − 5 = −3, which is not a natural number. Integers, rationals and reals all contain the difference of any two of their members.

6. The modulus of the product (1 + i)(3 − 4i) is

  1. A
    10
  2. B
    5 + √2
  3. C
    5√2
  4. D
    √26
Show answer

Answer: C. |z1z2| = |z1||z2| = √2 × 5 = 5√2. Check: the product is 7 − i and √(49 + 1) = √50 = 5√2. Moduli multiply, they do not add.

7. The property a(b + c) = ab + ac for all real a, b, c is called

  1. A
    commutative property of addition
  2. B
    associative property of multiplication
  3. C
    distributive property of multiplication over addition
  4. D
    closure property of multiplication
Show answer

Answer: C. Multiplication is distributed over the sum b + c. Associativity is about regrouping, e.g. a(bc) = (ab)c.

8. The recurring decimal 0.2323... (23 recurring) written as a fraction is

  1. A
    232/999
  2. B
    23/100
  3. C
    23/90
  4. D
    23/99
Show answer

Answer: D. Let x = 0.2323...; then 100x = 23.2323... Subtracting gives 99x = 23, so x = 23/99.

9. The multiplicative inverse of 3 + 4i is

  1. A
    (3 − 4i)/5
  2. B
    (3 − 4i)/25
  3. C
    −3 − 4i
  4. D
    (3 + 4i)/25
Show answer

Answer: B. 1/(3 + 4i) = (3 − 4i)/((3 + 4i)(3 − 4i)) = (3 − 4i)/(9 + 16) = (3 − 4i)/25. Dividing by the modulus 5 instead of its square is the usual slip.

10. The conjugate of z = −2 + 5i is

  1. A
    −2 − 5i
  2. B
    2 − 5i
  3. C
    2 + 5i
  4. D
    5 − 2i
Show answer

Answer: A. The conjugate keeps the real part and changes the sign of the imaginary part only.

Start the chapter testAbout the FSc Part 1 Maths test

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Ways to practise this chapter

Number systems: questions students ask

How many Number systems MCQs are there?

20, each with the answer and a short explanation, across 2 topics: Real numbers, Complex numbers. Every chapter test draws ten of them, so you can take it many times.

Is the FSc Part 1 Maths chapter 1 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

Can I read the explanations in Urdu?

Yes. In practice mode and on your results you can switch the explanations to Urdu.

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