Number Systems MCQ Quiz

30 questions

1. Which of the following real numbers possesses a non-terminating and non-recurring decimal expansion?

   1. 22/7
   2. 3.1416
   3. π
   4. √144

2. How many rational numbers lie strictly between 3/7 and 4/7?

   1. None
   2. Exactly one
   3. Exactly ten
   4. Infinitely many

3. Express 0.474747... as a simplified fraction in the form p/q, where p and q are integers and q ≠ 0.

   1. 47/99
   2. 47/100
   3. 43/90
   4. 47/90

4. The decimal expansion of the rational number 13/125 will terminate after how many decimal places?

   1. 1
   2. 2
   3. 3
   4. 4

5. Simplify the expression (√11 - √7)(√11 + √7).

   1. 4
   2. 18
   3. √4
   4. 4√77

6. Rationalise the denominator of 1/(√5 - √3) to get its simplest form.

   1. (√5 - √3)/2
   2. (√5 + √3)/2
   3. √5 + √3
   4. (√5 + √3)/8

7. Find the value of (81)^(-1/4) × (27)^(1/3).

   1. 1
   2. 3
   3. 1/3
   4. 9

8. If a is a non-zero rational number and b is an irrational number, then the product a × b is always:

   1. Rational
   2. Irrational
   3. An integer
   4. Zero

9. The sum of the two irrational numbers (√3 + 2) and (5 - √3) is:

   1. Irrational
   2. Rational
   3. Undefined
   4. Zero

10. Simplify the surd expression √48 - √75 + √12.

    1. √3
    2. 2√3
    3. 3√3
    4. 0

11. Which of the following is an irrational number lying strictly between 2 and 2.5?

    1. √3
    2. √5
    3. √7
    4. √8

12. To represent √9.3 geometrically on a number line, segment AB = 9.3 units is drawn and extended to C by 1 unit. What is the radius of the semicircle constructed on diameter AC?

    1. 9.3 units
    2. 10.3 units
    3. 5.15 units
    4. 4.65 units

13. Convert 0.2353535... into a fraction in the form p/q.

    1. 233/990
    2. 235/990
    3. 233/900
    4. 235/999

14. A rational number p/q in its lowest terms has a terminating decimal expansion if and only if the prime factorization of q contains no prime factors other than:

    1. 2 and 3
    2. 2 and 5
    3. 3 and 5
    4. 2, 3, and 5

15. Evaluate the expression (64/125)^(-2/3).

    1. 16/25
    2. 25/16
    3. 4/5
    4. 5/4

16. Which of the following mathematical identities is FALSE for positive real numbers a and b?

    1. √(ab) = √a × √b
    2. √(a/b) = √a / √b
    3. √(a + b) = √a + √b
    4. (√a + √b)(√a - √b) = a - b

17. What is the simplest rationalising factor of ∛4?

    1. ∛2
    2. ∛4
    3. 2
    4. √2

18. If x = 2 + √3, find the value of x + 1/x.

    1. 2√3
    2. 4
    3. -2√3
    4. 2

19. Evaluate the simplified value of ∜[(625)^(-2)].

    1. 25
    2. 1/25
    3. 5
    4. 1/5

20. If 3^(x - 1) = 27, then what is the value of x?

    1. 3
    2. 4
    3. 2
    4. 5

21. Which of the following numbers is rational?

    1. √23
    2. √225
    3. 0.1010010001...
    4. 3π

22. Evaluate (-32)^(3/5).

    1. -8
    2. 8
    3. -6
    4. 16

23. If (5 + 2√3)/(7 + 4√3) = a + b√3, where a and b are rational numbers, what is the value of a?

    1. 11
    2. -11
    3. 1
    4. -1

24. Simplify the exponent expression (2³⁰ + 2²⁹ + 2²⁸)/(2³¹ + 2³⁰ - 2²⁹).

    1. 1/2
    2. 7/10
    3. 7/5
    4. 1

25. Which of the following statements about the number 0 is TRUE?

    1. It is an irrational number.
    2. It is a rational number.
    3. It cannot be written in p/q form.
    4. It has a non-terminating non-repeating decimal expansion.

26. Determine the simplified value of ∛(√0.000064).

    1. 0.2
    2. 0.02
    3. 0.4
    4. 0.04

27. Find the value of √[(4 - √17)²].

    1. 4 - √17
    2. √17 - 4
    3. 1
    4. 17 - 4

28. If 2^x = 8^(y + 1) and 9^y = 3^(x - 9), what is the value of x + y?

    1. 27
    2. 21
    3. 18
    4. 15

29. What type of number is obtained from the expression (2 + √3)² + (2 - √3)²?

    1. An irrational number
    2. A prime number
    3. A non-integer fraction
    4. A composite rational number

30. If x = 7 - 4√3, what is the value of √x + 1/√x?

    1. 4
    2. 2
    3. 2√3
    4. 7