# Discrete Mathematics | Mathematical Functions MCQs

Discrete Mathematics | Mathematical Functions MCQs: This section contains multiple-choice questions and answers on Mathematical Functions in Discrete Mathematics.
Submitted by Anushree Goswami, on July 17, 2022

1. Which of the following is/are mathematical function(s)?

1. Floor functions
2. Ceiling functions
3. Remainder functions
4. All of the above

Answer: D) All of the above

Explanation:

The following are mathematical functions -

1. Floor functions
2. Ceiling functions
3. Remainder functions

2. For any real number x, the floor function is equal to ___ or equal to the value of x times the greatest integer f (x)?

1. One less than
2. Two less than
3. Five less than
4. Much less than

Explanation:

For any real number x, the floor function is equal to one less than or equal to the value of x times the greatest integer f (x).

3. Floor function is denoted by -?

1. {x}
2. [x]
3. (x)
4. <x>

Explanation:

Floor function is denoted by [x].

4. What is the floor value of [-2, 4]?

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

Explanation:

The floor value of [-2, 4] is -3.

5. When x is a real number, the ceiling function h (x) represents the smallest integer _____ to x?

1. Greater
2. Greater or equal
3. Lesser
4. Lesser or equal

Explanation:

When x is a real number, the ceiling function h (x) represents the smallest integer greater or equal to x.

6. What is the ceiling value of [3, 143]?

1. 2
2. 4
3. 3
4. 143

The ceiling value of [3, 143] is 4.

7. When a is ____ by m, an integer remainder is obtained?

1. Multiplied
2. Divided
4. Subtracted

Explanation:

When a is divided by m, an integer remainder is obtained.

8. Remainder function is denoted by -?

1. a(MOD m)
2. a(m MOD)
3. a(m)
4. None

Explanation:

Remainder function is denoted by a(MOD m).

9. a (MOD m) is the ____ integer t such that a = Mq + t?

1. Duplicate
2. Unique
3. Variance
4. Variable

Explanation:

a (MOD m) is the unique integer t such that a = Mq + t.

10. What is the remainder value of 20 (MOD 3)?

1. 18
2. 3
3. 6
4. 2

Explanation:

The remainder value of 20 (MOD 3) is 2.

11. In f (n) = k^n , where n is a +ve integer, the function f is called the base k ____ function?

1. Unique
2. Identity
3. Variance
4. Exponential

Explanation:

In f (n) = k^n , where n is a +ve integer, the function f is called the base k exponential function.

12. k^t is equal to -?

1. k+k+...k
2. k.…k
3. k-k-...k
4. k/k/….k

Explanation:

k^t means k.k….k.

13. k^0 is equal to -?

1. K
2. 1
3. 0
4. None

Explanation:

k^0 means 1.

14. k^-M is equal to -?

1. 1/k^M
2. k^M
3. M^k
4. 1/M^k

Explanation:

k^-M is equal to 1/k^M.

15. If a/b is a rational number, exponential function k^a/b is equal to -?

1. b√k^a
2. (b√k)^M
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

If a/b is a rational number, exponential function k^a/b is equal to b√k^a or (b√k)^M.

16. What is the value of 3^-5?

1. 15
2. -15
3. 243
4. 1/243

Explanation:

The value of 3^-5 = 1/3^5 = 1/3.3.3.3.3 = 1/243.

17. If A=B=R and f(n):A->B where n>1, then -?

1. fn (x)=log(x) the base n of x
2. f (x)=logn(x) the base x of n
3. fn (x)=logn(y) the base x of n
4. fn (x)=logn(x) the base n of x

Answer: D) fn (x)=logn(x) the base n of x

Explanation:

If A=B=R and f(n):A->B where n>1, then fn (x)=logn(x) the base n of x.

18. Which of the following statement is TRUE?

1. k^n and k = logn (x) are equivalent.
2. n^k and k = logn (x) are equivalent.
3. n^k and k = log (x) are equivalent.
4. nk and k = logn (x) are equivalent.

Answer: B) n^k and k = logn (x) are equivalent.

Explanation:

n^k and k = logn (x) are equivalent.

19. logn (1) is equal to -?

1. 1
2. 0
3. N
4. None

Explanation:

logn (1) is equal to 0 as n^0=1.

20. logn (n)=1 is equal to -?

1. 1
2. n
3. 0
4. None

Explanation:

logn n=1 is equal to 1 as n^1=n.

21. What is the value of log2 (16)?

1. 2
2. 4
3. 8
4. 16

Explanation:

log2 (16) is equal to 4 as 2^4=16.