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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)?
- Floor functions
- Ceiling functions
- Remainder functions
- All of the above
Answer: D) All of the above
Explanation:
The following are mathematical functions -
- Floor functions
- Ceiling functions
- 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)?
- One less than
- Two less than
- Five less than
- Much less than
Answer: A) One 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 -?
- {x}
- [x]
- (x)
- <x>
Answer: B) [x]
Explanation:
Floor function is denoted by [x].
4. What is the floor value of [-2, 4]?
- -2
- 4
- -3
- 3
Answer: C) -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?
- Greater
- Greater or equal
- Lesser
- Lesser or equal
Answer: B) Greater 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]?
- 2
- 4
- 3
- 143
Answer: B) 4
The ceiling value of [3, 143] is 4.
7. When a is ____ by m, an integer remainder is obtained?
- Multiplied
- Divided
- Added
- Subtracted
Answer: B) Divided
Explanation:
When a is divided by m, an integer remainder is obtained.
8. Remainder function is denoted by -?
- a(MOD m)
- a(m MOD)
- a(m)
- None
Answer: A) a(MOD m)
Explanation:
Remainder function is denoted by a(MOD m).
9. a (MOD m) is the ____ integer t such that a = Mq + t?
- Duplicate
- Unique
- Variance
- Variable
Answer: B) Unique
Explanation:
a (MOD m) is the unique integer t such that a = Mq + t.
10. What is the remainder value of 20 (MOD 3)?
- 18
- 3
- 6
- 2
Answer: D) 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?
- Unique
- Identity
- Variance
- Exponential
Answer: D) 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 -?
- k+k+...k
- k.…k
- k-k-...k
- k/k/….k
Answer: B) k.k.…k
Explanation:
k^t means k.k….k.
13. k^0 is equal to -?
- K
- 1
- 0
- None
Answer: B) 1
Explanation:
k^0 means 1.
14. k^-M is equal to -?
- 1/k^M
- k^M
- M^k
- 1/M^k
Answer: A) 1/k^M
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 -?
- b√k^a
- (b√k)^M
- Both A and B
- 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?
- 15
- -15
- 243
- 1/243
Answer: D) 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 -?
- fn (x)=log(x) the base n of x
- f (x)=logn(x) the base x of n
- fn (x)=logn(y) the base x of n
- 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?
- k^n and k = logn (x) are equivalent.
- n^k and k = logn (x) are equivalent.
- n^k and k = log (x) are equivalent.
- 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
- 0
- N
- None
Answer: A) 1
Explanation:
logn (1) is equal to 0 as n^0=1.
20. logn (n)=1 is equal to -?
- 1
- n
- 0
- None
Answer: A) 1
Explanation:
logn n=1 is equal to 1 as n^1=n.
21. What is the value of log2 (16)?
- 2
- 4
- 8
- 16
Answer: B) 4
Explanation:
log2 (16) is equal to 4 as 2^4=16.