This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Floor and Ceiling Function”.

1. A floor function map a real number to :

a) smallest previous integer

b) greatest previous integer

c) smallest following integer

d) none of the mentioned

View Answer

Explanation: Floor function f(x) is the largest integer not greater than x.

2. A ceil function map a real number to :

a) smallest previous integer

b) greatest previous integer

c) smallest following integer

d) none of the mentioned

View Answer

Explanation: Ceil function f(x) is the smallest integer not less than x.

3. A function f(x) is defined as f(x) = x – [x], where [.] represents GIF then:

a) f(x) will be intergral part of x

b) f(x) will be fractional part of x

c) f(x) will always be 0

d) none of the mentioned

View Answer

Explanation: A integral part of a number is subtracted from that number we are left with the fractional part of that number.

4. Floor(2.4) + Ceil(2.9) is equal to :

a) 4

b) 6

c) 5

d) none of the mentioned

View Answer

Explanation: Floor(2.4) = 2, Ceil(2.9) = 3, 2 + 3 = 5.

5. State whether the given statement is true or false

For some integer n such that x < n < x + 1, ceil(x) < n .

a) True

b) False

View Answer

Explanation: If x < n < x + 1 then ceil(x) = n.

6. State whether the given statement is true or false

For some number x, Floor(x) <= x <= Ceil(x).

a) True

b) False

View Answer

Explanation: Floor function f(x) is the largest integer not greater than x and ceil function f(x) is the smallest integer not less than x.

7. If x, and y are positive numbers both are less than one, then maximum value of floor(x + y) is?

a) 0

b) 1

c) 2

d) -1

View Answer

Explanation: Since x < 1 and y < 1 this implies x + y < 2 which means maximium value of floor(x + y) is 1.

8. If x, and y are positive numbers both are less than one ,then maximum value of ceil(x + y) is?

a) 0

b) 1

c) 2

d) -1

View Answer

Explanation: Since x < 1 and y < 1 this implies x + y < 2 which means maximum value of ceil(x + y) is 2.

9. If X = Floor(X) = Ceil(X) then :

a) X is a fractional number

b) X is a Integer

c) X is less than 1

d) none of the mentioned

View Answer

Explanation: Only in case of integers X = Floor(X) = Ceil(X) holds good.

10.State True or False.

Let n be some integer greater than 1,then floor((n-1)/n) is 1.

a) True

b) False

View Answer

Explanation: Since (n-1)/n will always be less than one thus f floor((n-1)/n) is 0.

**Sanfoundry Global Education & Learning Series – Discrete Mathematics.**

To practice all areas of Discrete Mathematics, __here is complete set of 1000+ Multiple Choice Questions and Answers__.