Discrete Mathematics | Week 5
Quiz
Link : Discrete Mathematics Week 5 (nptel.ac.in)
1. Which of the following is(are) true for the given function?
f: R → R
f(x)=x2+2 where, R is a set of real number
a. 𝑓 is not injective
d. 𝑓 is not surjective
2. Consider the following table:
We can think of this as a function 𝑓 from the set of students to the set of integers between 160 and 170. Now pick out the correct statement from the following.
d. 𝑓 is neither one to one nor onto
3. Let 𝑓: 𝑅→𝑅 such that f(x)=x/2+7
b. 𝑓 is bijective
4. If a function is defined as 𝑓(𝑥)=2𝑥+15 then the value of f-1(25) is
b. 5
5. Set 𝐶 has cardinality 𝑝 and a total of 5040 bijective functions. What is the value of 𝑝2?
d. 49
6. find the domain and range of the following real-valued function. f(x)=√(3−x)
d. domain= {𝑥 ∈ R | 𝑥 ≤ 3}
range= {𝑥 ∈ R | 𝑥 ≥ 0}
7. If 𝑓 and 𝑔 are function from 𝑅 to 𝑅 and 𝑓(𝑥)=3𝑥2+𝑥−13 and 𝑔(𝑥)=20/(3𝑥+8) then 𝑓o𝑔 (12) is.
c. −1443/121
8. Let us define a function 𝑓: Z→Z as follows,
f(x)= {x/2 if x is even, 0 if x is odd
Z is a set of integers.
a. onto but not one-to-one
9. The relation 𝑅 is defined as 𝑅 = {(x, y): 𝑥, y ∈ N, 𝑥 + y = 5} then the range is?
d. {1,2,3,4}
10. Let 𝐴 be set with cardinality 𝑛 and set 𝐵 with cardinality 𝑚, there are a total of 3024 one to one function from 𝐴 to 𝐵, what are the values of 𝑛 and 𝑚 respectively?
b. 4 and 9
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