Discrete Mathematics Week 5 NPTEL

                     

These are the solution of Discrete Mathematics Week 5 NPTEL Assignment 5 Answers

Course name: Discrete Mathematics

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Q1) Which of the following is(are) true for the given function?
f:R→Rf(x)=x2+2𝑓:𝑅→𝑅𝑓(𝑥)=𝑥2+2
R is a set of real numbers.

a. 𝑓 is not injective
b. 𝑓 is bijective
c. 𝑓 is subjective
d. 𝑓 is not subjective
Answer: A, D


Q2) Consider the following table:

These are the solution of Discrete Mathematics Week 5 NPTEL Assignment 5 Answers

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.
a. 𝑓 is onto but not one-to-one.
b. 𝑓 is bijective.
c. 𝑓 is one to one but not onto.
d. 𝑓 is neither one to one nor onto.
Answer: D


These are the solution of Discrete Mathematics Week 5 NPTEL Assignment 5 Answers


Q3) Let f:R→R𝑓:𝑅→𝑅 such that f(x)=x2+7𝑓(𝑥)=𝑥2+7
a. 𝑓 is not a function
b. 𝑓 is bijective
c. 𝑓 is injective
d. 𝑓 is subjective
Answer: b. 𝑓 is bijective


Q4) If a function is defined as f(x)=2x+15𝑓(𝑥)=2𝑥+15 then the value of f−1(25)f−1(25) is
a. 3
b. 5
c. 39
d. 25
Answer: B


Q5) Set 𝐶 has cardinality 𝑝 and a total of 5040 bijective functions. What is the value of 𝑝2 ?
a. 144
b. 25
c. 81
d. 49
Answer: D


These are the solution of Discrete Mathematics Week 5 NPTEL Assignment 5 Answers
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Q6) find the domain and range of the following real-valued function. f(x)=3−x−−−−√𝑓(𝑥)=3−𝑥
a. domain={𝑥 ∈ R | 𝑥 ≤ 3}
range={𝑥 ∈ R | 𝑥 ≤ 0}
b. domain={𝑥 ∈ R | 𝑥 ≠ 3}
range={𝑥 ∈ R|𝑥 ≥ 3}
c. domain={𝑥 ∈ R | 𝑥 ≥ 3}
range={𝑥 ∈ R | 𝑥 ≥ 0}
d. domain={𝑥 ∈ R | 𝑥 ≤ 3}
range={𝑥 ∈ R | 𝑥 ≥ 0}
Answer: D


Q7) If f and g are function from R𝑅 to R𝑅 and f(x)=3×2+x−13𝑓(𝑥)=3𝑥2+𝑥−13 and g(x)=203x+8𝑔(𝑥)=203𝑥+8 then fog(12)𝑓o𝑔(12) is.
a. −267/49
b. 20/1301
c. −1443/121
d. 5/11
Answer: C


These are the solution of Discrete Mathematics Week 5 NPTEL Assignment 5 Answers


Q8) Let us define a function f:Z→Z𝑓:Z→Z as follows,
f(x)={x20if x is evenif x is oddf(x)={x2if x is even0if x is odd
ZZ is a set of integers.

a. onto but not one-to-one.
b. one-to-one but not onto.
c. one-to-one and onto.
d. neither one-to-one nor onto.
Answer: A


Q9) The relation 𝑅 is defined as 𝑅 = {(𝑥,y) : 𝑥 ,y ∈ N, 𝑥 + y = 5} then the range is?
a. {2,4}
b. {2,3,4}
c. {2,3}
d. {1,2,3,4}
Answer: D


These are the solution of Discrete Mathematics Week 5 NPTEL Assignment 5 Answers


Q10) Let 𝐴 be set with cardinality 𝑛 and set 𝐵 with cardinality 𝑚, there are a total of 3024 one to one functions from 𝐴 to 𝐵, what are the values of 𝑛 and 𝑚 respectively?
a. 4 and 8
b. 4 and 9
c. 6 and 7
d. 7 and 6
Answer: B


These are the solution of Discrete Mathematics Week 5 NPTEL Assignment 5 Answers

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These are the solution of Discrete Mathematics Week 5 NPTEL Assignment 5 Answers