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:Rβ†’Rf(x)=x2+2𝑓:𝑅→𝑅𝑓(π‘₯)=π‘₯2+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:Rβ†’R𝑓:𝑅→𝑅 such that f(x)=x2+7𝑓(π‘₯)=π‘₯2+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(π‘₯)=2π‘₯+15 then the value of fβˆ’1(25)fβˆ’1(25) is
a. 3
b. 5
c. 39
d. 25
Answer: B


Q5) Set 𝐢 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)=3βˆ’xβˆ’βˆ’βˆ’βˆ’βˆšπ‘“(π‘₯)=3βˆ’π‘₯
a. domain={π‘₯ ∈ R | π‘₯ ≀ 3}
range={π‘₯ ∈ R | π‘₯ ≀ 0}
b. domain={π‘₯ ∈ R | π‘₯ β‰  3}
range={π‘₯ ∈ R|π‘₯ β‰₯ 3}
c. domain={π‘₯ ∈ R | π‘₯ β‰₯ 3}
range={π‘₯ ∈ R | π‘₯ β‰₯ 0}
d. domain={π‘₯ ∈ R | π‘₯ ≀ 3}
range={π‘₯ ∈ R | π‘₯ β‰₯ 0}
Answer: D

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Q7) If f and g are function from R𝑅 to R𝑅 and f(x)=3×2+xβˆ’13𝑓(π‘₯)=3π‘₯2+π‘₯βˆ’13 and g(x)=203x+8𝑔(π‘₯)=203π‘₯+8 then fog(12)𝑓o𝑔(12) is.
a. βˆ’267/49
b. 20/1301
c. βˆ’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:Zβ†’Z𝑓:Zβ†’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 = {(π‘₯,y) : π‘₯ ,y ∈ N, π‘₯ + 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 𝐡 with cardinality π‘š, there are a total of 3024 one to one functions from 𝐴 to 𝐡, what are the values of 𝑛 and π‘š 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