### Discrete Mathematics Week 5 NPTEL

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

**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+2R 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:**

**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 oddZZ 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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