# 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:RβRf(x)=x2+2π:π
βπ
π(π₯)=π₯2+2R is a set of real numbers.**

a. π is not injective

b. π is bijective

c. π is subjective

d. π is not subjective

**Answer: A, D**

**Q2) Consider the following table:**

**We can think of this as a function π from the set of students to the set of integers between 160 and 170. Now pick out the correct statement from the following.**

a. π is onto but not one-to-one.

b. π is bijective.

c. π is one to one but not onto.

d. π 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:RβRπ:π
βπ
such that f(x)=x2+7π(π₯)=π₯2+7**

a. π is not a function

b. π is bijective

c. π is injective

d. π is subjective**Answer: b. π is bijective**

**Q4) If a function is defined as f(x)=2x+15π(π₯)=2π₯+15 then the value of fβ1(25)fβ1(25) is**

a. 3

b. 5

c. 39

d. 25**Answer: B**

**Q5) Set πΆ has cardinality π and a total of 5040 bijective functions. What is the value of π2 ?**

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)=3βxβββββπ(π₯)=3βπ₯**

a. domain={π₯ β R | π₯ β€ 3}

range={π₯ β R | π₯ β€ 0}

b. domain={π₯ β R | π₯ β 3}

range={π₯ β R|π₯ β₯ 3}

c. domain={π₯ β R | π₯ β₯ 3}

range={π₯ β R | π₯ β₯ 0}

d. domain={π₯ β R | π₯ β€ 3}

range={π₯ β R | π₯ β₯ 0}**Answer: D**

**Q7) If f and g are function from Rπ
to Rπ
and f(x)=3×2+xβ13π(π₯)=3π₯2+π₯β13 and g(x)=203x+8π(π₯)=203π₯+8 then fog(12)πoπ(12) is.**

a. β267/49

b. 20/1301

c. β1443/121

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:ZβZπ:ZβZ 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 π
is defined as π
= {(π₯,y) : π₯ ,y β 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 π΄ be set with cardinality π and set π΅ with cardinality π, there are a total of 3024 one to one functions from π΄ to π΅, what are the values of π and π 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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