# 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 โ R f(x)=x^{2}+**

**2 where**

**,**

**R is a set of real number**

**a. ๐ is not injective**

**d. ๐ is not surjective**

**2. Consider the following table:**

**We can think of this as a function ๐ from the set of students to the set of integers between 160 and 170. Now pick out the correct statement from the following.**

ย **d.ย ๐ is neither one to one nor onto**

**3. Let ๐: ๐
โ๐
such that f(x)=x/2+7**

**b.** **๐ is bijective**

**4. If a function is defined as ๐(๐ฅ)=2๐ฅ+15 then the value of f ^{-1}(25) is**

** b. 5**

**5. Set ๐ถ has cardinality ๐ and a total of 5040 bijective functions. What is the value of ๐ ^{2}**

**?**

**d. 49**

**6. find the domain and range of the following real-valued function. f(x)=โ(3โx)**

**d. ****domain= {๐ฅ โ R | ๐ฅ โค 3}range=**

**{๐ฅ โ R | ๐ฅ โฅ 0}**

**7. If ๐ and ๐ are function from ๐
to ๐
and ๐(๐ฅ)=3๐ฅ ^{2}+๐ฅโ13 and ๐(๐ฅ)=20/(3๐ฅ+8) then ๐o๐ (12) is.**

**c. โ1443/121**

**8. Let us define a function ๐: ZโZ as follows,f(x)= {x/2 if x is even, 0 if x is oddZ is a set of integers.**

**a. onto but not one-to-one**

**9. The relation ๐
is defined as ๐
= {(x, y): ๐ฅ, y โ N, ๐ฅ + y = 5} then the range is?**

**d. {1,2,3,4}**

**10. Let ๐ด be set with cardinality ๐ and set ๐ต with cardinality ๐, there are a total of 3024 one to one function from ๐ด to ๐ต, what are the values of ๐ and ๐ respectively?**

**b. 4 and 9**