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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 β†’ R
f(x)=x2+
2 where, R is a set of real number

a. 𝑓 is not injective

d.  π‘“ is not surjective

Explanation

2. 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.

Β d. 𝑓 is neither one to one nor onto

Explanation

3. Let π‘“: 𝑅→𝑅 such that f(x)=x/2+7

 b. π‘“ is bijective

Explanation

4. If a function is defined as π‘“(π‘₯)=2π‘₯+15 then the value of f-1(25) is

 b. 5

Explanation

5. Set 𝐢 has cardinality 𝑝 and a total of 5040 bijective functions. What is the value of 𝑝2?

d. 49

Explanation

6. find the domain and range of the following real-valued function. f(x)=√(3βˆ’x)

d. domain= {π‘₯ ∈ R | π‘₯ ≀ 3}
range=
{π‘₯ ∈ R | π‘₯ β‰₯ 0}

Explanation

7. If π‘“ and π‘” are function from π‘… to π‘… and π‘“(π‘₯)=3π‘₯2+π‘₯βˆ’13 and π‘”(π‘₯)=20/(3π‘₯+8) then π‘“o𝑔 (12) is.

c. βˆ’1443/121

Explanation

8. Let us define a function 𝑓: Zβ†’Z as follows,
f(x)= {x/2 if x is even, 0 if x is odd
Z is a set of integers.

a. onto but not one-to-one

Explanation

9. The relation 𝑅 is defined as 𝑅 = {(x, y): π‘₯, y ∈ N, π‘₯ + y = 5} then the range is?

d. {1,2,3,4}

Explanation

10. Let 𝐴 be set with cardinality 𝑛 and set 𝐡 with cardinality π‘š, there are a total of 3024 one to one function from 𝐴 to 𝐡, what are the values of 𝑛 and π‘š respectively?

b. 4 and 9

Explanation

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