Module 4 Module 4 Module 4

Module 4 Quiz - Results

Attempt 1 of 1

Written Dec 4, 2023 6:31 PM - Dec 4, 2023 6:46 PM

Attempt Score 15 / 20 - 75 % Overall Grade (Highest Attempt) 15 / 20 - 75 %

True or False Question 1

The harmonic series

is divergent.

Question 2

Your quiz has been submitted successfully.

∑ +∞

n=1

1 n

True False

The Principle of Mathematical Induction allows us to prove a quantified proposition of the form

Question 3

Let A\B={a∈ A| a∉ B}. If A is uncountable and B is uncountable then A\B can be countable.

Question 4

There is a bijection between the set of the positive integers and the set of infinitely long bit strings.

Question 5

The number of binary operations on a set with 4 elements is greater than 4x10⁹.

Question 6

The binomial coefficients are defined by

∃n ∈ Z ⁺ , P(n) .

True False

True False

True False

True False

Question 7

The general solution of the recurrence relation given by

has two degrees of freedom.

Question 8

The probability of an event must be non-negative and less than 1.

Fill in the blanks Question 9

___1296___

Question 10

___945___

( n

r ) = n ⋅ (n − 1) ⋯ (n − r + 1)

r! .

True False

a n = a n−1 + a n−2 − 3a n−3 , a 0 = 1

True False

True False

There are 8 different cubes with edge lengths 1,2,3,4,5,6,7,8. What is their total volume? Remember, only input the digits of your answer. No spaces or commas or units of volume.

What is the coefficient of x³ in the expansion of (3x-1)⁷ ?

Remember, only input the digits of your answer. No spaces or commas.

Question 11

___19/64___

Question 12

___277200___ (3326400)

Question 13

___71/500___ (25 %) ___29/500___ (25 %) ___96/500___ (24/125)

___92/500___ (23/125) Question 14

___1540___ (50 %)

What is the probability that a bit string of length 9 will start with two zeros or end with four ones?

Give your answer as an exact fraction in lowest terms. To input a fraction, say 9 over 13, put 9/13.

How many distinct words can be made from the letters in HELPLESSNESS ? Only enter the digits of your answer, no spaces or commas.

Give your answers as exact fractions in lowest terms! To input a fraction, say 31 over 500, put 31/500

A number is chosen at random from the set S={1,2,3,...,500}.

What is the probability that it is divisible by 7?

What is the probability that it is divisible by 17?

What is the probability that it is divisible by 7 or 17?

What is the probability that it is divisible by exactly one of 7 and 17?

How many solutions are there of the equation

where x₁, x_2, x₃ and x₄ are non-negative integers.

x 1 + x 2 + x 3 + x 4 = 19

___190___ (50 %) A Recurrence Relation Question 15

___3___ (50 %) ___2___ (50 %)

Done

How many of these solution have x₂ = 1 ?

The general solution of the recurrence relation a_n=a_n-1+12a_n-2 is

If a₀=5 and a₁=6, then the value of c₁ is

a _n = c ₁ 4 ⁿ + c ₂ (−3) ⁿ .

and the value of c₂ is