MCQ Questions

Question No. 1

Complete each of the following statements.

Answer :

a) −3 = … mod 2

b) −9 = … mod 7

c) −12 = … mod 8

d) −15 = … mod 5

e) −16 = … mod 3

f) −19 = … mod 4

g) −49 = … mod 3

h) −34 = … mod 6

i) −20 = … mod 7

j) −29 = … mod 9

k) −34 = … mod 12

l) −58 = … mod 10

Question No. 2

Do each of the following additions in the given modulus.

Question No. 3

Write down the residues of each of the following.

Answer :

a) mod 2

b) mod 4

c) mod 5

d) mod 12

Question No. 4

Look carefully at your answers to questions 1 and 2.

Answer :

a) Compare the questions and answers in questions 1a) and 2a), 1b) and 2b) and so on. What do you notice?

b) Is a ⊕ b (mod n) = b ⊕ a (mod n)? Give a reason for your answer.

Question No. 5

Do each of the following subtractions in the given modulus.

Question No. 6

Do each of the following multiplications in the given modulus.

Question No. 7

Work in pairs. 1. a) If a = 25, b = 34 and n = 7, find the values of: i) [(a mod n) × (b mod n)] mod n ii) ab mod n b) If a = 58, b = 17 and n = 5, find the values of: i) [(a mod n) × (b mod n)] mod n ii) ab mod n c) Look carefully at your answers to questions a) and b). Formulate a statement about [(a mod n) × (b mod n)] mod n and ab mod n. 2. a) If a = 17 and n = 5, find the value of [(a mod n) + (−a mod n)] mod n. b) If a = 51 and n = 9, find the value of [(a mod n) + (−a mod n)] mod n. c) Lo

Question No. 8

An electric train runs around a circular track that is 5 m long. What is the shortest distance along the track from the starting point of the train if it has travelled the following distances?

Answer :

a) 4 m

b) 7 m

c) 11 m

d) 18 m

Question No. 9

Mrs Ladele has an investment which will mature in 92 months’ time. If it is March now, in which month will her investment mature?

Answer :

Question No. 10

At a college cafeteria, pizza is served every Wednesday and hot dogs are served every nine days. If both are on the menu today, prove that they will both be on the menu in 189 days’ time.

Answer :

Question No. 11

Pekun was born on Friday 10th October 2014. On what day of the week will his 21st birthday fall?

Answer :

Question No. 12

A bank has a security check built into its credit card numbers that works as follows: Each number consists of 13 digits. The first 12 digits are the card number and the 13th digit is a check digit. The 13th digit is chosen in such a way that the sum of the 13 digits is 9 (mod 10).

Answer :

a) Calculate the 13th digit for each of the following card numbers: i) 568 515 111 221 ii) 371 298 226 647 iii) 334 153 312 518 iv) 491 382 828 361

b) Explain mathematically how, if one of the digits of the card number is entered incorrectly, the bank will be able to pick up the fact that the card number is incorrect.

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