Basic Discrete Mathematics

Find the missing number in the sequence: 5, 10, 15, ___, 25, 30.

• 20

• 35

• 18

• 24

Determine the missing term in the sequence: 4, 12, __, 108, 324, 972

• 24

• 38

• 36

• 72

p: The bear is huge.

       q: The bear is a wild animal.

       r: The bear can eat human meat.

 Translate the following symbolic form into proper English.

( ∼ r ∧ ∼ p) → ∼ q

• If the bear can not eat human meat and the bear is not huge then, the bear is a wild animal.

• The bear is huge and the bear is a wild animal.

• If the bear can eat human meat and the bear is not huge then, the bear is a wild animal.

• If the bear can not eat human meat and the bear is not huge then, the bear is not a wild animal.

What is logically equivalent to the following statements? “ I pass only if you pass” (Note that is equivalent to not pass.)

• You pass only if I pass

• If you fail then I fail

• If you pass then I pass

• You fail if I pass

n ≥ 1

1³ + 2³ + 3³ + · · · + n³ = [n(n + 1)/2]²

What would be the appropriate first step in proving the above mathematical induction?

• put n = 1

• put n = -1

• put n = 0

• none of these

If 4 Maths books are selected from 6 different Maths books and 3 English books are chosen from 5 different English books, how many ways can the seven books be arranged on a shelf?

• None of these ways

• 750000 ways

• 756000 ways

• 480000 ways

At a dinner party, 6 men and 6 women sit at a round table. In how many ways can they sit if men and women alternate?

• 86400 ways

• 43200 ways

• 36 ways

• 1246 ways

How many words with seven letters are there that start with a vowel and end with an A? (Note that they do not have to be real words and letters can be repeated.)

• 45087902

• 64387659

• 12765800

• 59406880

In how many ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?

• 120

• 720

• 4320

• 2160

• None of these

How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

• 5

• 10

• 15

• 20