Free Printable Gem of DMGT

1.

The degree of any vertex of graph is .... ?

a)

The number of edges incident with vertex

b)

Number of vertex in a graph

c)

Number of vertices adjacent to that vertex

d)

Number of edges in a graph

2.

Which of the above graphs is/are NOT planar?

a)

G1

b)

G2

c)

G3

d)

G4

3.

What is the number of edges present in a complete graph having n vertices?

a)

(n*(n+1))/2

b)

(n*(n-1))/2

c)

n

d)

Information given is insufficient

4.

What is the number of edges present in a cycle having n vertices?

a)

n+1

b)

2n

c)

n/2

d)

n

5.

Which of the following graphs is isomorphic to

a)

A

b)

B

c)

C

d)

D

6.

This symbol, ∧, means?

a)

and

b)

or

c)

not

d)

implies

7.

This symbol, ↔, means?

a)

and

b)

or

c)

if and only if

d)

implies

8.

What type of logic is this table showing:

a)

AND

b)

OR

c)

NOR

d)

XOR

9.

If $p\wedge\ q\$ is false and $p\vee q$ is true , then which of the following is not True.

a)

$p\vee q$

b)

$p\leftrightarrow q$

c)

$\sim p\vee\sim q$

d)

$q\vee\sim p$

10.

The negation of inverse of $\sim p\rightarrow q\$ is

a)

$q\wedge p$

b)

$\sim p\wedge\sim q$

c)

$p\wedge q$

d)

$\sim q\rightarrow\sim p$

11.

Examine $\left(p\wedge q\right)\wedge\left(\sim p\vee\sim q\right)$

a)

Tautology

b)

Contradiction

c)

Contingency

d)

None of these

12.

x+y=10 is a proposition

a)

True

b)

False

13.

pv~p is

a)

Tautology

b)

contingency

c)

contradiction

14.

p: Ram is coward q: ram is lazy r: ram is rich Identify statement for "It is not true that ram is not rich"

a)

~pv~q

b)

~pv~r

c)

~(~r)

d)

~(~q)

15.

Which one is set?

a)

A group of clever students

b)

A group of kind students

c)

A group of students that get 80 in Math test

d)

A group of funny students

16.

Left Pocket (L) = {pencils, erasers, pens}
Right Pocket (R) = {gloves, paper, coins, phone}
What is L ∪ R?

a)

∅

b)

{pencils, erasers, pens}

c)

{gloves, paper, coins, phone}

d)

{pencils, erasers, pens, gloves, paper, coins, phone}

17.

What does this symbol ( ⊆ ) represent in set theory?

a)

Union

b)

Intersection

c)

Disjointed

d)

Subset

18.

From the above Venn diagram, what is the set (S ∪ T) ∩ V?

a)

{casey, drew, jade, glen}

b)

{alex, glen, hunter, jade}

c)

{casey, drew, glen}

d)

{drew, jade}

19.

How many students do not ski or ice skate?

a)

10

b)

16

c)

22

d)

28

20.

How many students do not snowboard?

a)

21

b)

22

c)

28

d)

29

21.

What statement does the shaded region represent?

a)

A or B and C

b)

Not C

c)

A or B

d)

B and C or A

22.

Determine if the statement is true or false.
{10, 12, 14, 16} ⊆ {1,2,3,4,...99}

a)

True

b)

False

23.

Which of the following represents the shaded region?

a)

(A ⋃ B)'

b)

(A ∩ B)'

c)

A'

d)

B'

24.

The ordinary enumerator of the selection of r objects out of n objects with unlimited repetition is

a)

C( n + r - 1, r)

b)

C(n, r)

c)

P(n, r)

d)

S (n, r)

25.

C(n, 0) + C(n, 1) + C(n, 2) + . . . + C(n, n) =

a)

2 ^ n

b)

n ^ 2

c)

n !

d)

n^n

26.

Commutative is not satisfied in

a)

permutation

b)

combination

27.

The exponential enumerator for the permutation of a single object with no repetition is

a)

1

b)

1 + x

c)

(1+x) ^ 2

d)

1/ (1 +x)

28.

Permutation or Combination: A group of 40 people are going to run a race. The top three runners earn gold, silver, and bronze medals.

a)

permutation

b)

combination

29.

How would you solve?
A book club offers a choice of 8 books from a list of 40. In how many ways can a member make a collection?

a)

Permutation

b)

Combination

c)

Factorial

d)

MPC

30.

Permutation or Combination: A group of 14 people need to take an elevator to the top floor. They will go in groups of seven. They are deciding who will take the elevator on its second trip.

a)

permutation

b)

combination

31.

solve the following combination: Amanda and Jimmy are planning trips to four countries this year. There are 8 countries they would like to visit. They are deciding which countries to skip.

a)

70

b)

45

c)

280

d)

260

32.

solve the following combination: Selecting which seven players will be in the batting order on a 9 person team.

a)

36

b)

30

c)

72

d)

18

33.

The ski club with ten members is to choose three officers for captain, co-captain and secretary. How many ways can those offices be filled?

a)

720

b)

120

c)

10!

34.

Gloria and Bob and five other people walk through a doorway one at a time. In how many ways can the seven people go through the doorway if Bob goes through the doorway after Gloria?

a)

$240$

b)

$5040$

c)

$720$

d)

$2520$

35.

Mr and Mrs Brown and their four children go to the cinema. They are randomly allocated six adjacent seats in a single row. What is the probability that the four children are allocated seats next to each other?

a)

$\frac{1}{15}$

b)

$\frac{1}{5}$

c)

$\frac{2}{5}$

d)

$\frac{1}{30}$

36.

Seven people are seated at a round table. What is the probability that two people, Jenny and Lindsay, do not sit next to one another?

a)

$\frac{1}{3}$

b)

$\frac{2}{21}$

c)

$\frac{2}{3}$

d)

$\frac{1}{30}$

37.

Three cards are selected at random from a standard pack of 52 cards.

What is the probability that at least two of them are clubs?

a)

$\frac{7}{425}$

b)

$\frac{117}{850}$

c)

$\frac{1}{68}$

d)

$\frac{64}{425}$

38.

A fair, six-sided die is thrown seven times. What is the probability, correct to three decimal places, that a ‘3’ occurs on exactly two of the seven throws?

a)

$0.011$

b)

$0.234$

c)

$0.022$

d)

$0.078$

39.

A car purchased for $25 000 depreciates by 10% of its purchase price each year. The value of the car after 4 years is:

a)

$2500

b)

$12500

c)

$15000

d)

$17500

40.

Which of the following recurrence relations is an example of linear decay?

a)

V₀ = 500, V_n+1 = V_n - 25

b)

V₀ = 500, V_n+1 = V_n + 25

c)

V₀ = 500, V_n+1 = 1.25V_n

d)

V₀ = 500, V_n+1 = 0.95V_n

41.

The next term in the sequence below is:

4, 9, 14, 19, 24, ...

a)

29

b)

34

c)

19

d)

-1

42.

The next term in the sequence below is:

2, 5, 11, 23, ...

a)

45

b)

46

c)

47

d)

48

43.

For the recurrence relation:

V₀ = 10, V_n+1 = V_n + 4

What is the second term in the sequence?

a)

10

b)

14

c)

18

d)

40

44.

If there is an edge joining these two vertices then the graph is said to be ---------

a)

Adjacent

b)

Non adjacent

c)

Incident

d)

Non incident

45.

What is the degree of vertex E?

a)

1

b)

2

c)

3

d)

4

e)

5

46.

Which Theorem is represented by the map presented?

a)

Kruskal's Theorem

b)

Four Color Theorem

c)

Prim's Theorem

d)

Coloring is fun!

Gem of DMGT

Total questions: 46

Worksheet time: 2hrs 44mins

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