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Unit 5 - Practice Quiz

PEA305

1 What is the value of ?

A.
B. 1
C. Undefined
D. Infinity

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

A. 120
B. 576
C. 720
D. 4320

3 Evaluate .

A. 120
B. 720
C. 240
D. 30

4 How many words can be formed by using all letters of the word "MISSISSIPPI"?

A. 34650
B. 34560
C. 35640
D. 36540

5 If , find the value of .

A. 10
B. 45
C. 90
D. 20

6 In how many ways can 5 people be seated around a circular table?

A. 120
B. 24
C. 60
D. 12

7 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?

A. 5
B. 10
C. 15
D. 20

8 Find the number of diagonals in a decagon (10-sided polygon).

A. 35
B. 45
C. 90
D. 20

9 A committee of 5 is to be formed out of 6 men and 4 women. In how many ways can this be done if at least 2 women are included?

A. 180
B. 186
C. 196
D. 120

10 In a party, everyone shakes hands with everyone else. If there are 66 handshakes, how many people are there?

A. 11
B. 12
C. 13
D. 10

11 How many different necklaces can be made from 10 different beads?

A.
B.
C.
D.

12 There are 4 different routes from A to B and 3 different routes from B to C. In how many ways can a person go from A to C via B?

A. 7
B. 12
C. 64
D. 1

13 In how many ways can 5 prizes be distributed among 4 students if each student may get any number of prizes?

A.
B.
C.
D.

14 How many triangles can be formed by joining 12 points, 7 of which are collinear?

A. 220
B. 35
C. 185
D. 175

15 If , find .

A. 5
B. 6
C. 7
D. 8

16 What is the rank of the word "CAT" in a dictionary?

A. 1
B. 3
C. 5
D. 6

17 In how many ways can 3 boys and 3 girls sit in a row so that boys and girls alternate?

A. 36
B. 72
C. 18
D. 12

18 Find the number of parallelograms that can be formed from a set of 4 parallel lines intersecting another set of 3 parallel lines.

A. 6
B. 12
C. 18
D. 9

19 How many 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4 without repetition?

A. 120
B. 96
C. 100
D. 24

20 The number of terms in the expansion of is:

A.
B.
C.
D.

21 In how many ways can 6 distinct books be arranged on a shelf?

A. 120
B. 720
C. 36
D. 6

22 A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?

A. 64
B. 129
C. 84
D. 45

23 Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?

A. 10
B. 20
C. 25
D. 5!

24 In how many ways can the letters of the word "APPLE" be arranged?

A. 120
B. 60
C. 24
D. 6

25 Number of rectangles in a chessboard ( grid) is:

A. 64
B. 1296
C. 204
D. 1024

26 Probability is a value between:

A. -1 and 1
B. 0 and 1 (inclusive)
C. 1 and 100
D. 0 and infinity

27 What is the probability of getting a number greater than 4 when rolling a standard die?

A. 1/6
B. 1/3
C. 1/2
D. 2/3

28 Two coins are tossed simultaneously. What is the probability of getting at least one head?

A. 1/4
B. 1/2
C. 3/4
D. 1

29 A card is drawn from a pack of 52 cards. The probability of getting a Queen of club or a King of heart is:

A. 1/13
B. 2/13
C. 1/26
D. 1/52

30 If , what is the probability of 'not E'?

A. 0.05
B. 0.95
C.
D. 1

31 Two dice are thrown simultaneously. What is the probability that the sum of the numbers is 9?

A. 1/9
B. 1/12
C. 1/6
D. 4/36

32 Three unbiased coins are tossed. What is the probability of getting exactly two heads?

A. 1/8
B. 3/8
C. 1/2
D. 7/8

33 From a well-shuffled pack of 52 cards, one card is drawn at random. What is the probability that the card is a face card?

A. 3/13
B. 4/13
C. 1/13
D. 1/4

34 If A and B are mutually exclusive events, then is:

A. 1
B.
C. 0.5
D.

35 What is the probability of selecting a prime number from the set {1, 2, 3, ..., 10}?

A. 2/5
B. 1/2
C. 3/10
D. 4/10

36 In a leap year, find the probability that there are 53 Sundays.

A. 1/7
B. 2/7
C. 3/7
D. 53/366

37 Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart is:

A. 3/20
B. 29/34
C. 47/100
D. 13/102

38 A bag contains 6 white and 4 black balls. Two balls are drawn at random. Find the probability that they are of the same colour.

A. 1/2
B. 7/15
C. 8/15
D. 1/9

39 For independent events A and B, ?

A.
B.
C.
D.

40 A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?

A. 1/4
B. 1/24
C. 3/4
D. 23/24

41 If , and , find .

A. 0.9
B. 0.7
C. 0.1
D. 0.8

42 Conditional probability is given by:

A.
B.
C.
D.

43 Two dice are thrown. Find the probability that the product of the numbers appearing is odd.

A. 1/2
B. 1/4
C. 3/4
D. 5/36

44 What is the probability of drawing an Ace from a deck of cards?

A. 1/52
B. 4/52
C. 1/26
D. 12/52

45 Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

A. 1/2
B. 2/5
C. 8/20
D. 9/20

46 The odds in favor of an event are 3:5. The probability of the event occurring is:

A. 3/5
B. 5/3
C. 3/8
D. 5/8

47 Two events A and B are such that , and . Then A and B are:

A. Mutually Exclusive
B. Independent
C. Dependent
D. Exhaustive

48 A card is drawn from a pack of cards. Find the probability that it is a King or a Red card.

A. 7/13
B. 15/26
C. 1/2
D. 28/52

49 In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?

A. 1/10
B. 2/5
C. 2/7
D. 5/7

50 A jar contains 3 red marbles and 7 green marbles. If one marble is drawn, returned, and then a second marble is drawn, what is the probability that both are red?

A. 9/100
B. 9/90
C. 1/10
D. 3/10