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Quantitative Aptitude - Permutation & Combination - Formula & Concept Quiz

# Quiz
1
Discuss
Formula & Concept

What is the sum of all 4 digit numbers that can be formed by the digits 1, 2, 3, 4 each exactly once

  • 1]

    55566

  • 2]

    66660

  • 3]

    56456

  • 4]

    84738

Solution
2
Discuss
Formula & Concept

If P(A)=2/5​, P(B)=3/10​ and P(A ∩ B) =51​, then P(A' | B'). P(B' | A') is equal to

  • 1]

    5/6

  • 2]

    5/7

  • 3]

    25/42

  • 4]

    1

Solution
3
Discuss
Formula & Concept

If A and B are two independent events with P(A) = 3/5 and P(B) = 4/9 , then P(A' ∩ B' ) equals

  • 1]

    4/15

  • 2]

    8/45

  • 3]

    1/3

  • 4]

    2/9

Solution
4
Discuss
Formula & Concept

If A, B and C are mutually exclusive and exhaustive events of a random experiment such that P(B)=3/2​P(A) and P(C)=1/2​P(B), then P(A∪C)=

  • 1]

    3/13

  • 2]

    6/13

  • 3]

    7/13

  • 4]

    10/13

Solution
5
Discuss
Formula & Concept

A biased coin in tossed thrice. What is the probability that heads turns out at least twice considering that the probability of a head is 60%?

  • 1]

    0.648

  • 2]

    0.234

  • 3]

    0.348

  • 4]

    .839

Solution
6
Discuss
Formula & Concept

The value of  75P2

  • 1]

    5450

  • 2]

    5555

  • 3]

    5550

  • 4]

    5656

Solution
7
Discuss
Formula & Concept

How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?

  • 1]

    40

  • 2]

    400

  • 3]

    5040

  • 4]

    2520

Solution
8
Discuss
Formula & Concept

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

  • 1]

    120

  • 2]

    720

  • 3]

    4320

  • 4]

    2160

Solution
9
Discuss
Formula & Concept

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

  • 1]

    10080

  • 2]

    4989600

  • 3]

    120960

  • 4]

    None of these

Solution
10
Discuss
Formula & Concept

In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

  • 1]

    63

  • 2]

    90

  • 3]

    126

  • 4]

    45

Solution
11
Discuss
Formula & Concept

In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

  • 1]

    159

  • 2]

    194

  • 3]

    205

  • 4]

    209

Solution
12
Discuss
Formula & Concept

In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?

  • 1]

    32

  • 2]

    48

  • 3]

    36

  • 4]

    60

Solution
13
Discuss
Formula & Concept

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?

  • 1]

    32

  • 2]

    48

  • 3]

    64

  • 4]

    96

Solution
14
Discuss
Formula & Concept

In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?

  • 1]

    266

  • 2]

    5040

  • 3]

    11760

  • 4]

    86400

Solution
15
Discuss
Formula & Concept

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

  • 1]

    5

  • 2]

    10

  • 3]

    15

  • 4]

    20

Solution
16
Discuss
Formula & Concept

 

In how many ways can the letters of the word 'LEADER' be arranged?

  • 1]

    360

  • 2]

    720

  • 3]

    120

  • 4]

    None Of These

Solution
17
Discuss
Formula & Concept

How many words can be formed from the letters of the word "SIGNATURE" so that vowels always come together.

  • 1]

    17280

  • 2]

    4320

  • 3]

    720

  • 4]

    80

Solution
18
Discuss
Formula & Concept

From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least three men are in the committee. In how many ways can it be done?

  • 1]

    624

  • 2]

    702

  • 3]

    756

  • 4]

    812

Solution
19
Discuss
Formula & Concept

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

  • 1]

    50400

  • 2]

    2430

  • 3]

    6540

  • 4]

    12800

Solution
20
Discuss
Formula & Concept

A box contains two white balls, three black balls and four red balls. Balls of the same colour are distinct. The number of ways in which three balls can be drawn from the box if atleast one black ball is to be included in the draw, is

  • 1]

    32

  • 2]

    64

  • 3]

    128

  • 4]

    None Of These

Solution
21
Discuss
Formula & Concept

Three unbiased coins are tossed. What is the probability of getting at most two heads ?

  • 1]

    3/4

  • 2]

    1/4

  • 3]

    3/8

  • 4]

    7/8

Solution
22
Discuss
Formula & Concept

In a simultaneous throw of two dice, what is the probability of getting a total of 7?

  • 1]

    1/6

  • 2]

    1/4

  • 3]

    2/3

  • 4]

    3/4

Solution
23
Discuss
Formula & Concept

Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

  • 1]

    1/2

  • 2]

    3/4

  • 3]

    3/8

  • 4]

    5/16

Solution
24
Discuss
Formula & Concept

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

  • 1]

    1/10

  • 2]

    2/5

  • 3]

    2/7

  • 4]

    5/7

Solution
25
Discuss
Formula & Concept

One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is not a face card (Jack, Queen and King only)?

  • 1]

    5/13

  • 2]

    10/13

  • 3]

    1/13

  • 4]

    1/26

Solution
26
Discuss
Formula & Concept

From a pack of 52 playing cards, two cards are drawn together at random. Calculate the probability of both the cards being the Kings.

  • 1]

    1/15

  • 2]

    25/57

  • 3]

    35/256

  • 4]

    None Of These

Solution
27
Discuss
Formula & Concept

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

  • 1]

    3/20

  • 2]

    29/34

  • 3]

    47/100

  • 4]

    13/102

Solution
28
Discuss
Formula & Concept

A box contains 5 green, 4 yellow and 3 white marbles. three marbles are drawn at random. What is the probability that all they are not of the same colour?

  • 1]

    3/44

  • 2]

    3/55

  • 3]

    52/55

  • 4]

    41/44

Solution
29
Discuss
Formula & Concept

A speaks truth in 75% cases and B in 80% of the cases. In what percentage of the cases are they likely to contradict each other, narrating the same incident?

  • 1]

    5%

  • 2]

    15%

  • 3]

    35%

  • 4]

    45%

Solution
30
Discuss
Formula & Concept

12 person are seated at a round table. Number of ways of selecting 2 persons not adjacent to each other is

  • 1]

    10

  • 2]

    11

  • 3]

    54

  • 4]

    48

Solution
31
Discuss
Formula & Concept

If ,​, are probabilities of three mutually exclusive events, then

  • 1]

  • 2]

  • 3]

  • 4]

    None Of These

Solution

Answer :1/2

32
Discuss
Formula & Concept

If four dice are thrown together, then what is the probability that the sum of the numbers appearing on them is 25 ?

  • 1]

    0

  • 2]

    1/2

  • 3]

    1

  • 4]

    1/1296

Solution
33
Discuss
Formula & Concept

 

In a single throw with four dice,the probability of throwing seven is

  • 1]

    20/64

  • 2]

    24/65

  • 3]

    22/84

  • 4]

    24/84

Solution
34
Discuss
Formula & Concept

A fair coin is tossed 5 times. What is the probability of getting at least three heads on consecutive tosses?

  • 1]

    3/16

  • 2]

    1/4

  • 3]

    7/24

  • 4]

    5/16

Solution
35
Discuss
Formula & Concept

A coin is tossed 5 times. What is the probability that head appears an odd number of times?

  • 1]

    1/2

  • 2]

    2/3

  • 3]

    1/3

  • 4]

    1

Solution
36
Discuss
Formula & Concept

Find the probability that a leap year selected at random will contain 53 Sundays

  • 1]

    2/7

  • 2]

    3/7

  • 3]

    2/3

  • 4]

    5/6

Solution
37
Discuss
Formula & Concept

What is the probability of getting at least one six in a single throw of three unbiased dice?s

  • 1]

    91/216

  • 2]

    1/216

  • 3]

    200/216

  • 4]

    17/216

Solution
38
Discuss
Formula & Concept

A person tosses an unbiased coin. When head turns up, he gets Rs.8 and tail turns up he loses Rs.4. If 3 coins are tossed, what is probability that he gets a profit of Rs.12?

  • 1]

    3/8

  • 2]

    5/8

  • 3]

    3/4

  • 4]

    1/8

Solution

Person will get profit of Rs 12 only when there is 2H (Head) and 1T (Tail)

H + H + T = 12

8 + 8 + (-4) = 12

Total outcome of 2 head and 1 tail = 23 = 8

i.e (T, H, TH, HT, HH, HHT, HTH, THH)

Total event with 2H and 1 T is 3

therfore probability = 3/8

39
Discuss
Formula & Concept

The number of triangles that can be formed by choosing the vertices from a set of 12 points, seven of which lie on the same straight line, is

  • 1]

    185

  • 2]

    175

  • 3]

    115

  • 4]

    105

Solution
40
Discuss
Formula & Concept

In how many ways the letters of the word “UNDERDOG” can be arranged such that the first and last letters are same and no two vowels are together?

  • 1]

    72

  • 2]

    96

  • 3]

    132

  • 4]

    144

  • 5]

    None of these

Solution
41
Discuss
Formula & Concept

Three chairs are arranged in a row facing three other chairs. 4 boys and 2 girls are to be seated on these chairs such that girls are always facing each other. In how many ways can they be seated?

  • 1]

    96

  • 2]

    72

  • 3]

    144

  • 4]

    120

Solution
42
Discuss
Formula & Concept

Six boys and 4 girls are to be seated in two separate rows with five chairs each, such that two particular girls are always together and all the girls are not in the same row. In how many ways can they be seated?

  • 1]

    15 * 7!

  • 2]

    20 * 8!

  • 3]

    18 * 7!

  • 4]

    (16 * 8! – 4! * 6!)

Solution
43
Discuss
Formula & Concept

A, B, C, D and E sit on five chairs all of which are facing north. C will sit only on the leftmost chair and B will not sit anywhere to the left of A. In how many ways they can be seated?

  • 1]

    10

  • 2]

    18

  • 3]

    36

  • 4]

    12

Solution
44
Discuss
Formula & Concept

Four letters are selected from the word “CAPAME” and are rearranged to form four letter words. How many words can be formed?

  • 1]

    120

  • 2]

    90

  • 3]

    180

  • 4]

    192

Solution
45
Discuss
Formula & Concept

A basketball team of 5 players is to be selected from a group of 10 men and 8 women players. A volley ball team of 6 players is to be selected from a group of 8 men and 7 women players. Find the difference in the number of ways in which both the teams are selected, given that each team has only 2 female players.

  • 1]

    1890

  • 2]

    1920

  • 3]

    1950

  • 4]

    1990

Solution
46
Discuss
Formula & Concept

Find the number of ways in which mixed double tennis game can be arranged amongst 9 married couples if no husband and wife play in the same game

  • 1]

    1515

  • 2]

    1500

  • 3]

    1512

  • 4]

    1550

Solution
47
Discuss
Formula & Concept

If a team of 4 persons is to be selected from 8 males and 8 females, then in how many ways can the selections be made to include at least 1 female

  • 1]

    3500

  • 2]

    1875

  • 3]

    1750

  • 4]

    3000

Solution
48
Discuss
Formula & Concept

A committee of 8 members is to be selected from a group of 12 male and 10 female members. In how many ways the committee is selected such that at most two and at least one male member are there in the committee?

  • 1]

    13540

  • 2]

    14200

  • 3]

    15300

  • 4]

    16400

Solution
49
Discuss
Formula & Concept

A five-letter word is to be formed from a group of 5 vowels and 4 consonants, using at least one vowel and at least one consonant. In how many ways the word having a greater number of consonants than vowels can be formed?

  • 1]

    40

  • 2]

    42

  • 3]

    45

  • 4]

    52

Solution
50
Discuss
Formula & Concept

A polygon has 44 diagonals. What is the number of its sides?

  • 1]

    7

  • 2]

    8

  • 3]

    9

  • 4]

    11

Solution
51
Discuss
Formula & Concept

How many parallelograms will be formed if 7 parallel horizontal lines intersect 6 parallel vertical lines?

  • 1]

    42

  • 2]

    294

  • 3]

    315

  • 4]

    258

Solution
52
Discuss
Formula & Concept

A teacher has to choose the maximum different groups of three students from a total of six students. Of these groups, in how many groups there will be included in a particular student?

  • 1]

    12

  • 2]

    10

  • 3]

    8

  • 4]

    6

Solution
53
Discuss
Formula & Concept

How many four-digit numbers, each divisible by 4 can be formed using the digits 5, 6, 7, 8, 9, repetition of digits being allowed in any number?

  • 1]

    75

  • 2]

    100

  • 3]

    125

  • 4]

    150

Solution
54
Discuss
Formula & Concept

There are seven pairs of black shoes and five pairs of white shoes. They are all put into a box and shoes are drawn one at a time. To ensure that at least one pair of black shoes are taken out, what is the number of shoes required to be drawn out?

  • 1]

    12

  • 2]

    13

  • 3]

    17

  • 4]

    18

Solution
55
Discuss
Formula & Concept

How many 5 digit even numbers with distinct digits can be formed using the digits 1, 2, 5, 5, 4?

  • 1]

    16

  • 2]

    24

  • 3]

    36

  • 4]

    48

Solution
56
Discuss
Formula & Concept

There are three rooms in a motel: one single, one double, and one for four persons. How many ways are there to house seven persons in these rooms?

  • 1]

    7! / 1! 2! 3! 

  • 2]

    7! 

  • 3]

    7! / 3

  • 4]

    7! / 3!

Solution
57
Discuss
Formula & Concept

If C(n, 7) = C(n, 5), find n

  • 1]

    12

  • 2]

    15

  • 3]

    18

  • 4]

    -1

Solution
58
Discuss
Formula & Concept

There are 8 orators A, B, C, D, E, F, G, and H. In how many ways can the arrangements be made so that A always comes before B and B always comes before C.

  • 1]

    8! / 3!

  • 2]

    8! / 6!

  • 3]

    5! x 3!

  • 4]

    8! / (5! x 3!) 

Solution
59
Discuss
Formula & Concept

If 18Cr = 18Cr+2 ; find rC5.

  • 1]

    56

  • 2]

    63

  • 3]

    49

  • 4]

    42

Solution
60
Discuss
Formula & Concept

The number of circles that can be drawn out of 10 points of which 7 are collinear is

  • 1]

    130

  • 2]

    85

  • 3]

    45

  • 4]

    72

Solution
61
Discuss
Formula & Concept

How many rectangles can be formed out of a chess board ?

  • 1]

    1740

  • 2]

    1230

  • 3]

    1296

  • 4]

    204

Solution
62
Discuss
Formula & Concept

How many natural numbers can be made with digits 0, 7, 8 which are greater than 0 and less than a million?

  • 1]

    496

  • 2]

    728

  • 3]

    486

  • 4]

    1084

Solution
63
Discuss
Formula & Concept

One red flower, three white flowers, and two blue flowers are arranged in a line such that
I. No two adjacent flowers are of the same color.
II. The flowers at the two ends of the line are of different colors.
In how many different ways can the flowers be arranged?

  • 1]

    2

  • 2]

    4

  • 3]

    6

  • 4]

    10

Solution
64
Discuss
Formula & Concept

Two variants of the CAT paper are to be given to 12 students. In how many ways can the students be placed in two rows of six each so that there should be no identical variants side by side and that the students sitting one behind the other should have the same variant. Find the number of ways this can be done

  • 1]

    2 x 12C6 x (6!)2

  • 2]

    2 x 6! x 6!

  • 3]

    2 x 12C6 x 6!

  • 4]

    None of these

Solution
65
Discuss
Formula & Concept

A, B, C, and D are four points, any three of which are non-collinear. Then, the number of ways to construct three lines each joining a pair of points so that the lines do not form a triangle is

  • 1]

    7

  • 2]

    8

  • 3]

    9

  • 4]

    24

Solution
66
Discuss
Formula & Concept

How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition), when the digit at the unit’s place must be greater than that in the ten’s place?

  • 1]

    60

  • 2]

    54

  • 3]

    51 / 3

  • 4]

    2 x 4!

Solution
67
Discuss
Formula & Concept

There are 6 letters for 3 envelopes. In how many different ways can the envelopes be filled?

  • 1]

    120

  • 2]

    130

  • 3]

    100

  • 4]

    110

Solution
68
Discuss
Formula & Concept

From among the 36 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?

  • 1]

    1360

  • 2]

    1060

  • 3]

    1160

  • 4]

    1260

Solution
69
Discuss
Formula & Concept

The students in a class are seated, according to their marks in the previous examination. Once, it so happens that four of the students got equal marks and therefore the same rank. To decide their seating arrangement, the teacher wants to write down all possible arrangements one in each of separate bits of paper in order to choose one of these by lots. How many bits of paper are required?

  • 1]

    24

  • 2]

    12

  • 3]

    36

  • 4]

    48

Solution
70
Discuss
Formula & Concept

In how many ways can a cricketer can score 200 runs with fours and sixes only?

  • 1]

    13

  • 2]

    19

  • 3]

    16

  • 4]

    17

Solution
71
Discuss
Formula & Concept

There are 20 people among whom two are sisters. Find the number of ways in which we can arrange them around a circle so that there is exactly one person between the two sisters.

  • 1]

    2! x 19!

  • 2]

    18!

  • 3]

    18! x 2!

  • 4]

    19!

Solution
72
Discuss
Formula & Concept

Seven different objects must be divided among three people. In how many ways can this be done if one or two of them must get no objects?

  • 1]

    36

  • 2]

    84

  • 3]

    180

  • 4]

    381

Solution
73
Discuss
Formula & Concept

How many integers between 1000 and 10000 have no digits other than 4, 5, or 6?

  • 1]

    91

  • 2]

    71

  • 3]

    51

  • 4]

    81

Solution
74
Discuss
Formula & Concept

A number lock on a suitcase has 3 wheels each labeled with 10 digits from 0 to 9. If the opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible?

  • 1]

    720

  • 2]

    760

  • 3]

    780

  • 4]

    680

Solution
75
Discuss
Formula & Concept

If (n + 2)! = 2550 (n!); find ’n’

  • 1]

    49

  • 2]

    35

  • 3]

    38

  • 4]

    43

Solution
76
Discuss
Formula & Concept

In how many ways can 10 people line up at a ticket window of a railway station?

  • 1]

    36,28,800

  • 2]

    34,82,800

  • 3]

    33,44,800

  • 4]

    33,28,800

Solution
77
Discuss
Formula & Concept

How many words, with or without meaning, can be formed using all letters of the word EQUATION using each letter exactly once?

  • 1]

    38,320

  • 2]

    39,320

  • 3]

    38,400

  • 4]

    40,320

Solution
78
Discuss
Formula & Concept

Ten participants are participating in a competition. In how many ways can the first three prizes be won?

  • 1]

    920

  • 2]

    680

  • 3]

    720

  • 4]

    820

Solution
79
Discuss
Formula & Concept

It is required to seat 5 boys and 4 girls in a row so that the girls occupy the even places. How many such arrangements are possible?

  • 1]

    2880

  • 2]

    2148

  • 3]

    3280

  • 4]

    3680

Solution
# Quiz
Quantitative Aptitude

Quantitative Aptitude

  • Introduction
  • Number
    • Formula & Concept
  • AP and GP
    • Formula & concept
  • Problem On Ages
    • Formula & Concept
  • Percentages
    • Formulaes and Concept
  • Profit and Loss
    • Formula & Concept
  • Ratio & Proportions
    • Formula & Concepts
  • Time and work
    • Formulae & Concepts
  • Time and Distance
    • Formula & Concept
  • Problem On Trains
    • Formula & Concept
  • Permutation & Combination
    • Formula & Concept
  • HCF & LCM
    • Formula & Concept
  • Simple Interest
    • Formula & Concept
  • Compound Interest
    • Formula & Concept
  • Decimal Fraction
    • Formula & Concept
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  • Square Roots and Cube Roots
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  • Average
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  • Variation
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  • Linear Equation
    • Formula & Concept
  • Quadratic Equation
    • Formula & Concept
  • Boats and Streams
    • Formula & Concept
  • Problem On Races
    • Formula & Concept
  • Pipes and Cisterns
    • Formula & Concept

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