# Quiz 1

Question 1

Time: 00:00:00
Find the number of ways you can fill a 3*3 grid ( with 4 corners defined as a,b,c,d) if you have 3 white marbles and 6 black marbles?

9c3

9c3

6c3

6c3

9c3+6c3

9c3+6c3

9c3+6c3/3!

9c3+6c3/3!

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Question 2

Time: 00:00:00
How many 5 digit number can be formed out of digits 0,2,4,6,8 that is divisible by 8?

26

26

30

30

38

38

96

96

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Question 3

Time: 00:00:00
In a locality, there are ten houses in a row. On a particular night, a thief planned to steal from three houses of locality. In how many ways can he plan such that no two houses are next to each other?

56

56

73

73

80

80

100

100

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#### PrepInsta User

Initially, let\'s remove the 3 houses where the thief planned to steal from. Then we are left with 10 ? 3 = 7 houses as numbered below. * 1 * 2 * 3 * 4 * 5 * 6 * 7 * Now there are 8 positions as marked as * above to place the 3 houses (from where the thief steals) such that no two such houses are next to each other. This can be done in 8C3 ways. Hence, required number of ways = 8C3 = 8 × 7 × 6 3 × 2 × 1 = 56

Question 4

Time: 00:00:00
Boxes numbered 1, 2, 3, 4 and 5 are kept in a row and them which are to be filled with either a red or a blue ball, such that no two adjacent boxes can be filled with blue balls. Then, how many different arrangements are possible, given that all balls of a given color are exactly identical in all respects?

8

8

10

10

15

15

22

22

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#### PrepInsta User

Total number of ways of filling the 5 boxes numbered as (1, 2, 3, 4 and 5) with either blue or red balls = 25 = 32. Now, let us determine the number of ways of filling the boxes such that the adjacent boxes are filled with blue. If we decide to have 2 adjacent boxes with blue, it can be done in 4 ways, viz. (12), (23), (34) and (45). If we decide to have 3 adjacent boxes filled with blue, it can be done in 3 ways, viz. (123), (234) and (345). If we decide to have 4 adjacent boxes filled with blue, it can be done in 2 ways, viz. (1234) and (2345). And all 5 boxes can have blue in only 1 way. Hence, the total number of ways of filling the boxes such that adjacent boxes have blue = (4 + 3 + 2 +1) = 10. Hence, the number of ways of filling up the boxes such that no two adjacent boxes have blue = 32 - 10 = 22

Question 5

Time: 00:00:00
How many 3 digit numbers can be formed with 2 consecutive same numbers?

160

160

171

171

180

180

256

256

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Question 6

Time: 00:00:00
Sherlock Homes and Dr. Watson have to travel from Rajeev Gandhi Chowk to Indira Gandhi International Airport via the Metro. They have enough coins of 1, 5, 10 and 25 paise. Sherlock Homes agree to pay for Dr. Watson only if he tells all the possible combinations of coins that can be used to pay for the ticket. How many combinations are possible if the fare is 50 paise?

52

52

49

49

44

44

45

45

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#### PrepInsta User

10a + 5b + 10c + 25d = 50 0 0 0 0 2 --> 1 0121 2 0311 4 0501 6 0050 1 0240 3 0430 5 0620 7 0810 9 0 10 0 0 11 ----------------- 49

Question 7

Time: 00:00:00
Amir has 3 deserts every Sunday...he stocked up 10 different chocolates and 12 diff icecreams, given that he never has the same combination and doesn't 3 chocolates nor 3 icecreams, how many Sundays it requires for his stock to be over?

1045

1045

1200

1200

2400

2400

7200

7200

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Question 8

Time: 00:00:00
There is a circular table. It has 60 chairs. Dracula came and sit on a chair beside another person. What is the minimum no. of person will be so, that wherever he sits he always gets to sit beside a person?

30

30

20

20

15

15

10

10

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Question 9

Time: 00:00:00
In how man ways can 10 identical presents be distributed among 6 children so that each gets at least one present.

9c5

9c5

16c6

16c6

15c5

15c5

6 ^ 10

6 ^ 10

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Question 10

Time: 00:00:00
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

1

126

126

64

64

63

63

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["0","40","60","80","100"]
["Need more practice! \r\n","Keep trying! \r\n","Not bad! \r\n","Good work! \r\n","Perfect! \r\n"]

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