# AMCAT Permutation and Combinations Quiz-1

Question 1

Time: 00:00:00
Harry was given homework by his class teacher.He did not like math at all.
Harry needs help in finding out the rank of the word GREAT if the letters of the word EGART are rearranged to form 5 letter words such that none of the words repeat and the results arranged in ascending order as in a dictionary.

47

47

56

56

84

84

32

32

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Question 2

Time: 00:00:00
On the occasion of his birthday, Rahul invited all of his pals to a party at his father's farm.
The seating arrangement called for 5 males and 4 females, with the females taking the even-numbered seats. How many of these configurations are possible?

2020

2020

1440

1440

2880

2880

1550

1550

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Question 3

Time: 00:00:00
Max and his father were on a flight from Australia to Dubai. However, they each managed to forget how to open their bag's lock. Three dials with six different letter markings each make up the letter lock.How many unsuccessful efforts to unlock the latch can be made because Harry's mother will be furious if the bag is permanently locked?

268

268

234

234

215

215

286

286

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Question 4

Time: 00:00:00
Seema is playing a game at a stall in a fair. She needs to throw the ball in the ring with the number which can be calculated by the following riddle : How many 6-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 and 7 so that the digits should not repeat and the second last digit is even. Seema wants to know this number so that she can win the game.

760

760

425

425

840

840

720

720

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Question 5

Time: 00:00:00
20 people in total participated. Find the number of arrangements that may be made so that there is always one person between each of the two representatives, Mohan and Mohit, at a circular table.

$2 \times (18!)$

$2 \times (18!)$

$(3!) \times (18!)$

$(3!) \times (18!)$

17!

17!

$2 \times (17!)$

$2 \times (17!)$

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Question 6

Time: 00:00:00
In the city of Nadar, parallel highways p and q run from north to west and from east to south, respectively. How many rectangles are created by these highways' sides?

$\frac{pq}{4}$

$\frac{pq}{4}$

$\frac{(pq)(p-1)(q-1)}{4}$

$\frac{(pq)(p-1)(q-1)}{4}$

$\frac{(p-1)(q-1)}{4}$

$\frac{(p-1)(q-1)}{4}$

None of the above

None of the above

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Question 7

Time: 00:00:00
12 ants were seen crawling across an entomologist's table. There were exactly 10 men and 2 women among them. He noted that they weren't crawling on the table in a straight line, but rather in a random order, with never three of them in a row. All four ants were suddenly in a single line as three of the male ants started to follow one of the female ants.Then the maximum number of distinct straight lines that the entomologist can draw passing through any two ants is

61

61

42

42

74

74

66

66

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Question 8

Time: 00:00:00
Manish finished his studies and began working in an electrical shop. Four different black bulbs, three different white bulbs, and five different yellow bulbs are provided. The number of possible bulb combinations, assuming at least one yellow and one black bulb, is thus :

3000

3000

2880

2880

4250

4250

3720

3720

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Question 9

Time: 00:00:00
An ill spider lived in a region of frigid terrain.So he set up a shoe and a pair of socks for each of its eight legs.Given that the sock must go on before the shoe in each leg, how many distinct ways can the octopus put on its socks and shoes?

$\frac{8!}{2}$

$\frac{8!}{2}$

$\frac{8!}{3} \times 2^{3}$

$\frac{8!}{3} \times 2^{3}$

$\frac{1}{2})^{8} \times 16!$

$\frac{1}{2})^{8} \times 16!$

None of the above

None of the above

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Question 10

Time: 00:00:00
The transport government has been ordered to mark neon flags on the road by the Supreme court due to an increase in the number of road accidents at night. Six flags are marked on a straight road and five flags are marked on another road which is parallel to the first road. How many straight lines, including the first two, can be formed with these flags connecting both sides of the road?

32

32

46

46

48

48

25

25

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["0","40","60","80","100"]
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