In a of a test paper, there are five items each under List-A and List-B. The examinees are required to match each item under List-A with its corresponding correct item under List-B. Further, it is given that: (i) no examinee has given the correct answer (

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Q: 97 (IAS/2004)
In a of a test paper, there are five items each under List-A and List-B. The examinees are required to match each item under List-A with its corresponding correct item under List-B. Further, it is given that:
(i) no examinee has given the correct answer
(ii) answers of no two examinees are identical What is the maximum number of examinees who took this test?

question_subject: 

Logic/Reasoning

question_exam: 

IAS

stats: 

0,2,3,1,1,2,1

keywords: 

{'examinees': [0, 0, 1, 0], 'test paper': [0, 0, 1, 0], 'corresponding correct item': [0, 0, 1, 0], 'test': [2, 2, 8, 3], 'examinee': [0, 0, 1, 0], 'maximum number': [1, 0, 1, 2], 'items': [3, 4, 8, 15], 'item': [1, 0, 1, 20]}

The question asks the maximum number of exam takers given that none of them answered correctly, and no two have the same answers. The crux of this problem lies in permutations. There are 5 items in List-A needing to be matched with items in List-B. Five items can be wrongly arranged in 5! or 120 ways. Since no examinee has given the correct answer, the arrangement where all answers are correct is deducted. So, the number of ways to have all answers incorrect is 120 - 1 = 119.

Option 1 and 2 (24 and 26) are incorrect because they do not account for all possible incorrect permutations. Option 4 (129) is wrong as it surpasses the total permutations (120). Hence, Option 3 (119) is the correct answer as it provides the maximum number of unique incorrect arrangements that can be made by the examinees.