JEE Main 2022MathematicsPermutation CombinationHardNumerical

JEE Main 2022 — Permutation Combination Question with Solution

JEE Main 2022 (24 Jun Shift 1)

Question

In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct. There are 3 marks for each correct answer, -2 marks for each wrong answer and 0 mark if the question is not attempted. Then, the number of ways a student appearing in the examination gets 5 marks is _____

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Show full solutionCorrect answer: 40
Correct answer
40

Step-by-step explanation

Let the marks obtained in each of the five MCQ be x1, x2, x3, x4, x5

Now, x1+x2+x3+x4+x5=5

Only one possibility satisfies the above equation i.e.  3,3,3,-2,-2

Hence, total number of ways =5!3!2!×2×2=40

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About this question

This is a previous-year question from JEE Main 2022, covering the Permutation Combination chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.