JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Permutations and Combinations

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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_.

Answer: 40

Solution

To score 5 marks, the only possibility is: 3 correct answers (3×3=9 marks) and 2 wrong answers (2×(-2)=-4 marks), giving 9-4=5.

Number of ways to choose which 3 questions are correct:

(3 5) = 10

.

For each correct question, 1 choice (the correct one). For each of the 2 wrong questions, 2 choices (the two incorrect options).

Total:

10 \times 1^{3} \times 2^{2} = 10 \times 4 = 40

JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Integer answer

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