JEE Main 2022 · 24 Jun · Shift 1 · Mathematics Q22

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MathematicsInteger+4 / -1Question 22 of 90

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 ______.

Your answer

Answer and worked solution

Official answer: 40

Marks equation. With $r$ right and $w$ wrong answers, $3r-2w=5$ and $r+w\le5$ .

Only solution: $r=3$ , $w=2$ .

Count. Choose the 3 right questions ( $\binom53=10$ ); the other 2 are wrong, each in 2 ways ( $2^2=4$ ).

Total $10\times4=40$ .

Answer: 40

Topics:Binomial distribution Combinations

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JEE Main 2022 · 24 Jun · Shift 1, Mathematics question 22