Verified Solution • 2025–26 Session moderate

QJEEM22Maa38f: JEE Main 2022 Mathematics - Class 11 JEEM22Maa38f Solution: In an examination, there are 5 multiple choice questions with 3 …

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 ____________.

Step-by-Step Verified Solution

Let student marks xx correct answers and yy incorrect. So

3x−2y=53 x-2 y=5 and x+y≤5x+y \leq 5 where x,y∈Wx, y \in \mathrm{W}

Only possible solution is (x,y)=(3,2)(x, y)=(3,2)

Students can mark correct answers by only one choice but for an incorrect answer, there are two choices. So total number of ways of scoring 5 marks =5C3(1)3⋅(2)2=40={ }^{5} C_{3}(1)^{3} \cdot(2)^{2}=40

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring