Multiple Correct Answer Questions in IIT JAM Mathematics Exam

Introduction
In the IIT JAM Mathematics Exam, there are multiple choice questions (MCQs) with multiple correct answers. These questions are designed to assess the depth of knowledge and understanding of the candidates. The marking scheme for such questions is different from the regular single correct answer MCQs.

Marking Scheme
The marking scheme for multiple correct answer questions in the IIT JAM Mathematics Exam is as follows:

1. Correct Response: For each correct response, candidates are awarded +1 mark.
2. Incorrect Response: For each incorrect response, candidates are awarded -1/3 (negative one-third) mark.
3. Unattempted Questions: No marks are deducted for unattempted questions.

Distribution of Marks
The marks for multiple correct answer questions are awarded based on the following criteria:

1. Selecting all correct options: If the candidate selects all the correct options and does not select any incorrect option, then +1 mark is awarded.
2. Selecting some correct options: If the candidate selects some correct options and does not select any incorrect option, then partial marks are awarded based on the proportion of correct options selected.
3. Selecting correct and incorrect options: If the candidate selects both correct and incorrect options, then marks are awarded or deducted based on the following formula:

Marks = (Number of Correct Options Selected)/(Total Number of Correct Options) - (Number of Incorrect Options Selected)/(Total Number of Incorrect Options)

If the calculated marks are positive, they are awarded; otherwise, they are deducted.

Example
Let's consider an example to understand the marking scheme better. Suppose a question has four options, out of which three are correct and one is incorrect. The total weightage of the question is 4 marks.

If a candidate selects all the correct options and does not select the incorrect option, then the candidate is awarded +1 mark.

If a candidate selects two correct options and does not select the incorrect option, then the candidate is awarded (2/3) * 1 = 0.67 marks.

If a candidate selects one correct option and does not select the incorrect option, then the candidate is awarded (1/3) * 1 = 0.33 marks.

If a candidate selects two correct options and one incorrect option, then the candidate is awarded (2/3) * 1 - (1/1) * (1/3) = 0.67 - 0.33 = 0.34 marks.

If a candidate selects one correct option and one incorrect option, then the candidate is awarded (1/3) * 1 - (1/1) * (1/3) = 0.33 - 0.33 = 0 marks.

Conclusion
In the IIT JAM Mathematics Exam, multiple correct answer questions are scored based on the marking scheme mentioned above. It is important for candidates to carefully analyze the options and select all the correct ones while avoiding the incorrect options to maximize their score in these questions.