In an objective type test of 90 questions, 5 marks are allotted for every correct answer and 2 marks are deducted for every wrong answer. After attempting the entire 90 question, a student got a total of 387 marks. What is the number to incorrect responses?

Correct Option (A)

The problem requires determining the number of incorrect responses based on a given scoring system and a student's total score.

• Total number of questions: 90
• Marks awarded for each correct answer: 5
• Marks deducted for each incorrect answer: 2
• Student's total score: 387

First, calculate the maximum possible score achievable if all questions were answered correctly:

Maximum score = \(90 \times 5 = 450 marks\).

Next, determine the effective mark reduction associated with each incorrect answer. An incorrect response results in a loss of marks in two ways:

• The 5 marks that would have been gained for a correct answer are forfeited.
• An additional 2 marks are deducted as a penalty.

Therefore, each incorrect answer effectively reduces the total score by a combined \(5 + 2 = 7 marks\) from the maximum potential score.

The total marks lost by the student, when compared to the maximum possible score, are calculated as:

Marks lost = \(450 - 387 = 63 marks\).

Finally, to ascertain the number of incorrect responses, divide the total marks lost by the effective mark reduction per incorrect answer:

Number of incorrect responses = \(\frac{63}{7} = 9\).

Incorrect Options:

Options B (13), C (27), and D (43) are incorrect. These values do not correspond to the number of incorrect responses when applying the specified scoring criteria and the student's achieved score. Such results would arise from miscalculations or an incorrect application of the scoring rules.