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 all the 90 questions, a student got a total of 387 marks. What is the number of incorrect responses ?

Total number of questions are 90, and 5 marks are given for every correct answer. So, maximum marks possible = 90 × 5 = 450

Now, 2 marks are deducted for every wrong answer. Essentially, it means that every incorrect answer will decrease the maximum score by 5 + 2 = 7 marks.

We know that, the student got 387 marks. So, reduction from maximum marks = 450 – 387 = 63

Hence, the number of incorrect responses = 63/7 = 9