Sarthaks Test
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In an objective type test containing 25 questions. A student is to be awarded +5 marks for every correct answer, –5 for every incorrect answer and zero for not writing any answer. Mention the ways of scoring 110 marks by a student.

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Marks scored = +110

So, minimum correct responses

= 110 ÷ (+5) = 22

Case 1

Correct responses = 22

Marks for 1 correct response = + 5

Marks for 22 correct respones

= +110 (22 × 5)

Marks scored = +110

Marks obtained for incorrect answer = 0

So, no incorrect response

And, therefore, 3 were unattempted

Case 2

Correct responses = 23

Marks from 23 correct responses

= + 115 (23 × 5)

Marks scored = + 110

Marks obtained for incorrect answers

= 110 – (+115)

= –5

Marks for 1 incorrect answer = –5

Number of incorrect responses

= (–5) ÷ (–5)

= 1

So, 23 correct, 1 incorrect and 1 unattempted.

Case 3

Correct responses = 24

Marks from 24 correct responses = + 120 (24 × 5)

Marks scored = + 110

Marks obtained for incorrect answers = +110 – (+120)

= –10

Number of incorrect responses

= (–10) ÷ (–5) = 2

Thus the number of questions = 24 + 2 = 26. Whereas,

total number of questions is 25. So, this case is not

possible.

So, the possible ways are:

• 22 correct, 0 incorrect, 3 unattempted

• 23 correct, 1 incorrect, 1unattempted.

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