Answer

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**Hint:**We are given information about a class test consisting of 15 questions in which 4 marks are given for every correct answer and -2 marks are given for every incorrect answer.

(a) Teena got 10 incorrect answers and so 5 answers were correct. In order to calculate the total marks, we will multiply the incorrect answers with the associated marks getting deducted and this to the product of number of correct answers and the associated marks for correct answer, that is, \[\left( 10\times (-2) \right)+\left( 5\times 4 \right)\].

(b) Her friend who got -4 marks but got 8 correct answers, there must be some discrepancy while adding up the marks. Here, it is given that she got 8 questions correctly so that means the rest of 7 questions were attempted incorrectly.

Hence, we have the required values.

**Complete step-by-step solution:**

According to the given question, we are given information about a class test consisting of 15 questions in which 4 marks are given for every correct answer and -2 marks are given for every incorrect answer. We are asked to solve the two sub questions based on this given information regarding the class test.

Firstly, we have,

(a) We are given that Teena attempted all questions but she got 10 questions incorrect.

So, we have,

Total number of questions = 15

No. of incorrect answers = 10

So, no. of correct answers = 5

So, the total score would be the sum of the product of number of correct answers and associated marks and the number of incorrect answers and associated marks, so we get,

Total marks obtained \[=\left( 5\times 4 \right)+\left( 10\times (-2) \right)\]

\[\Rightarrow 20+\left( -20 \right)\]

\[\Rightarrow 0marks\]

Therefore, Teena scored 0 marks in the class test.

Next, we have,

(b) her friend scored -4 marks but she got 8 correct answers.

This given information contradicts itself as there is a mistake in adding up the marks. We are asked to find the number of incorrect answers.

Total number of questions = 15

Number of correct answers = 8

So, the number of incorrect answers = \[15-8=7\]

So, the total marks that she gets is,

\[\Rightarrow \left( 8\times 4 \right)+\left( 7\times (-2) \right)\]

\[\Rightarrow 32-14=18marks\]

So, the marks given in the question and the marks that we obtained are clearly very different and it contradicts.

**Therefore, the number of incorrect answers is 7.**

**Note:**In the above solution part (b), the question is slightly wrong regarding the marks of Teena’s friend. As no way can we get a total score of -4 marks. It can be shown as follows,

Let the number of correct answers be x, then the number of incorrect answers are \[15-x\],

So, we have the total score as,

\[\left( (15-x)\times (-2) \right)+\left( x\times 4 \right)=-4\]

If we solve this, we get the value of ‘x’ as,

\[\Rightarrow \left( -30+2x \right)+4x=-4\]

\[\Rightarrow -30+6x=-4\]

\[\Rightarrow 6x=-4+30\]

\[\Rightarrow 6x=26\]

Which gives us a value of

\[\Rightarrow x=4.33\]

Which is not possible.

Hence, the total of -4 marks is not even possible and so the friend must have lied or the totalling was not done properly.

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