In an examination, a student gets 4 marks for every correct answer, 1 for every unattempted question and 0 for every wrong answer. If there are 30 questions, which of the following total scores is not attainable by a student?

Let the number of correct answers be $c$, the number of unattempted questions be $u$, and the number of wrong answers be $w$.
Given:

$$\text{Total Questions: }c+u+w=30⟹c+u\le 30$$

$$\text{Total Score: }S=4c+1u+0w=4c+u$$

Let's check the attainability of the given options:

* For 114 (Option B): If $c=28$, then $4(28)=112$. We need $u=2$.
Check total questions constraint: $c+u=28+2=30\le 30$ ($w=0$). This is attainable.
* For 113 (Option A): If $c=28$, then $4(28)=112$. We need $u=1$.
Check total questions constraint: $c+u=28+1=29\le 30$ ($w=1$). This is attainable.
* For 117 (Option D): If $c=29$, then $4(29)=116$. We need $u=1$.
Check total questions constraint: $c+u=29+1=30\le 30$ ($w=0$). This is attainable.
* For 115 (Option C): If $c=28$, $4(28)=112$, we need $u=3$. Then $c+u=28+3=31>30$, which violates the total question limit.
If $c=29$, $4(29)=116$, which exceeds $115$.
Thus, a score of **$115$ is mathematically unattainable**.