In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct…

Let the marks obtained in each of the five MCQ be $x_1, x_2, x_3, x_4, x_5$

Now, $x_1+x_2+x_3+x_4+x_5=5$

Only one possibility satisfies the above equation i.e.  $3,3,3,-2,-2$

Hence, total number of ways $=\frac{5!}{3!2!}\times 2\times 2=40$