This exercise is a multiple choice questionnaire (MCQ) comprising five questions. The five questions are independent. For each question, only one of the four answers is correct.

\begin{enumerate}
  \item The solution $f$ of the differential equation $y' = -3y + 7$ such that $f(0) = 1$ is the function defined on $\mathbb{R}$ by:\\
  A. $f(x) = \mathrm{e}^{-3x}$\\
  B. $f(x) = -\frac{4}{3}\mathrm{e}^{-3x} + \frac{7}{3}$\\
  C. $f(x) = \mathrm{e}^{-3x} + \frac{7}{3}$\\
  D. $f(x) = -\frac{10}{3}\mathrm{e}^{-3x} - \frac{7}{3}$

  \item The curve of a function $f$ defined on $[0; +\infty[$ is given below.

  A bound for the integral $I = \int_{1}^{5} f(x)\,\mathrm{d}x$ is:\\
  A. $0 \leqslant I \leqslant 4$\\
  B. $1 \leqslant I \leqslant 5$\\
  C. $5 \leqslant I \leqslant 10$\\
  D. $10 \leqslant I \leqslant 15$

  \item Consider the function $g$ defined on $\mathbb{R}$ by $g(x) = x^2 \ln\left(x^2 + 4\right)$.

  Then $\int_{0}^{2} g'(x)\,\mathrm{d}x$ equals, to $10^{-1}$ near:\\
  A. 4.9\\
  B. 8.3\\
  C. 1.7\\
  D. 7.5

  \item A teacher teaches the mathematics specialization in a class of 31 final year students. She wants to form a group of 5 students. In how many different ways can she form such a group of 5 students?\\
  A. $31^5$\\
  B. $31 \times 30 \times 29 \times 28 \times 27$\\
  C. $31 + 30 + 29 + 28 + 27$\\
  D. $\binom{31}{5}$

  \item The teacher is now interested in the other specialization of the 31 students in her group:
  \begin{itemize}
    \item 10 students chose the physics-chemistry specialization;
    \item 20 students chose the SES specialization;
    \item 1 student chose the Spanish LLCE specialization.
  \end{itemize}
  She wants to form a group of 5 students containing exactly 3 students who chose the SES specialization. In how many different ways can she form such a group?\\
  A. $\binom{20}{3} \times \binom{11}{2}$\\
  B. $\binom{20}{3} + \binom{11}{2}$\\
  C. $\binom{20}{3}$\\
  D. $20^3 \times 11^2$
\end{enumerate}