A disclaimer is attached at the bottom of this post.
And now for questions number 10, 11, and 12. As always, your tentative solutions and / or comments are welcome in the comments thread below.
10. Succinctly describe a method to search for dark matter particles.
11. Estimate the ratio between the cross section of hadron production and the cross section of muon pair production in electron-positron annihilations, at the following center-of-mass energies: 2 GeV, 6 GeV, 12 GeV.
12. Draw the energy distribution of electrons emitted in the decay of muons at rest, and explain the features you sketched.
I offer these questions as a self-test of one's knowledge in particle physics. I am not part of the INFN selection committee. I have no connection to the selection committee, nor any insider information on how the exam will be structured. All I know about it is what is contained in the official call, available to everybody. I do have some previous experience with INFN selections of researchers, but this needs not be relevant for this year's selection.