Question

Which of the following is a possible set of quantum numbers for an electron?

(1, 1, 0, +½)
(2, 1, 2, +½)
(4, 2, 0, -½)
(3, -2, 1, -½)

Answer 1

The phrasing of this exercise means that we have to exclude 3 out of the 4 choices.
We have that the 4 quantum numbers that an electron has are the defining numbers of that electron. The first coordinate, the principal quantum number ncan take any positive value since it defines the shell in which that electron is.

The second number is called the orbital angular momentum number and takes the values from 0 to n-1 (the integer ones) where n is the principal number. Hence, we can disqualify options 1 and 4; the 1st because the principal and the orbital number are the same which is not possible and the 4th because the orbital number is negative which is not possible.

The third is the magnetic quantum number and takes values from -l to l (all integer values in between). Hence, it cannot be equal to n again, so option 2 is disqualified too.
The only remaining option that is correct is 3)

P.S. We have a 4th number, the spin number; this number can assume only the values +1/2 and -1/2