Question

How many possible values for pair l and m_{l} are there when n_1 = 3?

How many possible values for pair l and m_{l} are there when n_2 = 5?

Express your answer as an integer.

I understand the following solution:
"we know that for a particular value of n , l ranges from 0 ton-1
and m ranges from -l to + l including 0.
so here in this question
for n = 2 we have l value ranging from 0 to 1
now ml ranges from -l to + l
so for l = 0, we have m l = 0
and for l = 1 , we have ml = -1 , 0 , +1
so there are total 2 values of l and 3values of ml
now in the other case where n = 5
we have l values ranging from 0 to 4
so there are 5 possible values of l
and ml ranges from -l to + l , so total 2l + 1values
so ml possible values = 2*4 + 1
= 9
so there are 5 possible values of l and 9possible values of ml"

I tried to answer 6 for n = 3 and 45 for n = 5 but the answer is incorrect.

Answer 1

I must confess that I have no inkling of what "pair l" means although I understand the example you hve give but don't see the connection since the word "pair" is never used in the example.
For n = 3 there will be 3 possible values for l (0,1,2) and there will be 5 different values for ml. How that fits into "pair l" I don't know.
For n = 5, there will be 5 possible values for l (0,1,2,3,4) and 9 separate values for ml.