algorithm - Why is only one of the given statements about complexity classes correct? -

apparently correct answer following question (c), why other options not correct until know value of n?

if n=1, of these seem correct except (b)! going wrong?

which of following not o(n²)?

(a) 15¹⁰ * n + 12099
(b) n^1.98
(c) n³ / √n
(d) 2²⁰ * n

wikipedia says :-

big o notation describes limiting behavior of function when argument tends towards particular value or infinity, in terms of simpler functions. description of function in terms of big o notation provides upper bound on growth rate of function.

an upper bound means f(n) = n can expressed o(n), o(n²), o(n³), , others not in other functions o(1), o(log n).

so, going in same direction, can eliminate options shown below :-

1. 15¹⁰ * n + 12099 < c * n², n > √12100 i.e. n > 110 --- hence o(n²).

2. n^1.98 < n², n > 1 --- , o(n²).

3. n³ / √n = n^5/2 > n² n > 1 --- hence, isn't o(n²).

4. 2²⁰ * n = 1024*1024*n < c* n² n > 1 ,where c = 1024*1024 --- hence, o(n²).

hence, option doesn't satisfy o(n²) option c,i.e., f(n) = (n^3 / (sqrt(n))). here, so, (n³ / (sqrt(n))) isn't equal o(n²).