Q: Does "neck" have the same meaning in the following two sentences?

The horse won by a neck.

The bottle had a wide neck.

OPTIONS:
- different meanings
- the same meaning

A: different meanings

Q: Does "image" have the same meaning in the following two sentences?

The company tried to project an altruistic image.

The image of f(x) = x^2 is the set of all non-negative real numbers if the domain of the function is the set of all real numbers.

OPTIONS:
- different meanings
- the same meaning

A: different meanings

Q: Does "deference" have the same meaning in the following two sentences?

His deference to her wishes was very flattering.

In deference to your wishes.

OPTIONS:
- different meanings
- the same meaning

A:
different meanings