In the diagram, if a lightbulb is placed at d and b is closed (as shown), what will happen?

Provided that the batteries still have enough power for current to move in the circuit, replacing the resistor with the bulb and closing the switch will result in the bulb being turned on.

As time passes, the batteries will grow weaker and the light of the bulb will become dimmer and dimmer until it fades.

So, assuming that you are starting with brand new batteries (batteries with enough power) and a closed circuit (switch is closed), the correct choice would be:
The light bulb will be on

If there is any juice left in battery-A, then lightbulb-D will glow.

If the resistance-R of the filament-F in lightbulb-D is too small, then lightbulb-D will glow very brightly for a very short time, and will then burn out ... perhaps with an audible pop-P.