Will this circuit work ? 100 Leds project
No, that's a really bad circuit.  You have 100 LEDs, all in parallel.  Bad idea.

Since this is a assignment, I'm not going to give you a better circuit outright.  However, consider that LEDs want to be driven with a fixed current, not a fixed voltage.  The change in current due to a change in voltage is very large when the LED is lit.  Conversely, the voltage changes little as a function of changing current.

Now also consider that every LED will end up at a slightly different voltage when run at the same current.  If you put two such LEDs in parallel, then they both get the same voltage by definition of parallel.  The small difference in forward voltage of the two LEDs leads to a much large difference in current between the two LEDs.  Even worse, the LED that gets the higher current dissipates more power.  That makes it get hotter, which decreases it's forward voltage, which makes it take a larger share of the current, which makes it get even hotter, etc.

Think of a way to run LEDs, or groups of LEDs, at a fixed or reasonably controlled current.