When Umesh connects the bulbs one at a time, the filaments of the bulbs get burnt. This means the heat energy generated in the filament is beyond what it can tolerate. Hence, we need to reduce the heat generated across the filament. Now, the heat generated in a resistor is proportional to the amount of current flowing through it. Thus, we need to reduce the current flowing through the bulbs. 

A. If bulbs are connected in series, the effective resistance of the circuit increases, and hence current through the bulbs decreases. In this way, both the bulbs can be saved from burning.

B. Following are the characteristics of series connection:

• The effective resistance of the circuit is the sum of individual resistances of the resistors present in the circuit. 
• The effective resistance of the series circuit is always larger than the greatest resistance in the circuit.
• Current through various electrical components connected in series is the same.
• The source voltage gets divided across the electrical components connected in series.

C. The effective resistance of the circuit = 15Ω + 30Ω = 45Ω