Question

a number of bulbs are connected simultaneously in parallel across a cell .it is found that when number of cells is either 4or9 the total intensity remains the same what should be the number of bulbs for max total intensity

Answer 1

More information needed. Is it stated what the filaments of the bulbs are made from e.g. tungsten? Since the circuit is parallel, current flowing through each bulb should be the same, however this assumes that 4 cells allow current flow such that the bulbs are hot but not producing visible light. 9 cells is allowing enough current to flow that I would assume the filaments are on the verge of melting. Tungsten changes resistance at a value of about 3 x 10-3 Ohm/C. You would want the total resistance of the bulbs to be such that the temperature is just under the melting point of tungsten. I would assume max intensity is at max temperature. You aren't asked to calculate the intensity, are you?