a heater joined in parallel with a 60 W bulb is connected to d mains.if the 60 W bulb is replaced with 100 W bulb, will the rate of heat produced by the heater be more, less, or remain d same?

As the assembly is connected in parallel so the point to note is that the voltage across both the bulb and the heater will remain the same. To maintain this same voltage difference the current will change. We also know that power is given by v^2/r. Now when the 60 W bulb is changed with 100 W bulb, as the voltage difference (v) needs to be constant so obviously the resistance of the second bulb (100 W) has to be less then that of 60 W. ( as P = (V^2/R) i.e. we have decreased the resistance for the bulb and for the voltage drop to remain same, the current passing through bulb will increase. But remember this increased current will be supplied by the battery, and as the voltage drop across the heater is constant and its resistance is same as well, so no change in heat production by the heater will be observed.

Approved