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  1. False.

    The law of conservation of energy is always obeyed in all circumstances.

    When speaking of “efficiency” what is meant is the fraction of the energy which is usefully captured, which can never be 100%. All the energy is still present, obeying the conservation law, but not all that energy is usable.
    In the case of a power plant for instance, something like 63% of the energy from the burning fossil fuel gets converted to electrical energy, but the remaining 37% is lost as heat. The two kinds of energy still add up to 100% (thus the conservation law) but the conversion is only 67% efficient because of the inevitable heat loss.

burns fossil fuels, maximum theoretical efficiency of 63% obey law of conservation of energy?

A power plant that burns fossil fuels and has a maximum theoretical efficiency of 63% does not obey the law of conservation of energy.

True or False?