Option 1 states that statements I and III are correct. Let`s analyze each statement individually to determine their validity.

Statement I: "Water is a good solvent for ionic compound but poor solvent for covalent compound." This statement is correct. Water has a polar nature due to its bent molecular structure and the presence of hydrogen bonding. This polar nature allows water to dissolve ionic compounds (which consist of ions with opposite charges) because water molecules can surround and separate the ions, effectively dissolving them. On the other hand, covalent compounds, which consist of sharing electrons between atoms, are less likely to dissolve in water because they do not have charged ions.

Statement III: "Water has maximum density at the temperature 277° K." This statement is also correct. Water has a unique property where its density increases as it cools down from room temperature (about 298° K) until it reaches about 277° K. After that, the density decreases as it freezes into ice. This is why ice floats on water, as it is less dense than liquid water at temperatures below 277° K.

In summary, option 1 is correct, as both statements I and III are valid.