Answer: option (4) thallium.
Explanation:
1) You have to look at the normal boling and mleting points of the elements.
2) To be liquid the normal melting point must be lower than 758 K and the normal boiling point must be greater than 758 K.
3) The look at the data in a handbook of properties or in internet, and build a table.
4) The given temperature, 758K, is 758 - 273.15 = 484.85 °C.
Element Normal melting Normal boiling State at 484.85 °C
point (°C) point (°C)
(1) gold 1064 2700 solid
(2) silver 961.8 2162 solid
(3) platinum 1768 3825 solid
(4) thallium 303.5 1457.8 liquid
Then, the only element of the choices whose melting point is less than 758 K (484.85) and its boiling point is greater than that, at 1 atm is thallium. So, it is liquid.