Following statements are given:
(1) The average kinetic energy of a gas molecule decreases when the temperature is reduced.
(2) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature.
(3) The average kinetic energy of a gas molecule decreases with increase in volume.
(4) Pressure of a gas increases with increase in temperature at constant volume.
(5) The volume of gas decreases with increase in temperature.
Choose the correct answer from the options given below:

We need to determine which statements about kinetic theory of gases are correct.

Statement (1): The average kinetic energy of a gas molecule decreases when the temperature is reduced.

The average kinetic energy of a gas molecule is $$KE = \frac{3}{2}k_BT$$.

Since KE is directly proportional to temperature, reducing the temperature reduces the kinetic energy. This is correct.

Statement (2): The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature.

Since $$KE = \frac{3}{2}k_BT$$, the average kinetic energy depends only on temperature. At constant temperature, even if pressure increases, the average kinetic energy remains the same. This is incorrect.

Statement (3): The average kinetic energy of a gas molecule decreases with increase in volume.

Again, average kinetic energy depends only on temperature, not on volume. This is incorrect.

Statement (4): Pressure of a gas increases with increase in temperature at constant volume.

From Gay-Lussac's law: $$\frac{P}{T} = \text{constant}$$ at constant volume. So pressure increases with temperature. This is correct.

Statement (5): The volume of gas decreases with increase in temperature.

From Charles's law at constant pressure: $$V \propto T$$. Volume increases (not decreases) with temperature. This is incorrect.

The correct statements are (1) and (4) only.

Hence, the correct answer is Option A.