The necessary condition for nuclear fusion is
a) high temperature and high pressure
b) low temperature and low pressure
c) high temperature and low pressure
d) low temperature and high pressure

Hint: For nuclear fusion to take place, the individual nuclei should have sufficient kinetic energy in order to come close to each other. Similarly high density of the nuclei should be available as this would increase the rate of fusion. Therefore will first verify how the nuclear fusion varies with change in temperature and pressure.

Complete step-by-step answer:
To begin with let us first define nuclear fusion.
The process in which two light nuclei combine to form a single heavier nucleus is called nuclear fusion.
For fusion reactions to take place there are some of the necessary conditions that need to be obeyed. The nuclei consists of net positive charge. When two nuclei are brought close to one another the Coulombic force of repulsion prevents them from coming together. Hence the nuclei of an atom needs to have sufficient kinetic energy in order to overcome this repulsion. The energy of a nuclei is directly proportional to the surrounding temperature. Hence we can conclude that high temperature is necessary for nuclear fusion to take place.
Let us say in a given space there exists some nuclei. If the density of the nuclei in the given space is high enough then the rate of fusion will be faster. This is because the frequency of collision between the any two nuclei will be more. Since the density of the nuclei in a given space is increased the pressure in that space will also increase. Hence, high pressure is also essential for nuclear fusion to take place.
From the above conditions we can conclude that both high temperature and pressure is necessary for nuclear fusion to take place.

So, the correct answer is “Option A”.

Note: It is to be noted that temperature of the order ${{10}^{6}}$ is required for fusion reaction to take place. These conditions exist in the interior of the sun and cannot be easily met in a laboratory. Hence, the process of nuclear fusion takes place in thermonuclear reactors where these conditions are met.