Is diode linear or nonlinear?

Hint: A diode is a semiconductor device made by combining p type semiconductors and n type semiconductors. A linear device is the one which follows a linear relationship between the input and output while a non-linear device does not have a linear relationship between input and output.

Complete answer:
A diode is a semiconductor device which is made by connecting a p-type and n-type semiconductor together. A diode can either be reverse bias or forward bias. Forward bias means when the positive terminal of battery is connected to p-type while the negative terminal of the battery is connected to n-type.
A linear device is that which follows the following properties of linearity-
The output changes with the same amount as the input. This property is known as homogeneity or scaling. Therefore,
$f(ax)=af(x)$
Adding two inputs together is the same as applying each input individually. This property is known as additivity. Therefore,
$f({{x}_{1}}+{{x}_{2}})=f({{x}_{1}})+f({{x}_{2}})$
Since the diode does not follow any of the properties in forward or reverse bias, it is not a linear device. The i-v graph of a diode in forward and reverse bias is not a straight line while the graph for linear devices gives a straight curve.

Note:
P-type semiconductors contain holes as charge carriers while the n-type contains electrons as charge carriers. A junction is formed between p-type and n-type where the holes and electrons combine. The junction is very thin in forward bias while the junction is wide in reverse bias. Very small current flows in reverse bias while in forward bias large current flows.