Q. Why V-I curve of verification ohm's law have linear form but it take experimental form for measurement of diode characteristics.?
The linear V-I curve of Ohms law is self defining. Ohm's law expresses a linear relationship, so things that obey Ohm's law will be linear and things that are linear obey Ohm's law. But not every material obeys Ohm's law and so we describe that as non resistive behaviour. In fact most materials go non linear at some extreme of temperature / voltage gradient / current density etc. and we just shrug it off by saying - it's not resistive in that range then, and thus Ohm's law doesn't apply. But semiconductor material can be formed into devices that are highly non linear even in normal DC conditions, so the V-I curve doesn't follow Ohm's law and they are not considered in terms of DC resistance. The reason has to do with the crystal structure of very pure silicon versus intentionally introduced impurities. If you want a more detailed understanding then search on YouTube for "p type, n type materials and junctions"
A conducting diode"s resistance is not constant. The resistance of a conducting diode is nonlinearly proportional to the current through the diode.
You need the physics and math behind resistors and diodes for a full explanation. See the links. I think you mean "exponential"...