Why is wavelength of violet colour less than wavelength of blue colour? The wavelength of light of specific colour increases as we go from left to right in the visible colour spectrum:  "VIBGYOR". 
Wavelength of green lies between wavelengths of blue and yellow. To me, this makes logical sense because when blue and yellow are mixed, it gives green. (By "mixed", i mean the simultaneous presence of two colours at the same place give rise to a new colour).
Wavelength of orange lies between wavelengths of red and yellow. To me, this also makes logical sense because when red and yellow are mixed, it gives orange.
Now, when it comes to violet, its wavelength is the least in the visible spectrum. It is made by the mixture of red and blue. So according to my logic, it should lie between red and blue in the spectrum. But it doesn't, its wavelength is less than wavelength of blue.
How is this possible?
 A: Color is a double valued concept, different in physics and in perception.
In Physics there is a one to one correspondence between color seen in the visible spectrum and the frequency of light.

The whole electromagnetic spectrum covers many frequencies above and below the visible, which are the colors seen in rainbows.
The second value/definition of color comes from  biology the way it is perceived by the brain as  mixtures of frequencies.

Electromagnetic spectrum with visible light highlighted


You say:

So according to my logic, it should lie between red and blue in the spectrum. But it doesn't, its wavelength is less than wavelength of blue.
How is this possible?

Because the mixture of frequencies to be perceived as a given color by the brain is seen in the chart. The brain sees the single frequency colors as shown in the first figure, but when frequencies are added new colors and hews are seen.
As the chart is not a simple function it happens that violet does no follow the simplified  rule you expect. There is an article in Wikipedia on color vision.
A: I'd like to challenge your idea that the fact that a mix of red and blue gives something resembling violet implies that violet must be between red and blue.
In practice, what you get from such mixture is a shade of purple. See the figure below. Here the black dashed line from blue to red covers the colors you can get by changing the amount of red and blue in the mixture. The purest violet is on the bottom-most part of the border of the colored shape (the visible gamut).
On the other hand, if you mix violet and sky blue, you can get the set of colors covered by the green dotted line in the diagram. See that blue is among the colors you can get from this mixture.

Do these two facts conflict? No. Most colors are not spectral: they are desaturated. Together they fill a two-dimensional shape, on which the internal points can be found as mixtures of pairs of spectral colors. And the pairs are not unique: e.g. you can get white by mixing orange and sky-blue, or by mixing yellow and royal-blue, etc.. So what you call violet is not a point in this gamut—rather it is an area, where you can pick any point and still call it violet.
A: You are confused and I understand because even on this site, you can read phrases like "our eyes have cones for Red, Green and Blue light" and "Red light activates the Red cones".
Reception


*

*It is a common misconception that the receptors in our eyes are so, that the different types of cones correspond specifically just to Red, Green and Blue light. In reality, the three types of cones are sensitive for a range of Short, Mid and Long (depending on where they are positioned in the visible scale) wavelengths. It is very important to understand that they cover a range of wavelengths, and that they overlap.



https://en.wikipedia.org/wiki/Spectral_sensitivity
Even if you wanted to put a arbitrary conventional color coding for these, you would have to put Yellow, Green and Blue instead of RGB. But these cones have a range of sensitivity, and multiple types of cones could be sensitive for the same wavelength photons. All along the visible wavelength range, there isn't a single position where only one type of cone would be sensitive, that is, every single wavelength photon would activate multiple types of cones.


*It is another misconception that whenever  monochromatic light shines into our eyes, only one type of cone gets activated. In reality, whenever light shines on our eyes, may it be monochromatic or not, multiple types of cones get activated, it is just the level of activation that is different for different wavelength photons. Whenever monochromatic red light shines into our eyes, even if the photons would be all the same wavelength, they activate both the Long and Mid cones. The more the Long cone gets activated, the more reddish the shade is, the more the Mid range cone gets activated, the more Orange/Yellowish the shade is perceived by our brain.


Perception
Our brain is the one that perceives the colors as a combination of signals from the cones, and our brain is the one that perceives violet as a combination of signals from the Short and Long cones too. The more the Short cones get activated, the more violet the shade of the color is perceived by the brain, the more the Long cone gets activated, the more Bluish the shade is perceived by the brain. So this is the answer to your question, violet is the end of the spectrum, where the Short cone's activity dominates. In fact, you need to add the Long cone's activity to get away from the end of the spectrum, and move towards blue.
It is too correct, that a certain perceived color in the brain can be produced by multiple different combinations of signals from the three types of cones.
A: In reality our retinas have three specific cones for picking up and identifying light. These cones account for the colors red, green, and blue. There is no specific cone for identifying violet, but when the red cone and blue cone are activated simultaneously, we perceive violet. Another way to think about it, violet contains slightly higher energy than blue, which means higher frequency and lower wavelength. So, if you add the lowest energy color we can see (red) to the highest we can see (blue) you get slightly more than blue (violet!). I hope this helps!
A: Your question boils down to "Why is light at the short-wavelength end of the visible spectrum perceived as violet?"; and it is based on the assumption that we perceive the color of a wavelength as a sort of average of the perceived color of amount of light in nearby parts of the spectrum.
The assumption is not correct.  Our retinas have three types of light receptors (each sensitive to a different overlapping portion of the spectrum), and encode the received spectrum in terms of the amount of activation of those receptors.  That encoded representation is sent to our brains where we interpret it as color.  This article describes it well, and specifically addresses perception of violet.  Briefly put, our visual system has evolved to encode that particular portion of the spectrum differently, in terms of the mix of blue and red receptor responses rather than, e.g., blue alone or blue and green. The blue, green, and red receptors all respond to some degree in the short-wavelength range, but the ratios of their responses are quite different in that range than in other parts of the spectrum, so our visual system can encode that range (for a single wavelength) differently.
Note that it is possible to "spoof" our eyes into perceiving the color violet as if there were short wavelengths present, by presenting a mix of wavelengths that stimulates the R, G, and B sensors in the right ratio.
