a = 6 \, - 5 , b = 5 \, - 2, c = 2 - 3 then point out the correct alternative among the four alternatives given below ?

Answer: Option D

$$\begin{array}{rl}& a=\sqrt{6}-\sqrt{5}\\ & b=\sqrt{5}-2\\ & c=2-\sqrt{3}\\ & \text{Rationalize all the terms}\\ & a=\frac{\sqrt{6}-\sqrt{5}}{\sqrt{6}+\sqrt{5}}\times \sqrt{6}+\sqrt{5}\\ & =\frac{1}{\sqrt{6}+\sqrt{5}}\\ & b=\frac{\sqrt{5}-2}{\sqrt{5}+2}\times \sqrt{5}+2\\ & =\frac{1}{\sqrt{5}+2}\\ & =\frac{1}{\sqrt{5}+\sqrt{4}}\\ & c=\frac{2-\sqrt{3}}{2+\sqrt{3}}\times 2+\sqrt{3}\\ & =\frac{1}{2+\sqrt{3}}\\ & =\frac{1}{\sqrt{4}+\sqrt{3}}\\ & \text{Now, }\\ & a=\frac{1}{\sqrt{6}+\sqrt{5}}\\ & b=\frac{1}{\sqrt{5}+\sqrt{4}}\\ & c=\frac{1}{\sqrt{4}+\sqrt{3}}\end{array}$$
Now the term whose denominator is largest is the smallest term.
So, a < b < c