Explanation:

Lassaigne's test is a chemical test used to detect the presence of nitrogen in organic compounds. It involves the conversion of nitrogen to sodium cyanide, which can then be detected by its characteristic reactions.

In Lassaigne's test for nitrogen, the organic compound is heated with a small piece of sodium metal. The nitrogen present in the compound reacts with sodium to form sodium cyanide (NaCN). This sodium cyanide is then extracted by boiling the mixture with water and the resulting solution is tested for the presence of cyanide ions.

The test involves the following steps:

1. Sodium Fusion: The organic compound is mixed with solid sodium and heated strongly. Nitrogen present in the compound reacts with sodium to form sodium cyanide (NaCN).

2. Extraction: The mixture obtained from the sodium fusion step is dissolved in water and the solution is extracted with ether to remove any nonpolar impurities.

3. Acidification: The aqueous solution is then acidified with dilute sulfuric acid to convert the sodium cyanide to hydrogen cyanide (HCN).

4. Testing for Cyanide Ions: The presence of cyanide ions (CN-) is confirmed by adding a few drops of ferrous sulfate solution followed by a few drops of ferric chloride solution. A deep red coloration or precipitate indicates the presence of cyanide ions.

Now let's analyze each compound and see why Lassaigne's test of nitrogen will fail for option B:

a) HNCONH.NH.HCl: This compound contains nitrogen atoms in the form of an amide group (-CONH-) and amine group (-NH2). Both these groups can react with sodium to form sodium cyanide, thus Lassaigne's test will be successful for this compound.

b) HNNH.2HCl: This compound does not contain any nitrogen atoms that can react with sodium to form sodium cyanide. The presence of hydrogen atoms in place of nitrogen makes it impossible for Lassaigne's test to detect nitrogen in this compound. Hence, Lassaigne's test of nitrogen will fail for this compound.

c) HNCONH: This compound contains a nitrogen atom in the form of an amide group (-CONH-). Like compound a, this compound can react with sodium to form sodium cyanide, and Lassaigne's test will be successful for it.

d) CH-N=N-CH: This compound contains a nitrogen atom in the form of a diazo group (-N=N-). This group can react with sodium to form sodium cyanide, and Lassaigne's test will be successful for this compound.

Therefore, among the given options, Lassaigne's test of nitrogen will fail for compound b) HNNH.2HCl, as it does not contain any nitrogen atoms that can react with sodium to form sodium cyanide.