Principle of Lassaigne’s test

In Lassaigne’s test, the organic compound is fused with sodium so that covalently bonded elements are converted into ionic salts:

• Nitrogen gives sodium cyanide, $\mathrm{NaCN}$.
• Halogen gives sodium halide, $\mathrm{NaX}$.

For a compound to give positive tests for both nitrogen and halogen, it must contain:

• at least one carbon atom and nitrogen together, so that $\mathrm{CN^-}$ can form,
• and also a halogen.

Without carbon, nitrogen cannot form cyanide in sodium fusion, so nitrogen test will be negative.

Check each option

Option A: $\mathrm{NH_2OH\cdot HCl}$

• Contains $N$ and $Cl$.
• But it has no carbon.
• Therefore, $\mathrm{NaCN}$ cannot form.
• So nitrogen test is negative.

Hence, not correct.

Option B: $\mathrm{N_2H_4\cdot HCl}$

• Contains $N$ and $Cl$.
• But again no carbon is present.
• So cyanide cannot form.
• Nitrogen test is negative.

Hence, not correct.

Option C: $\mathrm{CH_3NH_2\cdot HCl}$

• Contains carbon, nitrogen, and chlorine.
• On sodium fusion:
  • $C + N \rightarrow \mathrm{CN^-}$, giving nitrogen test positive.
  • $Cl \rightarrow \mathrm{Cl^-}$, giving halogen test positive.
• Therefore both tests are positive.

Hence, correct.

Option D: $\mathrm{NH_4Cl}$

• Contains $N$ and $Cl$.
• But no carbon.
• So nitrogen cannot give cyanide.
• Nitrogen test is negative.

Hence, not correct.

Conclusion

The only compound that gives positive Lassaigne’s test for both nitrogen and halogen is:

$\boxed{\mathrm{CH_3NH_2\cdot HCl}}$

So the correct option is C.