Given below are two statements :
Statement I : The identification of `Ni^(2+)` is carried out by dimethyl glyoxime in the presence of `NH_4OH`.
Statement II : The dimethyl glyoxime is a bidentate neutral ligand.
In the light of the above statements, choose the correct answer from the options given below:

Options

A. Statement I is true but Statement II is false.
B. Both Statement I and Statement II are false
C. Statement I is false but Statement II is true
D. Both Statement I and Statement II are true

Answer

To solve the problem, we need to analyze both statements provided in the question regarding the identification of `Ni^(2+)` using dimethyl glyoxime (DMG) and the nature of DMG as a ligand.

### Step-by-Step Solution:

1. **Understanding Statement I**:
- Statement I claims that the identification of `Ni^(2+)` is carried out by dimethyl glyoxime in the presence of `NH_4OH`.
- This statement is **correct**. Dimethyl glyoxime (DMG) is indeed used to detect nickel ions (`Ni^(2+)`). When nickel(II) ions react with DMG in the presence of ammonium hydroxide, a red precipitate of nickel dimethylglyoxime complex is formed, which confirms the presence of nickel.

2. **Understanding Statement II**:
- Statement II claims that dimethyl glyoxime is a bidentate neutral ligand.
- This statement is **incorrect**. While DMG is a bidentate ligand because it can coordinate to a metal ion through two donor atoms (the nitrogen atoms), it is not neutral. The structure of DMG contains an anionic form (due to the presence of a negative charge on the oxygen in the deprotonated form), which makes it a negatively charged ligand.

3. **Conclusion**:
- From the analysis, we conclude that Statement I is correct and Statement II is incorrect. Therefore, the correct answer to the question is that one statement is correct and the other is incorrect.

### Final Answer:
- **One statement is correct and the other is incorrect.**