In which case racemic mixture is obtained on mixing its mirror images (d & l form) is 1:1 molar ratio:

Options

A. trans-`[Co(gly)_(3)]`
B. `[Ni(DMG)_(2)]`
C. cis-`[Cu(gly)_(2)]`
D. `[Zn(en)(gly)]^(+)`

Explanation

To determine in which case a racemic mixture is obtained when mixing its mirror images (dextro and levo forms) in a 1:1 molar ratio, we need to analyze the optical activity of the given compounds. A racemic mixture is formed when equal amounts of two enantiomers (dextro and levo forms) are combined, resulting in a compound that is optically inactive.

### Step-by-Step Solution:

1. **Understanding Optical Activity**:
- A compound is optically active if it has a non-superimposable mirror image. This means that when you place a mirror next to the compound, the image cannot be perfectly aligned with the original compound.
- For a compound to be optically active, it must not have any plane of symmetry or point of symmetry.

2. **Analyzing the First Option - Trans Cobalt Glycerin Thrice**:
- The structure involves glycerin (NH2CH2COO-) ligands. For simplicity, we represent it as N-O.
- In the trans configuration, the ligands are arranged such that there is no plane of symmetry.
- When we take the mirror image, it results in a non-superimposable image, indicating that it is optically active.
- Therefore, if we mix equal amounts of the dextro and levo forms, we obtain a racemic mixture.

3. **Analyzing the Second Option - Ni(DMG)2**:
- DMG (Dimethylglyoxime) has two nitrogen donor atoms.
- This compound has a plane of symmetry, making it optically inactive.
- Since it cannot form dextro and levo forms, it cannot produce a racemic mixture.

4. **Analyzing the Third Option - Cis Glycerin Twice**:
- In this case, the central atom is copper, and the arrangement of ligands is such that there are two identical ligands adjacent to each other.
- This creates a plane of symmetry, making it optically inactive.
- Thus, it cannot form a racemic mixture.

5. **Analyzing the Fourth Option - Zinc Ethylene Diamine**:
- Ethylene diamine has two nitrogen donor atoms and is coordinated with glycerin.
- This compound also has a plane of symmetry, rendering it optically inactive.
- Therefore, it cannot produce a racemic mixture.

### Conclusion:
The only compound that can form a racemic mixture when mixing its mirror images in a 1:1 molar ratio is **Trans Cobalt Glycerin Thrice**.