Explanation:
The FCC lattice is a face-centered cubic lattice in which atoms are present at the corners and center of each face of the cube. The atoms present at different positions in the lattice are denoted by A, B, C, and D. The body diagonal of the cube passes through the center of the cube and connects the opposite corners of the cube.

Determination of atoms in different positions:
To determine the atoms present in different positions in the FCC lattice, we need to follow the given information:
- A atoms are present at the corners of the cube.
- B atoms are present at the center of each face of the cube.
- C atoms are present at the octahedral voids of the cube.
- D atoms are present at the tetrahedral voids of the cube.

Calculation of atoms present on the body diagonal:
The body diagonal of the cube connects the opposite corners of the cube. Let's consider the cube with edge length 'a'. The body diagonal of the cube is given by the formula:

d = a√3

Now, we need to calculate the number of atoms present on the body diagonal of the cube.

For the first option, 2A, C, 2D:
- The body diagonal passes through two opposite corners of the cube, which are occupied by two A atoms.
- The body diagonal also passes through the center of the cube, which is occupied by one C atom.
- The body diagonal passes through two tetrahedral voids of the cube, which are occupied by two D atoms.

Therefore, the number of atoms present on the body diagonal in the first option is: 2A + C + 2D.

For the second option, 2A, 2B, 2C:
- The body diagonal passes through two opposite corners of the cube, which are occupied by two A atoms.
- The body diagonal also passes through the center of two opposite faces of the cube, which are occupied by two B atoms.
- The body diagonal passes through the center of the cube, which is occupied by one C atom.

Therefore, the number of atoms present on the body diagonal in the second option is: 2A + 2B + 2C.

For the third option, 2A, 2B, D:
- The body diagonal passes through two opposite corners of the cube, which are occupied by two A atoms.
- The body diagonal also passes through the center of two opposite faces of the cube, which are occupied by two B atoms.
- The body diagonal passes through one tetrahedral void of the cube, which is occupied by one D atom.

Therefore, the number of atoms present on the body diagonal in the third option is: 2A + 2B + D.

A