Study the following information carefully and answer the questions given below.
Seven boxes- A, B, C, D, E, F and G are kept one above another in a single stack but not necessarily in the same order.
Only two boxes are kept between box A and box F. Box B is kept two boxes above box F. Only three boxes are kept between box B and box G. The number of boxes kept above box G is one more than the number of boxes kept below box C. Box D is kept two boxes below box C. Box E does not kept below box D.

Which of the following statement(s) is/are not true?
I. No box is kept below box A
II. Box B is kept below box G
III. Even number of boxes are kept below box B

To determine the correct arrangement of the boxes, let us analyze the clues step-by-step. Let the positions of the seven boxes be numbered from 7 (topmost) to 1 (bottommost).

Step 1: Analyze the relationship between A, F, and B.
- Only two boxes are kept between box A and box F. This means their positions differ by 3.
- Box B is kept two boxes above box F. This means B is at position (F + 2).
From these clues, we have two main cases for the relative positions:
Case 1: A is above F (A is at F + 3). The order from top to bottom would be: A (F + 3), B (F + 2), Empty (F + 1), F (F).
Case 2: A is below F (A is at F - 3). The order from top to bottom would be: B (F + 2), Empty (F + 1), F (F), Empty (F - 1), Empty (F - 2), A (F - 3). This setup spans 6 consecutive positions.

Step 2: Place Box G using the relation with Box B.
- Only three boxes are kept between box B and box G. This means G is either at (B + 4) or (B - 4).
Let us test Case 2, which occupies 6 positions. The top box B must be at position 7 or 6.
- If B is at position 7: G must be at 7 - 4 = 3. Let's write the arrangement:
7: B, 6: Empty, 5: F, 4: Empty, 3: G, 2: A, 1: Empty.
Now apply: "The number of boxes kept above box G (position 3) is one more than the number of boxes kept below box C."
There are 4 boxes above G (at position 3). Thus, there must be 4 - 1 = 3 boxes below C, placing C at position 4. But if C is at 4, then box D (kept two boxes below C) would be at 2, which is already occupied by A. So this subcase is invalid.
- If B is at position 6: G must be at 6 - 4 = 2. Let's write the arrangement:
7: Empty, 6: B, 5: Empty, 4: F, 3: Empty, 2: G, 1: A.
Now, the number of boxes above G (position 2) is 5. Therefore, the number of boxes below C must be 5 - 1 = 4. This means C is at position 5.
Now place D: Box D is two boxes below C (position 5 - 2 = 3).
The arrangement now becomes:
7: Empty, 6: B, 5: C, 4: F, 3: D, 2: G, 1: A.

Step 3: Place Box E.
- Box E is not kept below box D. Since D is at position 3, E must be in the only remaining empty slot at the top, which is position 7 (above D).
This gives us the final valid arrangement from top to bottom:
7: E
6: B
5: C
4: F
3: D
2: G
1: A

Step 4: Verify the statements.
- Statement I: "No box is kept below box A." Since A is at the bottommost position (1), this statement is True.
- Statement II: "Box B is kept below box G." Box B is at position 6 and G is at position 2, so B is kept above G. This statement is Not True.
- Statement III: "Even number of boxes are kept below box B." The boxes below B are C, F, D, G, and A (5 boxes). Since 5 is an odd number, this statement is Not True.

Therefore, statements II and III are not true.