A cuboid of dimensions 7 cm × 5 cm × 3 cm is painted red, green and blue colour on each pair of opposite faces of dimensions 7 cm × 5 cm , 5 cm × 3 cm , 7 cm × 3 cm respectively. Then the cuboid is cut and separated into various cubes each of side length 1 cm . Which of the following statements is/are correct? 1. There are exactly 15 small cubes with no paint on any face. 2. There are exactly 6 small cubes with exactly two faces, one painted with blue and the other with green. Select the correct answer using the code given below:

The cuboid has dimensions 7 cm x 5 cm x 3 cm. It is cut into 1 cm x 1 cm x 1 cm cubes. Total number of small cubes = 7 * 5 * 3 = 105.

Painting scheme:

1. 7 cm x 5 cm faces (top and bottom) are painted Red.
2. 5 cm x 3 cm faces (left and right sides) are painted Green.
3. 7 cm x 3 cm faces (front and back) are painted Blue.

Let's analyze each statement:

Statement 1: "There are exactly 15 small cubes with no paint on any face." Cubes with no paint are the inner cubes, which are not exposed to any surface. To find these, we effectively remove one layer of cubes from each side (length, width, and height). Number of unpainted cubes = (Length - 2) * (Width - 2) * (Height - 2) = (7 - 2) * (5 - 2) * (3 - 2) = 5 * 3 * 1 = 15 cubes. So, Statement 1 is correct.

Statement 2: "There are exactly 6 small cubes with exactly two faces, one painted with blue and the other with green." Cubes with exactly two faces painted are located along the edges of the cuboid, excluding the corner cubes. We need to find cubes painted with Blue and Green. Blue faces are the 7 cm x 3 cm faces (front and back). Green faces are the 5 cm x 3 cm faces (left and right sides). The edges where a Blue face meets a Green face are the vertical edges of the cuboid. These edges have a length of 3 cm. There are 4 such vertical edges in a cuboid. For an edge of length 'n' cm, the number of cubes with exactly two faces painted (excluding the two corner cubes at its ends) is (n - 2). In this case, for these edges, n = 3 cm. Number of cubes with Blue and Green paint on each such edge = (3 - 2) = 1 cube. Since there are 4 such edges, the total number of cubes with exactly two faces (one blue, one green) = 4 edges * 1 cube/edge = 4 cubes. The statement says there are exactly 6 such cubes. Our calculation shows 4. So, Statement 2 is incorrect.

Based on the analysis, only Statement 1 is correct.

The final answer is A