Three views of a cube following a particular motion are given below:

Correct Option (1)

: H

To determine the face opposite to A, we can utilize the principle of common faces in different views of a cube.

• Consider View 1 (showing A, K, B) and View 2 (showing H, K, M). The common face between these two views is K.
• By rotating the cube clockwise from the common face K, the sequence of faces in View 1 is K → B → A.
• Similarly, by rotating clockwise from K in View 2, the sequence of faces is K → M → H.
• Comparing these sequences, it is deduced that B is opposite M, and A is opposite H.
• As an alternative verification, consider View 1 (showing A, K, B) and View 3 (showing H, P, B). The common face is B.
• Rotating clockwise from B in View 1 yields the sequence B → A → K.
• Rotating clockwise from B in View 3 yields the sequence B → H → P.
• Comparing these sequences confirms that A is opposite H, and K is opposite P.

Both comparisons consistently indicate that H is the face opposite to A.

Incorrect Options:

The following options are incorrect for the reasons stated:

• P: Based on the comparison of View 1 and View 3, K is opposite P. Therefore, P cannot be opposite A.
• B: From View 1, B is shown as an adjacent face to A. Faces that are adjacent cannot be opposite to each other. Hence, B cannot be opposite A.
• M: From the comparison of View 1 and View 2, B is opposite M. Therefore, M cannot be opposite A.