The correct answer is b: BIDNHTSSX.
To solve this problem, we need to understand the pattern used to encode the word 'MATHEMATICS' into 'LBSIDNZUHDR'. Let's break it down step by step:
     ● Step 1: Analyze the Pattern  
       We need to compare each letter of 'MATHEMATICS' with 'LBSIDNZUHDR' to find the pattern or rule applied.
           ○ M -> L
           ○ A -> B
           ○ T -> S
           ○ H -> I
           ○ E -> D
           ○ M -> N
           ○ A -> Z
           ○ T -> U
           ○ I -> H
           ○ C -> D
           ○ S -> R
     ● Step 2: Identify the Transformation  
       By observing the transformation, we can see that each letter in 'MATHEMATICS' is shifted by a certain number of positions in the alphabet to get the corresponding letter in 'LBSIDNZUHDR'. Specifically:
           ○ M (13) -> L (12): Shift of -1
           ○ A (1) -> B (2): Shift of +1
           ○ T (20) -> S (19): Shift of -1
           ○ H (8) -> I (9): Shift of +1
           ○ E (5) -> D (4): Shift of -1
           ○ M (13) -> N (14): Shift of +1
           ○ A (1) -> Z (26): Shift of -1
           ○ T (20) -> U (21): Shift of +1
           ○ I (9) -> H (8): Shift of -1
           ○ C (3) -> D (4): Shift of +1
           ○ S (19) -> R (18): Shift of -1
       The pattern alternates between shifting by -1 and +1.
     ● Step 3: Apply the Pattern to 'CHEMISTRY'  
       Now, apply the same pattern to encode 'CHEMISTRY':
           ○ C (3) -> B (2): Shift of -1
           ○ H (8) -> I (9): Shift of +1
           ○ E (5) -> D (4): Shift of -1
           ○ M (13) -> N (14): Shift of +1
           ○ I (9) -> H (8): Shift of -1
           ○ S (19) -> T (20): Shift of +1
           ○ T (20) -> S (19): Shift of -1
           ○ R (18) -> S (19): Shift of +1
           ○ Y (25) -> X (24): Shift of -1
       Therefore, 'CHEMISTRY' is encoded as 'BIDNHTSSX'.
     Thus, the correct answer is b: BIDNHTSSX.