Step-by-step Solution:

Coding — ROTATE

Step 1: Infer the rule from examples

From the examples given:

• ACTOR → A3T15R
• DATE → D1T5

The rule used: consonants remain unchanged, and vowels are replaced by their alphabetical position (for example, \(A=1,\;E=5,\;I=9,\;O=15,\;U=21\)).

Step 2: Apply the rule to ROTATE

• \(R\) — consonant → \(R\)
• \(O\) — vowel → \(15\)
• \(T\) — consonant → \(T\)
• \(A\) — vowel → \(1\)
• \(T\) — consonant → \(T\)
• \(E\) — vowel → \(5\)

Step 3: Combine

The coded form of ROTATE is: R15T1T5.

Answer: (B) R15T1T5