✅ The given code 'TRAIN' to 'UTDMS' follows a specific letter shifting pattern.

The first letter 'T' (20) shifts +1 to 'U' (21), the second letter 'R' (18) shifts +2 to 'T' (20), the third letter 'A' (1) shifts +3 to 'D' (4), the fourth letter 'I' (9) shifts +4 to 'M' (13), and the fifth letter 'N' (14) shifts +5 to 'S' (19).

Applying this progressive forward shift pattern (+1, +2, +3, +4, +5) to 'PLANT':

'P' (16) + 1 = 'Q' (17), 'L' (12) + 2 = 'N' (14), 'A' (1) + 3 = 'D' (4), 'N' (14) + 4 = 'R' (18), 'T' (20) + 5 = 'Y' (25).

Therefore, 'PLANT' is coded as 'QNDRY'.

❌ Option B follows a different or incorrect shifting pattern.

❌ Option C incorrectly shifts the first letter and does not match the established pattern.

❌ Option D does not follow the identified progressive shifting rule.

✅ The coding pattern involves an alternating shift in the letter positions: +1, -2, +3, -4, and so on.

For `JUMP` to `KSPL`:

• J (+1) = K
• U (-2) = S
• M (+3) = P
• P (-4) = L

Applying this pattern to `SWING`:

• S (+1) = T
• W (-2) = U
• I (+3) = L
• N (-4) = J
• G (+5) = L

Therefore, `SWING` is coded as `TULJL`.

❌ Option B is incorrect because the last letter 'G' shifted by +5 should be 'L', not 'K'.

❌ Option C is incorrect because the second letter 'W' shifted by -2 should be 'U', not 'V'.

❌ Option D is incorrect as it does not follow the established alternating +1, -2, +3, -4, +5 pattern for any of its letters.

✅ The pattern applied is an alternating shift: the 1st letter shifts +1, the 2nd letter -2, the 3rd letter +3, the 4th letter -4, and so on, with the shift value increasing by 1 for each subsequent letter while alternating direction.

For "CODE":
C (+1) = D
O (-2) = M
D (+3) = G
E (-4) = A
Thus, CODE becomes DMGA.

Applying this pattern to "PRACTICE":
P (+1) = Q
R (-2) = P
A (+3) = D
C (-4) = Y (C=3, 3-4 = -1, which wraps around to 25th letter, Y)
T (+5) = Y
I (-6) = C
C (+7) = J
E (-8) = W (E=5, 5-8 = -3, which wraps around to 23rd letter, W)

Therefore, "PRACTICE" is coded as "QPDYYCJW".

❌ Options B, C, and D do not follow this specific alternating and increasing shift pattern, resulting in different coded words.

✅ The given coding for 'MATH' to 'NCWL' follows an increasing forward shift pattern for each letter.

✅ M (+1) = N, A (+2) = C, T (+3) = W, H (+4) = L.

✅ Applying this +1, +2, +3, +4, +5, +6, +7 pattern to 'SCIENCE': S (+1) = T, C (+2) = E, I (+3) = L, E (+4) = I, N (+5) = S, C (+6) = I, E (+7) = L.

✅ Thus, 'SCIENCE' is coded as 'TELISIL'.

❌ Option B (TDJFOEF) would be obtained if a consistent +1 shift was applied to all letters, which contradicts the established pattern.

❌ Option C (UEKGPFG) would result from a consistent +2 shift for all letters, which is not the given rule.

❌ Option D (TELIRIK) contains errors in the application of the variable shift pattern, specifically for the 5th and 7th letters (N+4=R instead of N+5=S, and E+6=K instead of E+7=L).

✅ First, let's decode the pattern: For 'TRAIN' to 'UTDMS', each letter is shifted forward by a number corresponding to its position in the word.

✅ T (1st letter) shifts +1 to U; R (2nd) shifts +2 to T; A (3rd) shifts +3 to D; I (4th) shifts +4 to M; N (5th) shifts +5 to S.

✅ Applying this rule to 'CLOUDY': C (1st) shifts +1 to D; L (2nd) shifts +2 to N; O (3rd) shifts +3 to R; U (4th) shifts +4 to Y; D (5th) shifts +5 to I.

✅ Finally, Y (6th) shifts +6. Counting Y -> Z (1) -> A (2) -> B (3) -> C (4) -> D (5) -> E (6), resulting in E.

✅ Therefore, 'CLOUDY' is coded as 'DNRYIE'.

❌ Options B, C, and D represent incorrect fixed shifts for all letters or miscalculations, especially with the wrap-around for 'Y'.