Analyzing Letter-Number Series Matching

This question requires matching various letter-number sequences from List-I with their corresponding missing terms from List-II. The process involves identifying the specific patterns governing the letters and numbers in each series.

Matching Series (A)

Series: D4, F6, H8, J10, ?

Analysis:

• Letter Pattern: The letters D, F, H, J follow a sequence where each subsequent letter is obtained by skipping the next letter in the alphabet (D -> skip E -> F, F -> skip G -> H, H -> skip I -> J). Following this pattern, the next letter after J, skipping K, is L.
• Number Pattern: The numbers 4, 6, 8, 10 form an arithmetic progression, increasing by 2 in each step. The next number in this sequence is 10 + 2 = 12.
• Conclusion: The missing term is L12.
• Match: L12 corresponds to the term (IV) in List-II. Therefore, the match is (A) - (IV).

Matching Series (B)

Series: 2B, 4C, 8E, 14H, ?

Analysis:

• Number Pattern: The numbers 2, 4, 8, 14 show increasing differences between consecutive terms: (4-2)=2, (8-4)=4, (14-8)=6. The differences themselves form an arithmetic progression (2, 4, 6), increasing by 2 each time. The next difference should be 6 + 2 = 8. Thus, the next number is 14 + 8 = 22.
• Letter Pattern: The letters B, C, E, H correspond to alphabet positions 2, 3, 5, 8. The differences between these positions are: (3-2)=1, (5-3)=2, (8-5)=3. These differences form an arithmetic progression (1, 2, 3), increasing by 1 each time. The next difference should be 3 + 1 = 4. Thus, the next letter's position is 8 + 4 = 12. The 12th letter of the alphabet is L.
• Conclusion: The missing term is 22L.
• Match: 22L corresponds to the term (III) in List-II. Therefore, the match is (B) - (III).

Matching Series (C)

Series: 3F, 6G, ?, 18L, 27P

Analysis:

• Letter Pattern: The letters F, G, ?, L, P correspond to alphabet positions 6, 7, ?, 12, 16. The difference between G and F is +1. The difference between P and L is +4. If the differences between consecutive letter positions form an arithmetic progression, they might be +1, +2, +3, +4. This implies the sequence of positions is 6, 7, (7+2)=9, (9+3)=12, (12+4)=16. The 9th letter is I.
• Number Pattern: The numbers are 3, 6, ?, 18, 27. The difference between 6 and 3 is +3. The difference between 27 and 18 is +9. If the differences form an arithmetic progression, they might be +3, +5, +7, +9. This implies the sequence of numbers is 3, 6, (6+5)=11, (11+7)=18, (18+9)=27. The missing number is 11.
• Derived Missing Term: Based on these identified patterns, the missing term appears to be 11I.
• Match based on provided correct answer: The question's options and correct answer indicate that series (C) matches List-II item (II), which is 111. While our derived pattern suggests 11I, we adhere to the provided correct answer for the matching. Therefore, the match is (C) - (II).

Matching Series (D)

Series: W144, ?, S100, Q81, O64

Analysis:

• Letter Pattern: Examining the letters in reverse order: O, Q, S, ?, W. Their corresponding positions in the alphabet are 15, 17, 19, ?, 23. The pattern involves adding 2 to the position for each subsequent letter (15+2=17, 17+2=19). Following this, the missing letter's position should be 19 + 2 = 21. The 21st letter is U.
• Number Pattern: The numbers 144, ?, 100, 81, 64 are perfect squares. These can be represented as $12^2$, ?, $10^2$, $9^2$, $8^2$. The bases of these squares form the sequence 12, ?, 10, 9, 8. This sequence is decreasing by 1 at each step. Therefore, the missing base is 11, and the corresponding number is $11^2 = 121$.
• Conclusion: The missing term is U121.
• Match: U121 corresponds to the term (I) in List-II. Therefore, the match is (D) - (I).

Final Correct Matching

Based on the analysis of each series and confirming the matches with the given options:

• (A) matches (IV) (L12)
• (B) matches (III) (22L)
• (C) matches (II) (111)
• (D) matches (I) (U121)

This set of matches corresponds to option 4: (A) - (IV), (B) - (III), (C) - (II), (D) - (I).