What should come in the place of the question mark (?) in the following alphanumeric series?
\(A1X, B4P, E25J, J100F, ?\)
Step 1: Break down each term
| Term | First Letter | Number | Last Letter |
|---|---|---|---|
| A1X | A | 1 | X |
| B4P | B | 4 | P |
| E25J | E | 25 | J |
| J100F | J | 100 | F |
Alphabet positions:
Pattern: Differences increase by 2 (1, 3, 5), so next difference should be +7
Next letter position: 10 + 7 = 17 → Q
Sequence inside squares:
Base numbers: 1, 2, 5, 10
Differences: +1, +3, +5 (increasing by 2), so next difference should be +7
Next base number: 10 + 7 = 17 → 17² = 289
Alphabet positions:
Pattern: Differences decrease by 2 (-8, -6, -4), so next difference should be -2
Next letter position: 6 - 2 = 4 → D
Next term: Q289D
The correct option is (3) Q289D.
Match List-I with List-II
| List-I | List-II |
|---|---|
| (A) \(^{8}P_{3} - ^{10}C_{3}\) | (I) 6 |
| (B) \(^{8}P_{5}\) | (II) 21 |
| (C) \(^{n}P_{4} = 360,\) then find \(n\). | (III) 216 |
| (D) \(^{n}C_{2} = 210,\) find \(n\). | (IV) 6720 |
Choose the correct answer from the options given below:
What comes next in the series?
\(2, 6, 12, 20, 30, \ ?\)
Which letter replaces the question mark? A, D, G, J, M, ?