Roll Number Rule for Batch Assignment

The problem describes a specific coding rule used to assign students to different batches based on their roll numbers. The rule is straightforward:

• If a roll number ends with an even digit (0, 2, 4, 6, 8), the student belongs to Batch 1.
• If a roll number ends with an odd digit (1, 3, 5, 7, 9), the student belongs to Batch 2.

We need to identify the correct pair of roll numbers corresponding to Batch 1 and Batch 2 based on this rule.

Applying the Coding Rule to Roll Numbers

Let's analyze the roll numbers provided in the options to see which pair correctly follows the rule.

Analyzing the Correct Option Pair

The identified correct pair is $E2894$ and $F3917$.

• Roll Number $E2894$:
  • The last digit is $4$.
  • $4$ is an even digit (since $4 \pmod{2} = 0$).
  • According to the rule, roll numbers ending in an even digit belong to Batch 1.
• Roll Number $F3917$:
  • The last digit is $7$.
  • $7$ is an odd digit (since $7 \pmod{2} = 1$).
  • According to the rule, roll numbers ending in an odd digit belong to Batch 2.

Therefore, the pair $E2894$ (Batch 1) and $F3917$ (Batch 2) perfectly matches the given coding rule.

Checking Other Options

Let's quickly verify why the other options are incorrect:

• Option 1: $D1400$ and $Cc3882$
  • $D1400$ ends in $0$ (even) - Batch 1.
  • $Cc3882$ ends in $2$ (even) - Batch 1.
  • This pair assigns both to Batch 1, which is incorrect.
• Option 3: $A3841$ and $B4537$
  • $A3841$ ends in $1$ (odd) - Batch 2.
  • $B4537$ ends in $7$ (odd) - Batch 2.
  • This pair assigns both to Batch 2, which is incorrect.
• Option 4: $G8763$ and $F4711$
  • $G8763$ ends in $3$ (odd) - Batch 2.
  • $F4711$ ends in $1$ (odd) - Batch 2.
  • This pair assigns both to Batch 2, which is incorrect.

Conclusion on Roll Number Classification

The coding rule clearly separates roll numbers into two batches based on the parity (even or odd) of their last digit. The correct pair representing this rule is $E2894$ for Batch 1 and $F3917$ for Batch 2.