NIMCET 2008 — Reasoning PYQ

1. Understand the Rule

To get the next term, you "read out loud" the digits of the current term, counting how many times each digit appears in a row.

• Row 1: $1$ (One '1') $\to$ Row 2: $11$

• Row 2: $11$ (Two '1's) $\to$ Row 3: $21$

• Row 3: $21$ (One '2', One '1') $\to$ Row 4: $1211$

• Row 4: $1211$ (One '1', One '2', Two '1's) $\to$ Row 5: $111221$

2. Finding the 10th Number

The 9th number provided is: $31131211131221$

Let's read it:

• Three '1's ($13$) — Wait, let's re-read carefully from the left:

• One '3' ($13$)

• Two '1's ($21$)

• One '3' ($13$)

• One '1' ($11$)

• One '2' ($12$)

• Three '1's ($31$)

• One '3' ($13$)

• One '1' ($11$)

• Two '2's ($22$)

• One '1' ($11$)

Combining these: $13211311123113112211$

3. Finding the 11th Number

Now we read the 10th number: $13211311123113112211$

• One '1' ($11$)

• One '3' ($13$)

• One '2' ($12$)

• Two '1's ($21$)

• One '3' ($13$)

• Three '1's ($31$)

• One '2' ($12$)

• One '3' ($13$)

• Two '1's ($21$)

• One '3' ($13$)

• Two '1's ($21$)

• Two '2's ($22$)

• Two '1's ($21$)

Combining these: $11131221133112132113212221$

Final Answer:

The next two numbers match the pattern found in Option (d).

Correct Option: (d)