CUET UG 2025 — General Test Quantitative Reasoning

The word OPERATE has 7 letters:

O - P - E - R - A - T - E

---

Counting the frequency of each letter:

• O → 1 time
• P → 1 time
• E → 2 times
• R → 1 time
• A → 1 time
• T → 1 time

The letter E appears twice, while all other letters appear once.

---

For permutations with repetition, the formula is:

$$\text{Number of arrangements} = \frac{n!}{r_1! \times r_2! \times ...}$$Number of arrangements=r1​!×r2​!×...n!​

where $n$n is the total number of letters and $r_1, r_2, ...$r1​,r2​,... are the frequencies of repeated letters.

---

For OPERATE:

$$\text{Number of arrangements} = \frac{7!}{2!}$$Number of arrangements=2!7!​

$$= \frac{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1}$$=2×17×6×5×4×3×2×1​

$$= \frac{5040}{2}$$=25040​

$$= 2520$$=2520

Therefore, the letters of the word OPERATE can be arranged in 2520 different ways.