CUET UG 2025 — General Test Quantitative Reasoning

The word QUANTITATIVE has 12 letters: Q-U-A-N-T-I-T-A-T-I-V-E

The letters that repeat are:

• A appears 2 times
• T appears 3 times
• I appears 2 times
• All other letters (Q, U, N, V, E) appear once

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When all T's must be together, treat the three T's as one single block [TTT].

After grouping the T's together:

Original count: 12 letters

New count: 12 - 3 + 1 = 10 units

The 10 units to arrange are: [TTT], Q, U, A, N, A, I, V, I, E

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Among these 10 units:

• A repeats 2 times
• I repeats 2 times
• The [TTT] block counts as 1 unit (no repetition)

Number of arrangements $= \dfrac{10!}{2! \times 2!}$=2!×2!10!​

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$$10! = 3,628,800$$10!=3,628,800

$$2! = 2$$2!=2

Number of ways $= \dfrac{3,628,800}{2 \times 2}$=2×23,628,800​

$$= \dfrac{3,628,800}{4}$$=43,628,800​

$$= 907,200$$=907,200

Therefore, the letters of QUANTITATIVE can be arranged in 907,200 ways with all T's together.