NIMCET 2025 — Mathematics PYQ

Step 1: Analyze the Given Word

The given word is BANGLORE.

• Total number of letters = $8$

• The letters are: B, A, N, G, L, O, R, E (All letters are distinct).

Step 2: Apply the Constraint (Form the Block)

The problem states that the specific string "ANGLE" must always appear together exactly in that order.

Let us bundle the letters A, N, G, L, E together into a single block/unit:

$$\text{Block}=[\text{ANGLE}]$$

Now, list the remaining letters of the word BANGLORE:

• B

• O

• R

Step 3: Count the Total Number of Units to Arrange

We now need to arrange the following units:

1. The single block $[\text{ANGLE}]$

2. The letter B

3. The letter O

4. The letter R

$$\text{Total number of units to arrange}=1+1+1+1=4\text{ units}$$

Step 4: Calculate the Permutations

• External Arrangement: The $4$ distinct units can be arranged among themselves in $4!$ ways.

  $$4!=4\times 3\times 2\times 1=24\text{ ways}$$

• Internal Arrangement: Because the question specifies that the string "ANGLE" must appear as a specific word/sequence, the internal order of these letters is fixed to exactly $1$ way (it cannot be shuffled into "NAGLE", "ELGNA", etc.).

Step 5: Find the Final Answer

$$\text{Total number of valid permutations}=4!\times 1$$

$$\text{Total Permutations}=24$$

Correct Option: (A) $24$