NIMCET 2025 — Mathematics PYQ

To form a $3$-digit number, we need to fill three places: the Hundreds place, the Tens place, and the Units place.

$$\text{[ Hundreds ] }\text{[ Tens ] }\text{[ Units ]}$$

We are given a pool of $5$ available digits: $\{0,1,2,3,5\}$. Repetition of digits is allowed.

Step 1: Fill the Hundreds Place

A standard $3$-digit number cannot start with the digit $0$ (otherwise, it becomes a $2$-digit number).

Therefore, the hundreds place can only be filled by the non-zero digits: $1,2,3,$ or $5$.

• Number of ways to fill the hundreds place = $4$ ways (any digit except $0$).

Step 2: Fill the Tens Place

Since repetition of digits is allowed, all $5$ available digits (including $0$) can be used to fill the tens place.

• Number of ways to fill the tens place = $5$ ways.

Step 3: Fill the Units Place

Similarly, because repetition is permitted, any of the $5$ available digits can be chosen for the units place.

• Number of ways to fill the units place = $5$ ways.

Step 4: Calculate the Total Number of $3$-Digit Numbers

According to the fundamental multiplication principle of counting, the total number of ways to complete the task is the product of the number of ways to fill each place individually:

$$\text{Total 3-digit numbers}=(\text{Ways for Hundreds})\times (\text{Ways for Tens})\times (\text{Ways for Units})$$

$$\text{Total 3-digit numbers}=4\times 5\times 5$$

$$\text{Total 3-digit numbers}=100$$

Final Answer

The correct option is (A).

The total number of three-digit numbers that can be formed is 100.