Which of the following numbers will not have `1`(one) at their unit's place ?
(i) `32^(2)`
(ii) `57^(2)`
(iii) `69^(2)`
(iv) `321^(2)`
(v) `265^(2)`

Answer

To determine which of the given numbers will not have `1` at their unit's place when squared, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the last digit of each number**:
- For `32`, the last digit is `2`.
- For `57`, the last digit is `7`.
- For `69`, the last digit is `9`.
- For `321`, the last digit is `1`.
- For `265`, the last digit is `5`.

2. **Square the last digit of each number**:
- **For `32`**:
- Last digit is `2`.
- Squaring `2`: \(2^2 = 4\).
- Unit's place is `4`.
- **For `57`**:
- Last digit is `7`.
- Squaring `7`: \(7^2 = 49\).
- Unit's place is `9`.
- **For `69`**:
- Last digit is `9`.
- Squaring `9`: \(9^2 = 81\).
- Unit's place is `1`.
- **For `321`**:
- Last digit is `1`.
- Squaring `1`: \(1^2 = 1\).
- Unit's place is `1`.
- **For `265`**:
- Last digit is `5`.
- Squaring `5`: \(5^2 = 25\).
- Unit's place is `5`.

3. **Determine which numbers do not have `1` at their unit's place**:
- From our calculations:
- `32^2` has unit's place `4` (not `1`).
- `57^2` has unit's place `9` (not `1`).
- `69^2` has unit's place `1` (is `1`).
- `321^2` has unit's place `1` (is `1`).
- `265^2` has unit's place `5` (not `1`).

4. **Final conclusion**:
- The numbers that do not have `1` at their unit's place when squared are:
- `32^2`
- `57^2`
- `265^2`

### Summary of Results:
The numbers that will not have `1` at their unit's place are **32^2, 57^2, and 265^2**.