A : Absolut error is unitless and dimensionless.
R : All type of errors are unitless and dimensionless.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).
C. If Assertion is true statement but Reason is false, then mark (3).
D. If both Assertion and Reason are false statements, then mark (4).

Answer

To solve the question regarding the assertion and reason about absolute error and its dimensionality, we can break it down into the following steps:

### Step 1: Understand Absolute Error
Absolute error is defined as the difference between the measured value and the actual (or true) value. Mathematically, it can be expressed as:
\[ \text{Absolute Error} = \text{Measured Value} - \text{Actual Value} \]

### Step 2: Analyze the Assertion
The assertion states that "Absolute error is unitless and dimensionless." To evaluate this, we can consider an example:
- If the measured value of a length is 21 mm and the actual value is 20 mm, then:
\[ \text{Absolute Error} = 21 \, \text{mm} - 20 \, \text{mm} = 1 \, \text{mm} \]
This shows that absolute error has a unit (mm) and thus has dimensions. Therefore, the assertion is **false**.

### Step 3: Analyze the Reason
The reason states that "All types of errors are unitless and dimensionless." We need to check if this is true.
- Absolute error, as shown, has units and dimensions.
- Relative error, however, is a ratio of absolute error to a mean value and is indeed dimensionless. But not all errors are unitless. Therefore, the reason is also **false**.

### Step 4: Conclusion
Since both the assertion and the reason are false, we conclude that the correct answer to the question is that both the assertion and the reason are false statements.

### Final Answer:
Both assertion and reason are false.

---