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 analyze the statements given in the question, we need to evaluate the assertion (A) and the reason (R) separately.

### Step-by-Step Solution:

**Step 1: Understand Absolute Error**
- Absolute error is defined as the difference between the measured value and the true value (or original value). Mathematically, it can be expressed as:
\[ \text{Absolute Error} = | \text{Measured Value} - \text{True Value} | \]
- Since absolute error is derived from the measured values, it carries the same units and dimensions as the measured quantity.

**Step 2: Evaluate Assertion (A)**
- The assertion states that "Absolute error is unitless and dimensionless."
- Since absolute error has the same dimensions and units as the measured value, this assertion is **incorrect**. Absolute error is not unitless or dimensionless; it has the same units as the measurement.

**Step 3: Understand Other Types of Errors**
- Other types of errors include relative error and percentage error.
- Relative error is defined as the absolute error divided by the true value:
\[ \text{Relative Error} = \frac{\text{Absolute Error}}{\text{True Value}} \]
- Since this is a ratio of two quantities with the same dimensions, the units cancel out, making relative error unitless and dimensionless.

**Step 4: Evaluate Reason (R)**
- The reason states that "All types of errors are unitless and dimensionless."
- This statement is also **incorrect** because, while relative error and percentage error are unitless, absolute error is not. Therefore, the reason does not hold true.

**Conclusion:**
- Both the assertion (A) and the reason (R) are incorrect.
- Thus, the correct answer is that both statements are false.