Statement-I: Random errors can be positive or negative. Statement-II: Cause of random errors are uncertain.

Options

A. Statement-1 is true and statement -2 is true
B. Statement -1 is true and statement-2 is false
C. Statement-1 is false and statement -2 is true
D. Statement-1 is false and statement -2 is false

Answer

To analyze the given statements, we will break down the concepts of random errors and their characteristics step by step.

### Step 1: Understanding Random Errors
Random errors are variations in measurements that occur due to unpredictable fluctuations in the measurement process. These errors can arise from various factors such as environmental conditions, instrument limitations, or human factors.

**Hint:** Think about the nature of measurements and what can cause variations.

### Step 2: Positive and Negative Errors
When we measure a quantity, the measured value can differ from the true value. If the measured value is less than the true value, it is termed a negative error. Conversely, if the measured value is greater than the true value, it is termed a positive error.

**Hint:** Consider how measurements can deviate from the actual value in both directions.

### Step 3: Characteristics of Random Errors
Random errors can be both positive and negative. This means that in a series of measurements, some may be higher than the true value (positive errors) and some may be lower (negative errors). This variability is a hallmark of random errors.

**Hint:** Reflect on the concept of randomness and how it applies to measurement outcomes.

### Step 4: Causes of Random Errors
The causes of random errors are often unpredictable and uncertain. Unlike systematic errors, which can often be traced back to specific causes, random errors arise from a multitude of factors that cannot be easily controlled or identified.

**Hint:** Think about why some errors are difficult to pinpoint and how they differ from systematic errors.

### Step 5: Conclusion
Both statements are correct:
- **Statement-I:** Random errors can indeed be positive or negative.
- **Statement-II:** The causes of random errors are uncertain.

Thus, the answer to the question is that both statements are correct.

**Final Answer:** Both Statement-I and Statement-II are correct.

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