Statement-1: The temperature dependence of resistance is usually given as `R=R_0(1+alphaDeltaT)`. The resistance of a wire changes from `100Omega to 150Omega` when its temperature is increased from `27^@C to 227^@C`. This implies that `alpha=2.5xx10^-3//^@C`.
Statement 2: `R=R_0(1+alphaDeltaT)` is valid only when the change in the temperature `DeltaT` is small and `DeltaR=(R-R_0) lt ltR_0`.

Options

A. Statement-1 is True,Statement-2 is True, Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement--1
C. Statement-1 is False, Statement-2 is True
D. Stement-1 is True, Statement-2 is False.

Explanation

To solve the problem, we need to analyze the two statements provided regarding the temperature dependence of resistance in a wire.

### Step 1: Understand the formula for resistance change
The formula given is:
\[ R = R_0(1 + \alpha \Delta T) \]
where:
- \( R \) is the resistance at the new temperature,
- \( R_0 \) is the initial resistance,
- \( \alpha \) is the temperature coefficient of resistance,
- \( \Delta T \) is the change in temperature.

### Step 2: Calculate the change in temperature
The initial temperature is \( 27^\circ C \) and the final temperature is \( 227^\circ C \). Therefore, the change in temperature (\( \Delta T \)) is:
\[ \Delta T = 227^\circ C - 27^\circ C = 200^\circ C \]

### Step 3: Calculate the change in resistance
The resistance changes from \( 100 \Omega \) to \( 150 \Omega \). Thus, the change in resistance (\( \Delta R \)) is:
\[ \Delta R = R - R_0 = 150 \Omega - 100 \Omega = 50 \Omega \]

### Step 4: Substitute values into the resistance formula
Using the formula:
\[ 150 = 100(1 + \alpha \cdot 200) \]

### Step 5: Solve for \( \alpha \)
Rearranging the equation:
\[ 1 + \alpha \cdot 200 = \frac{150}{100} \]
\[ 1 + \alpha \cdot 200 = 1.5 \]
\[ \alpha \cdot 200 = 0.5 \]
\[ \alpha = \frac{0.5}{200} = 0.0025 \, ^\circ C^{-1} = 2.5 \times 10^{-3} \, ^\circ C^{-1} \]

### Step 6: Analyze the validity of the statements
- **Statement 1**: The calculation shows that \( \alpha = 2.5 \times 10^{-3} \, ^\circ C^{-1} \) is correct based on the given resistance change. However, the formula \( R = R_0(1 + \alpha \Delta T) \) is typically valid for small changes in temperature.

- **Statement 2**: It states that the formula is valid only when \( \Delta T \) is small and \( \Delta R \) is much smaller than \( R_0 \). Given that \( \Delta T = 200^\circ C \) is not small, this statement is correct.

### Conclusion
- **Statement 1** is incorrect because the temperature change is significant, which violates the condition for the formula's validity.
- **Statement 2** is correct as it accurately describes the limitations of the formula.

Thus, the correct conclusion is that **Statement 1 is false and Statement 2 is true**.