The following statement(s) is (are) correct:

Options

A. A plot of log `k_(p)` versus 1/T is linear
B. A plot of log [X] versus time is linear for a first-order reaction, `X rarr P`
C. A plot of P versus 1/T is linear at constant volume
D. A plot of P versus 1/V is linear at constant

Explanation

To analyze the correctness of the statements provided in the question, we will evaluate each option step by step.

### Step 1: Evaluate Option 1
**Statement**: A plot of log Kp versus 1/T is linear.

**Explanation**: According to the Arrhenius equation, the rate constant (K) can be expressed as:
\[ K = A e^{-\frac{E_a}{RT}} \]
Taking the logarithm of both sides gives:
\[ \log K = \log A - \frac{E_a}{2.303RT} \]
Rearranging this, we can express it as:
\[ \log K = \log A - \frac{E_a}{2.303R} \cdot \frac{1}{T} \]
This is in the form of \( y = mx + c \), where:
- \( y = \log K \)
- \( m = -\frac{E_a}{2.303R} \)
- \( x = \frac{1}{T} \)
Thus, the plot of log Kp versus 1/T is indeed linear.

**Conclusion**: Option 1 is correct.

### Step 2: Evaluate Option 2
**Statement**: A plot of log concentration X versus time is linear for a first-order reaction X gives product.

**Explanation**: For a first-order reaction, the rate law can be expressed as:
\[ Kt = \log \frac{[X_0]}{[X]} \]
Rearranging gives:
\[ \log [X] = \log [X_0] - Kt \]
This can be rewritten as:
\[ \log [X] = \log [X_0] - Kt \]
This is again in the form of \( y = mx + c \), where:
- \( y = \log [X] \)
- \( m = -K \)
- \( x = t \)
Thus, the plot of log concentration X versus time is linear.

**Conclusion**: Option 2 is correct.

### Step 3: Evaluate Option 3
**Statement**: A plot of P versus 1/T is linear at constant volume.

**Explanation**: According to the ideal gas law, \( PV = nRT \). At constant volume, pressure (P) is directly proportional to temperature (T), which means:
\[ P \propto T \]
If we express this in terms of 1/T, we find that:
\[ P = \text{constant} \cdot T \]
This does not yield a linear relationship with respect to 1/T; instead, it results in a hyperbolic relationship. Therefore, the statement is incorrect.

**Conclusion**: Option 3 is not correct.

### Step 4: Evaluate Option 4
**Statement**: A plot of P versus 1/V is linear at constant temperature.

**Explanation**: At constant temperature, according to Boyle's law, pressure (P) is inversely proportional to volume (V):
\[ PV = \text{constant} \]
This can be rearranged to:
\[ P = \frac{\text{constant}}{V} \]
If we plot P versus 1/V, we get a linear relationship because:
\[ P = k \cdot \frac{1}{V} \]
where k is a constant. Thus, this statement is correct.

**Conclusion**: Option 4 is correct.

### Final Conclusion
The correct options are 1, 2, and 4.