STATEMENT-1 `:` As the drift velocity increases, the current flowing through the conductor decreases,
and
STATEMENT-2 `:` The current flowing through a conductor is directly proportional to drift velocity.

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 True, Statement-2 is True
D. Statement-1 is False , Statement-2 is True

Answer

To analyze the statements provided in the question, we can break down the concepts of drift velocity and current in a conductor step by step.

### Step 1: Understand the relationship between current and drift velocity
The current \( I \) flowing through a conductor is given by the formula:
\[ I = N \cdot A \cdot e \cdot v_d \]
where:
- \( N \) = number of charge carriers per unit volume (free electrons)
- \( A \) = cross-sectional area of the conductor
- \( e \) = charge of an electron (approximately \( 1.6 \times 10^{-19} \) coulombs)
- \( v_d \) = drift velocity of the charge carriers

### Step 2: Analyze Statement 1
Statement 1 claims that "as the drift velocity increases, the current flowing through the conductor decreases."

From the equation, we see that if \( v_d \) (drift velocity) increases, then \( I \) (current) also increases, assuming \( N \), \( A \), and \( e \) remain constant. Therefore, Statement 1 is **false**.

### Step 3: Analyze Statement 2
Statement 2 states that "the current flowing through a conductor is directly proportional to drift velocity."

From the same equation, we can see that current \( I \) is directly proportional to \( v_d \). Thus, if \( v_d \) increases, \( I \) also increases, confirming that Statement 2 is **true**.

### Conclusion
- **Statement 1**: False
- **Statement 2**: True

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

### Final Answer
- Statement 1 is false.
- Statement 2 is true.