STATEMENT-1: A man can cross river of width `d` in minimum time `t`. On increasing river velocity, minimum time to cross the river by man will remain uncharged.
STATEMENT-2: Velocity of river is perpendicular to width of river. So time to cross the river is independent of velcoity of river.

Options

A. Statement -1 is True, Statement-2 is Ture, Statement-2 is a correct explanantion for Statement-1.
B. Statement-1 is Ture, Statement-2 is Ture, Statement-2 is Not a correct explanantion for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Answer

To solve the problem, we need to analyze the two statements provided and determine their validity based on the principles of kinematics.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have a river of width \( d \).
- A man can cross this river in a minimum time \( t \).
- We need to evaluate the effect of increasing the river's velocity on the time taken to cross.

2. **Analyzing Statement 1**:
- The statement claims that if the river's velocity increases, the minimum time \( t \) to cross the river will remain unchanged.
- To analyze this, we need to consider the direction of the river's flow and the man's crossing.

3. **Analyzing Statement 2**:
- This statement asserts that the velocity of the river is perpendicular to the width of the river.
- Since the river's velocity is perpendicular, it does not affect the time taken to cross the river.

4. **Determining the Time to Cross the River**:
- The time \( t \) to cross the river can be calculated using the formula:
\[ t = \frac{d}{v_m} \]
where \( v_m \) is the velocity of the man crossing the river.
- The river's velocity \( v_r \) does not enter this equation because it is perpendicular to the direction of crossing.

5. **Conclusion on Statement 1**:
- Since the time to cross the river depends only on the width \( d \) and the man's velocity \( v_m \), increasing the river's velocity \( v_r \) does not change the minimum time \( t \).
- Therefore, Statement 1 is **true**.

6. **Conclusion on Statement 2**:
- Since the river's velocity is indeed perpendicular to the width of the river, it confirms that the time to cross is independent of the river's velocity.
- Therefore, Statement 2 is also **true**.

7. **Final Evaluation**:
- Both statements are true, and Statement 2 correctly explains Statement 1.
- Thus, the answer is **A**: Both statements are true, and Statement 2 is the correct explanation for Statement 1.