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(A): A man is on the northern bank of a ...

(A): A man is on the northern bank of a river. To cross the river in a shortest time he should swim due south.
(R) : Man should move opposite to the river flow to cross in shortest time.

A

Both (A) and (R) are true and (R) is the correct explanation of (A)

B

Both (A) and (R) are true and (R) is not the correct explanation of (A)

C

(A) is true but (R) is false

D

(A) is false but (R) is true

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze the assertion (A) and the reason (R) given in the problem. ### Step-by-Step Solution: 1. **Understanding the Scenario**: - A man is on the northern bank of a river and wants to cross to the southern bank. - The river flows in a certain direction (let's assume east for this explanation). 2. **Assertion Analysis**: - The assertion states that to cross the river in the shortest time, the man should swim due south. - To minimize the time taken to cross the river, the man should swim directly across the river (perpendicular to the current) rather than downstream or upstream. This is because swimming directly south allows the man to cover the width of the river in the least amount of time. 3. **Reason Analysis**: - The reason states that the man should move opposite to the river flow to cross in the shortest time. - If the man swims directly opposite to the river flow (upstream), he will not only have to swim across the river but also against the current, which would increase the time taken to reach the opposite bank. 4. **Conclusion**: - The assertion (A) is correct because swimming directly south (perpendicular to the flow) minimizes the time taken to cross the river. - The reason (R) is incorrect because moving opposite to the river flow would not result in the shortest crossing time. 5. **Final Answer**: - Therefore, the correct conclusion is that assertion (A) is true, while reason (R) is false. ### Summary: - **Assertion (A)**: True - **Reason (R)**: False
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