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A man can row a boat with a speed of 10 kmph in still water. The river flows at 6 kmph. If he crosses the river from one bank to the other along the shortest possible path, time taken to cross the river of width 1 km is:
1. 1/8 h
2. 1/4 h
3. 1/2 h
4. 1 h

To a stationary man, the rain is falling on his back with a velocity v at an angle $\mathrm{\theta }$ with vertical. To make the rain-velocity perpendicular to the man, he:
(1) must move forward with a velocity vsin$\mathrm{\theta }$.
(2) must move forward with a velocity vtan$\mathrm{\theta }$.
(3) must move forward with a velocity vcos$\mathrm{\theta }$.
(4) should move in the backward direction.

Raindrops are falling with a speed v vertically downwards and a man is running on a horizontal road with speed u. The magnitude of the velocity of the raindrops with respect to the man is:
1. v - u
2. v + u
3. \(\sqrt{\text{v}^2 + \text{u}^2 \over 2}\)
4. \(\sqrt{\text{v}^2 + \text{u}^2}\)

A man standing on a road holds his umbrella at 30° with the vertical to keep the rain away. He throws the umbrella and starts running at 10 km/hr. He finds that raindrops are hitting his head vertically. The speed of raindrops with respect to the road will be
1. 10 km/hr
2. 20 km/hr
3. 30 km/hr
4. 40 km/hr

The speed of a swimmer in still water is \(20\) m/s. The speed of river water is \(10\) m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes with respect to the north is given by:
1. \(45^{\circ}\) west of north
2. \(30^{\circ}\) west of north
3. \(0^{\circ}\) west of north
4. \(60^{\circ}\) west of north

A boat crosses a river with a velocity of 8 km/h. If the resulting velocity of boat is 10 km/h, then the velocity of river water is 
(1) 4 km/h
(2) 6 km/h
(3) 8 km/h
(4) 10 km/h

A ship A is moving Westwards with a speed of 10 kmh^-1 and a ship B 100 km south of A, is moving Northwards with a speed of 10 kmh^-1. The time after which the distance between them becomes shorest is
1. 0 h
2. 5 h 
3. 5$\sqrt{2}$ h
4. 10$\sqrt{2}$ h