A boat is moving with velocity of $3\hat{i}+4\hat{j}$ in river and water is moving with a velocity of $-3\hat{i}-4\hat{j}$ with respect to ground. Relative velocity of boat with respect to water is: 

1. $-6\hat{i}-8\hat{j}$

2. $6\hat{i}+8\hat{j}$

3. $8\hat{j}$

4. $6\hat{i}$

A boat moves with a speed of 5 km/h relative to water in a river flowing with a speed of 3 km/h and having a width of 1 km. The minimum time taken around a round trip(returning to the initial point) is:

1. 5 min

2. 60 min

3. 20 min

4. 30 min

A river is flowing from W to E with a speed of 5 m/min. A man can swim in still water with a velocity 10 m/min. In which direction should the man swim so as to take the shortest possible path to go to the south. 

1. 30° with downstream

2. 60° with downstream

3. 120° with downstream

4. South

A train is moving towards the east and a car is along the north at the same speed. The observed direction of the car to the passenger on the train is:
1. East-north direction
2. West-north direction
3. South-east direction
4. None of these

A ball P is dropped vertically and another ball Q is thrown horizontally from the  same height and at the same time. If air resistance is neglected, then 

1. Ball P reaches the ground first

2. Ball Q reaches the ground first

3. Both reach the ground at the same time

4. The respective masses of the two balls will decide the time

A frictionless wire $AB$ is fixed on a sphere of radius $R$. A very small spherical ball slips on this wire. The time taken by this ball to slip from $A$ to $B$ is:
          
1. $\frac{2 \sqrt{g R}}{g \cos \theta}$
2. $2 \sqrt{g R} . \frac{\cos \theta}{g}$
3. $2 \sqrt{\frac{R}{g}}$
4. $\frac{g R}{\sqrt{g\cos \theta}}$

A body is slipping from an inclined plane of height $h$ and length $l$. If the angle of inclination is $\theta$, the time taken by the body to come from the top to the bottom of this inclined plane is:
1. $\sqrt{\frac{2 h}{g}}$
2. $\sqrt{\frac{2 l}{g}}$
3. $\frac{1}{\sin \theta} \sqrt{\frac{2 h}{g}}$
4. $\sin \theta \sqrt{\frac{2 h}{g}}$

An airplane is moving with a velocity $u.$ It drops a packet from a height $h.$ The time $t$ taken by the packet to reach the ground will be:
1. $\sqrt{\frac{2 g}{h}}$
2. $\sqrt{\frac{2 u}{g}}$
3. $\sqrt{\frac{h}{2 g}}$
4. $\sqrt{\frac{2 h}{g}}$

An aeroplane is moving with horizontal velocity u at height h. The velocity of a packet dropped from it on the earth's surface will be (g is acceleration due to gravity) 

1. $\sqrt{u^2+2gh}$

2. $\sqrt{2gh}$

3. 2 gh

4. $\sqrt{u^2-2gh}$ 

A bullet is fired with a speed of $1000m/\sec$ in order to hit a target 100 m away. If $g=10m/s^2$, the gun should be aimed:

1. Directly towards the target

2. 5 cm above the target

3. 10 cm above the target

4. 15 cm above the target