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From a tower height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is :
1. $2\mathrm{gH}={\mathrm{nu}}^2\left(\mathrm{n}-2\right)$
2. $\mathrm{gH}=\left(\mathrm{n}-2\right){\mathrm{u}}^2$
3. $2\mathrm{gH}={\mathrm{n}}^2{\mathrm{u}}^2$
4. $\mathrm{gH}={\left(\mathrm{n}-2\right)}^2{\mathrm{u}}^2$

A person climbs up a stalled escalator in 60 s . If standing on the same but escalator running with constant velocity he takes 40 s. How much time is taken by the person to walk up the moving escalator?
1. 37 s
2. 27 s
3. 24 s
4. 45 s
 

A bullet loses ${\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{n}$}\right.\right)}^{th}$ of its velocity passing through one plank. The number of such planks that are required to stop the bullet can be:
1. $\frac{n^2}{2n-1}$
2. $\frac{2n^2}{n-1}$
3. infinite
4. n 

Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of 10 m/s and 40 m/s respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first?
(Assume stones do not rebound after hitting the ground and neglect air resistance, take $\mathrm{g}=10 \mathrm{m}/{\mathrm{s}}^2$).
(The figures are schematic and not drawn to scale)
1. 
2. 
3. 
4. 

Which of the following option correctly describes the variation of the speed v and acceleration 'a' of a point mass falling vertically in a viscous medium that applies a force f=-kv, where k is constant, on the body?
(Graph are schematic and not drawn to scale).
1. 
2. 
3. 
4. 

A body is thrown vertically upwards. Which of the following graphs correctly represent the velocity vs time?
1. 
2. 
3. 
4. 

Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity?
1. 
2. 
3. 
4. 

A car is standing 200 m behind a bus, which is also at rest. The two starts moving at the same instant but with different forward accelerations. The bus has acceleration $2 \mathrm{m}/{\mathrm{s}}^2$ and the car has acceleration $4 \mathrm{m}/{\mathrm{s}}^2$. The car will catch up with the bus after a time of :
1. $\sqrt{110}$ s
2. $\sqrt{120}$ s
3. $10\sqrt{2}$ s
4. 15 s

All the graph below are intended to represent the same motion. One of them does it incorrectly. Pick it up
1. 
2. 
3. 
4. 

The velocity time graphs of a car and a scooter are shown in figure. The difference between the distance travelled by the car and the scooter in 15 s and the time at which the car will catch up with the scooter are respectively:

1. 112.5 m and 22.5 s
2. 337.5 m and 25 s
3. 112.5 m and 15 s
4. 22.5 m and 10 s
 

An, automobile travelling at 40 km/h, can be stopped at a distance of 40 m by applying brakes. If the same automobile is travelling at 80 km/h the minimum stopping distance, in meters, is (assume no skidding).
1. 75 m
2. 100 m
3. 150 m
4. 160 m
 

The velocity displacement graph of a particle moving along a straight line is shown 

The most suitable acceleration-displacement graph will be
1. 
2. 
3. 
4. 

Two identical discs of the same radius R are rotating about their axes in opposite direction with the same constant regular speed $\omega$. The discs are in the same horizontal plane. At time t=0, the points P and Q are facing each other as shown in the figure. the relative speed between the two points P and Q is $v_r$. In one timeperiod (T) of rotation of the discs, $v_r$ as a function of time is best represented by

1. 
2. 
3. 
4. 

A ball is realeased from the top of the tower of height h meters. It takes T seconds to reach the ground. What is the position of the ball at $\frac{T}{3}$ seconds
1. $\frac{8h}{9}$ meters from the ground
2. $\frac{7h}{9}$ meters from the ground
3. $\frac{2h}{9}$ meters from the ground
4. $\frac{17h}{18}$ meters from the ground

A particle located at x=0 at time t=0, starts moving along with the positive x-direction with a velocity 'v' that varies $v=\alpha \sqrt{x}$. The displacement of the particle varies with time as
1. $t^2$
2. t
3. $t^{1/2}$
4. $t^3$