Which one of the following statements is not true?

A cyclist starts from the center \(\mathrm{O}\) of a circular park of radius \(1\) km, reaches the edge \(\mathrm{P}\) of the park, then cycles along the circumference, and returns to the center along \(\mathrm{QO}\) as shown in the figure. If the round trip takes \(10\) min, then the average speed of the cyclist is:
      

1. \(22.42\) km/h
2. \(23.32\) km/h
3. \(21.42\) km/h
4. \(27.12\) km/h

A cricketer can throw a ball to a maximum horizontal distance of 100 m. How much high above the ground, can the cricketer throw the same ball?

1. 50 m

2. 60 m

3. 75 m

4. 100 m

An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900 km/h. Then the ratio of its centripetal acceleration with the acceleration due to gravity is:

1. 5.4:1
2. 6.4:1
3. 4:1
4. 1:1

Three girls skating on a circular ice ground of radius \(200\) m start from a point \(P\) on the edge of the ground and reach a point \(Q\) diametrically opposite to \(P\) following different paths as shown in the figure. The correct relationship among the magnitude of the displacement vector for three girls will be:

1.  $A>B>C$

2. $C>A>B$

3. $B>A>C$

4. $A=B=C$

Rain is falling vertically with a speed of 30 m/s. A woman rides a bicycle with a speed of 10 m/s in the north to south direction. What is the direction in which she should hold her umbrella? [Given: tan 16º = 0.29 & tan 18º = 0.33]

1. 16º with the vertical, towards north

2. 18º with the vertical, towards north

3. 16º with the vertical, towards south

4. 18º with the vertical, towards south

A man can swim at a speed of \(4.0\) km/h in still water. How long does he take to cross a river \(1.0\) km wide if the river flows steadily at \(3.0\) km/h and he makes his strokes normal to the river current? 
1. \(20\) min
2. \(18\) min
3. \(15\) min
4. \(16\) min

In a harbor, the wind is blowing at the speed of 72 km/h, and the flag on the mast of a boat anchored in the harbor flutters along the N-E direction. If the boat starts moving at a speed of 51 km/h to the north, what is the direction of the flag on the mast of the boat?

1. Almost due north

2. Almost due east

3. Almost due west

4.Almost due south

The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 m/s can go without hitting the ceiling of the hall?

1. 150.5 m
2. 165.6 m
3. 145.3 m
4. 158.2 m

A stone tied to the end of a string 80 cm long is whirled in a horizontal circle at a constant speed. If the stone makes 14 revolutions in 25 sec, what is the magnitude of the acceleration of the stone?
1. 8.1 ms^-2
2. 7.7 ms^-2
3. 8.7 ms^-2
4. 9.9 ms^-2