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 \(100~\text{m}\). How much high above the ground, can the cricketer throw the same ball?
1. \(50~\text{m}\)
2. \(60~\text{m}\)
3. \(75~\text{m}\)
4. \(100~\text{m}\)

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: \(\tan 16^{\circ}= 0.29, \& \tan 18^{\circ}= 0.33]\)

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 \(72~\text{km/h}\), and the flag on the mast of a boat anchored in the harbor flutters along the \(\mathrm{N\text-E}\) direction. If the boat starts moving at a speed of \(51~\text{km/h}\) to the north, what is the direction of the flag on the mast of the boat?

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 \(25\) s, what is the magnitude of the acceleration of the stone?