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 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

A particle starts from the origin at \(t=0\) sec with a velocity of \(10\hat j~\text{m/s}\) and moves in the \(x\text-y\) plane with a constant acceleration of \((8.0\hat i +2.0 \hat j)~\text{m/s}^2\). At what time is the \(x\text-\)coordinate of the particle \(16\) m?
1. \(2\) s

A particle is moving along a circle such that it completes one revolution in \(40\) seconds. In \(2\) minutes \(20\) seconds, the ratio of \(|displacement| \over distance\) will be:
1. \(0\)
2. \(\frac{1}{7}\)
3. \(\frac{2}{7}\)
4. \(\frac{1}{11}\)

Consider the motion of the tip of the second hand of a clock. In one minute (assuming \(R\) to be the length of the second hand), its:

A person, reaches a point directly opposite on the other bank of a flowing river, while swimming at a speed of \(5\) m/s at an angle of \(120^\circ\) with the flow. The speed of the flow must be:
1. \(2.5\) m/s
2. \(3\) m/s
3. \(4\) m/s
4. \(1.5\) m/s

A car with a vertical windshield moves in a rain storm at a speed of \(40\) km/hr. The rain drops fall vertically with a constant speed of \(20\) m/s. The angle at which raindrops strike the windshield is:
1. \(\tan^{- 1} \frac{5}{9}\)
2. \(\tan^{- 1} \frac{9}{5}\)
3. \(\tan^{- 1} \frac{3}{2}\)
4. \(\tan^{- 1} \frac{2}{3}\)

A particle projected from origin moves in the \(x\text-y\) plane with a velocity \(\overrightarrow{v} = 3 \hat{i} + 6 x \hat{j}\)$\stackrel{}{\mathrm{}}$, where \(\hat i\) and \(\hat j\) are the unit vectors along the \(x\) and \(y\text-\)axis. The equation of path followed by the particle is:
1. \(y=x^2\)
2. \(y=\frac{1}{x^2}\)
3. \(y=2x^2\)
4. \(y=\frac{1}{x}\)

The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by
\(y =4 t - 2 t^{2}~ \text{m}\)  and \(x =3t\) metre, where \(t\) is in seconds and point of projection is taken as the origin. The angle of projection of projectile with vertical is:
1. \(30^{\circ}\)
2. \(37^{\circ}\)
3. \(45^{\circ}\)
4. \(60^{\circ}\)