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Q. No.A bus is going to the North at a speed of \(30\) kmph. It makes a \(90^{\circ}\) left turn without changing the speed. The change in the velocity of the bus is:
| 1. | \(30~\text{kmph}\) towards \(\mathrm{W}\) |
| 2. | \(30~\text{kmph}\) towards \(\mathrm{S\text-W}\) |
| 3. | \(42.4~\text{kmph}\) towards \(\mathrm{S\text-W}\) |
| 4. | \(42.4~\text{kmph}\) towards \(\mathrm{N\text-W}\) |
Two particles move from \(A\) to \(C\) and \(A\) to \(D\) on a circle of radius \(R\) and the diameter \(AB.\) If the time taken by both particles is the same, then the ratio of magnitudes of their average velocities is:
1. \(2\)
2. \(2\sqrt{3}\)
3. \(\sqrt{3}\)
4. \(\dfrac{\sqrt{3}}{2}\)
1. \(4~\text{m/s},\) \(53^\circ\) with \(x\)-axis
2. \(4~\text{m/s},\) \(37^\circ\) with \(x\)-axis
3. \(5~\text{m/s},\) \(53^\circ\) with \(y\)-axis
4. \(5~\text{m/s},\) \(53^\circ\) with \(x\)-axis
1. \(4\sqrt2~\text{ms}^{-1},45^\circ\)
2. \(4\sqrt2~\text{ms}^{-1},60^\circ\)
3. \(3\sqrt2~\text{ms}^{-1},30^\circ\)
4. \(3\sqrt2~\text{ms}^{-1},45^\circ\)
The position of a particle at time \(t\) is given by, \(x=3t^3\), \(y=2t^2+8t\), and \(z=6t-5\). The initial velocity of the particle is:
| 1. | \(20\) unit | 2. | \(10\) unit |
| 3. | \(5\) unit | 4. | \(13\) unit |
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
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Q. No.
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