Q. No.A cat is situated at point \(A\) (\(0,3,4\)) and a rat is situated at point \(B\) (\(5,3,-8\)). The cat is free to move but the rat is always at rest. The minimum distance travelled by the cat to catch the rat is:
1. \(5\) unit
2. \(12\) unit
3. \(13\) unit
4. \(17\) unit
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. \(\frac{1}{11}\)
1. \(45^\circ\)
2. \(30^\circ\)
3. \(60^\circ\)
4. \(90^\circ\)
The raindrops are falling with speed \(v\) vertically downwards and a man is running on a horizontal road with speed \(u.\) The magnitude of the velocity of the raindrops with respect to the man is:
1. \(v-u\)
2. \(v+u\)
3. \(\sqrt{{v}^2 + {u}^2 \over 2}\)
4. \(\sqrt{{v}^2 + {u}^2}\)
Rain is falling vertically downward with a speed of \(35~\text{m/s}.\) The wind starts blowing after some time with a speed of \(12~\text{m/s}\) in the east to the west direction. The direction in which a boy standing at the place should hold his umbrella is:
| 1. | \(\text{tan}^{-1}\Big(\frac{12}{37}\Big)\) with respect to rain |
| 2. | \(\text{tan}^{-1}\Big(\frac{12}{37}\Big)\) with respect to wind |
| 3. | \(\text{tan}^{-1}\Big(\frac{12}{35}\Big)\) with respect to rain |
| 4. | \(\text{tan}^{-1}\Big(\frac{12}{35}\Big)\) with respect to wind |
A particle starting from the point \((1,2)\) moves in a straight line in the XY-plane. Its coordinates at a later time are \((2,3).\) The path of the particle makes with \(x\)-axis an angle of:
| 1. | \(30^\circ\) | 2. | \(45^\circ\) |
| 3. | \(60^\circ\) | 4. | data is insufficient |
A particle is moving such that its position coordinates \((x,y)\) are \( (2~\text m, 3~\text m)\) at time \(t=0,\) \( (6~\text m, 7~\text m)\) at time \(t=2~\text s\) and \( (13~\text m, 14~\text m)\) at time \(t=5~\text s.\) The average velocity vector \((v_{avg})\) from \(t=0\) to \(t=5~\text s\) is:
| 1. | \(\frac{1}{5}\left ( 13\hat{i}+14\hat{j} \right )\) | 2. | \(\frac{7}{3}\left ( \hat{i}+\hat{j} \right )\) |
| 3. | \(2\left ( \hat{i}+\hat{j} \right )\) | 4. | \(\frac{11}{5}\left ( \hat{i}+\hat{j} \right )\) |
An aeroplane flies \(400\) m north and then \(300\) m west and then flies \(1200\) m upwards. Its net displacement is:
| 1. | \(1200\) m | 2. | \(1300\) m |
| 3. | \(1400\) m | 4. | \(1500\) m |
The position of a moving particle at time \(t\) is \(\overrightarrow{r}=3\hat{i}+4t^{2}\hat{j}-t^{3}\hat{k}.\) Its displacement during the time interval \(t=1\) s to \(t=3\) s will be:
| 1. | \(\hat{j}-\hat{k}\) | 2. | \(3\hat{i}-4\hat{j}-\hat{k}\) |
| 3. | \(9\hat{i}+36\hat{j}-27\hat{k}\) | 4. | \(32\hat{j}-26\hat{k}\) |
A particle moves along the positive branch of the curve \(y= \frac{x^{2}}{2}\) where \(x= \frac{t^{2}}{2}\), & \(x\) and \(y\) are measured in metres and in seconds respectively. At \(t= 2~\text{s}\), the velocity of the particle will be:
| 1. | \(\left(\right. 2 \hat{i} - 4 \hat{j})~\text{m/s}\) | 2. | \(\left(\right. 4 \hat{i} + 2 \hat{j}\left.\right)\text{m/s}\) |
| 3. | \(\left(\right. 2 \hat{i} + 4 \hat{j}\left.\right) \text{m/s}\) | 4. | \(\left(\right. 4 \hat{i} - 2 \hat{j}\left.\right) \text{m/s}\) |
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