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 traveled by the cat to catch the rat is:

1. 5 unit

2. 12 unit

3. 13 unit

4. 17 unit

Balls A and B are thrown from two points lying on the same horizontal plane separated by a distance of 120 m. Which of the following statements is correct?

1. The balls can never meet.

2. The balls can meet if the ball B is thrown 1 s later.

3. The two balls meet at a height of 45 m.

4. None of the above

A body is projected at an angle of $30°$ with the horizontal with a speed of 30 m/s. What is the angle made by the velocity vector with the horizontal after 1.5 sec? (g = 10$\mathrm{m}/{\mathrm{s}}^2$)

1. $0°$

2. $30°$

3. $60°$

4. $90°$

A particle moves along the positive branch of the curve y = $\frac{{\mathrm{x}}^2}{2}$ where x = $\frac{{\mathrm{t}}^2}{2}$, & x and y are measured in metres and in seconds respectively. At = 2s, the velocity of the particle will be

1. $(2\hat{\mathrm{i}}-4\hat{\mathrm{j}} )\mathrm{m}/\mathrm{s}$

2. $(4\hat{\mathrm{i}}+2\hat{\mathrm{j}} )\mathrm{m}/\mathrm{s}$

3. $(2\hat{\mathrm{i}}+4\hat{\mathrm{j}} )\mathrm{m}/\mathrm{s}$

4. $(4\hat{\mathrm{i}}-2\hat{\mathrm{j}} )\mathrm{m}/\mathrm{s}$

A deer wants to save her life from a lion. The lion follows a path whose equation is ${\mathrm{x}}^2+{\mathrm{y}}^2=16$. For saving her life, the deer needs to move on a path whose equation will be

1. ${\mathrm{x}}^2+{\mathrm{y}}^2=4$

2. ${\mathrm{x}}^2+{\mathrm{y}}^2=16$

3. ${\mathrm{x}}^2+{\mathrm{y}}^2-64=0$

4. Both (1)and(3) are correct

A particle rotates in a circular path starting from rest. If angular acceleration is 4 $rad/s^2$, then the time after which angle between net acceleration and tangential acceleration becomes $45°\; is$

1. 0.5 s

2. 0.25 s

3. 2 s

4. 4 s

The position of a moving particle at time t is $\overrightarrow{\mathrm{r}}=3\hat{\mathrm{i}}+4{\mathrm{t}}^2\hat{\mathrm{j}}-{\mathrm{t}}^3\hat{\mathrm{k}}$. Its displacement during the time interval t = 1 sec to t = 3 sec will be

1. $\hat{\mathrm{j}}-\hat{\mathrm{k}}$

2. $3\hat{\mathrm{i}}-4\hat{\mathrm{j}}-\hat{\mathrm{k}}$

3. $9\hat{\mathrm{i}}+36\hat{\mathrm{j}}-27\hat{\mathrm{k}}$

4. $32\hat{\mathrm{j}}-26\hat{\mathrm{k}}$

An object moves at a constant speed along a circular path in a horizontal XY plane with its centre at the origin. When the object is at x = –2m, its velocity is –(4 m/s)$\hat{\mathrm{j}}$. What is the object's acceleration when it is at y = 2m?

1. $-(8\mathrm{m}/{\mathrm{s}}^2) \hat{\mathrm{j}}$

2. $-(8\mathrm{m}/{\mathrm{s}}^2) \hat{\mathrm{i}}$

3. $-(4\mathrm{m}/{\mathrm{s}}^2) \hat{\mathrm{j}}$

4. $-(4\mathrm{m}/{\mathrm{s}}^2) \hat{\mathrm{i}}$

A particle has an initial velocity $\overrightarrow{\mathrm{u}}=(4\hat{i}-5\hat{j})$ m/s and it is moving with an acceleration $\overrightarrow{\mathrm{a}}=\left(\frac{1}{4}\hat{i}+\frac{1}{5}\hat{j}\right)m/s^2$. Velocity of the particle at t =2s will be

1. $(6\hat{\mathrm{i}}-4\hat{\mathrm{j}})\mathrm{m}/\mathrm{s}$

2. $(4.5\hat{i}-4.5\hat{\mathrm{j}})\mathrm{m}/\mathrm{s}$

3. $(4.5\hat{i}-4.6\hat{\mathrm{j}})\mathrm{m}/\mathrm{s}$

4. $(6\hat{\mathrm{i}}-4.6\hat{\mathrm{j}})\mathrm{m}/\mathrm{s}$

To the captain of a ship A travelling with velocity $\overrightarrow{v_A}=(3\hat{i}-4\hat{j})$ km/h, a second ship B appears to have a velocity ${\overrightarrow{v}}_B=\left(5\hat{i}+12\hat{j}\right)$ km/h. What is the true velocity of the ship B?

1. $2\hat{i}+16\hat{j} km/h$

2. $13\hat{i}+8\hat{j} km/h$

3. $-2\hat{i}-16\hat{j} km/h$

4. none of these