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1.

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 what angle with the  \(x\)-axis?
1. \(30^\circ\)
2. \(45^\circ\)
3. \(60^\circ\)
4. data is insufficient

2. The position of a particle is given by; \(\vec r(t)=4t\hat i+2t^2\hat j+5\hat k,\) where \(t\) is in seconds and \(r\) in metres. Find the magnitude and direction of the velocity \(v(t)\), at \(t=1~\text{s},\) with respect to the \(x\text-\)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.	\(3\sqrt2~\text{ms}^{-1},45^\circ\)

3.

The \(x\) and \(y\) coordinates of the particle at any time are \(x=5 t-2 t^2\) and \({y}=10{t}\) respectively, where \(x\) and \(y\) are in meters and \(\mathrm{t}\) in seconds. The acceleration of the particle at \(\mathrm{t}=2\) s is:

1.	\(5\hat{i}~\text{m/s}^2\)	2.	\(-4\hat{i}~\text{m/s}^2\)
3.	\(-8\hat{j}~\text{m/s}^2\)	4.	\(0\)

4.

A particle has an initial velocity (\(2\hat{i}+3\hat{j}\)) and an acceleration (\(0.3\hat{i}+0.2\hat{j}\)). The magnitude of velocity after \(10\) s will be:
1. \(9 \sqrt{2} ~\text{units} \)
2. \(5 \sqrt{2} ~\text{units} \)
3. \(5 ~\text{units} \)
4. \(9~\text{units} \)

5.

The velocity of a projectile at the initial point \(A\) is \(2\hat i+3\hat j~\text{m/s}.\) Its velocity (in m/s) at the point \(B\) is:
              

1.	\(-2\hat i+3\hat j~\)	2.	\(2\hat i-3\hat j~\)
3.	\(2\hat i+3\hat j~\)	4.	\(-2\hat i-3\hat j~\)

6. A particle moves so that its position vector is given by, \(\vec{r}=\cos \omega t ~\hat{x}+ \sin \omega t~ \hat{y },\) where \(\omega\) is a constant. Which of the following is true?

1.	The velocity and acceleration both are parallel to \(\vec{r }.\)
2.	The velocity is perpendicular to \(\vec{r }\) and acceleration is directed towards to origin.
3.	The velocity is parallel to \(\vec{r }\) and acceleration is directed away from the origin.
4.	The velocity and acceleration both are perpendicular to \(\vec{r}.\)

7.

A man standing on a road holds his umbrella at \(30^{\circ}\) with the vertical to keep the rain away. He throws the umbrella and starts running at \(10\) km/hr. He finds that raindrops are hitting his head vertically. The speed of raindrops with respect to the road will be:
1. \(10\) km/hr
2. \(20\) km/hr
3. \(30\) km/hr
4. \(40\) km/hr

8. The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is:

1.	\(\theta = \tan^{-1}\left(\frac{1}{4}\right)\)	2.	\(\theta = \tan^{-1}(4)\)
3.	\(\theta = \tan^{-1}(2)\)	4.	\(\theta = 45^{\circ}\)

9.

A particle moves in a circle of radius \(5\) cm with constant speed and time period \(0.2\pi\) s. The acceleration of the particle is:

1.	\(25\) m/s2	2.	\(36\) m/s2
3.	\(5\) m/s2	4.	\(15\) m/s2

10.

A projectile is fired from the surface of the earth with a velocity of \(5~\text{m/s}\) and at an angle \(\theta\) with the horizontal. Another projectile fired from another planet with a velocity of \(3~\text{m/s}\) at the same angle follows a trajectory that is identical to the trajectory of the projectile fired from the Earth. The value of the acceleration due to gravity on the other planet is:
(given \(g=9.8~\text{m/s}^2\) )

1.	\(3.5~\text{m/s}^2\)	2.	\(5.9~\text{m/s}^2\)
3.	\(16.3~\text{m/s}^2\)	4.	\(110.8~\text{m/s}^2\)