A satellite S is moving in an elliptical orbit around the earth. If the mass of the satellite is very small as compared to the mass of the earth, then:

1.	The angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant.
2.	The total mechanical energy of S varies periodically with time.
3.	The linear momentum of S remains constant in magnitude.
4.	The acceleration of S is always directed towards the centre of the earth.

Two particles \(\mathrm{A}\) and \(\mathrm{B}\), move with constant velocities \(\overrightarrow{{v}_1}\) and \(\overrightarrow{{v}_2}\) respectively. At the initial moment, their position vectors are \(\overrightarrow{{r}_1}\) and \(\overrightarrow{{r}_2}\) respectively. The condition for particles \(\mathrm{A}\) and \(\mathrm{B}\) for their collision will be:
1.\(\dfrac{\vec{r_1}-\vec{r_2}}{\left|\vec{r_1}-\vec{r_2}\right|}=\dfrac{\vec{v_2}-\vec{v_1}}{\left|\vec{v_2}-\vec{v_1}\right|}\)   
2. \(\vec{r_1} \cdot \vec{v_1}=\vec{r_2} \cdot \vec{v_2}\)   ${\mathrm{}}_{}$
3. \(\vec{r_1} \times \vec{v_1}=\vec{r_2} \times \vec{v_2}\)${\mathrm{ \; \; }}_{}$
4. \(\vec{r_1}-\vec{r_2}=\vec{v_1}-\vec{v_2}\) 

Two stones of masses \(m\) and \(2m\) are whirled in horizontal circles, the heavier one in a radius \(\frac{r}{2}\) and the lighter one in a radius \(r\). The tangential speed of lighter stone is \(n\) times that of the value of heavier stone when they experience the same centripetal forces. The value of \(n\) is:

A parallel plate air capacitor has capacitance \(C,\) the distance of separation between plates is \(d\) and potential difference \(V\) is applied between the plates. The force of attraction between the plates of the parallel plate air capacitor is:

The position vector of a particle \(\vec{R}\) as a function of time \(t\) is given by;
\(\overrightarrow{\mathrm{R}}=4 \sin (2 \pi \mathrm{t}) \hat{\mathrm{i}}+4 \cos (2 \pi \mathrm{t}) \hat{\mathrm{j}}\)
Where \(R\) is in meters, \(t\) is in seconds and \(\mathrm{\hat{i},\hat{j}}\) denotes unit vectors along \(\mathrm{x}\) and \(\mathrm{y}\)-directions, respectively. Which one of the following statements is wrong for the motion of the particle?

A series \(RC\) circuit is connected to an alternating voltage source. Consider two situations:
(1) When the capacitor is air-filled. 
(2) When the capacitor is mica filled. 
The current through the resistor is \(i\) and the voltage across the capacitor is \(V\) then:
1. \(V_a< V_b\)
2. \(V_a> V_b\)
3. \(i_a>i_b\)
4. \(V_a = V_b\)

A string is stretched between fixed points separated by \(75.0~\text{cm}\). It is observed to have resonant frequencies of \(420~\text{Hz}\) and \(315~\text{Hz}\). There are no other resonant frequencies between these two. The lowest resonant frequency for this string is:
1. \( 155 \mathrm{~Hz} \)
2. \( 205 \mathrm{~Hz} \)
3. \( 10.5 \mathrm{~Hz} \)
4. \( 105 \mathrm{~Hz}\)

The coefficient of performance of a refrigerator is \(5.\) If the temperature inside the freezer is \(-20^\circ \text{C},\) the temperature of the surroundings to which it rejects heat is:
1. \(31^\circ \text{C}\)
2. \(41^\circ \text{C}\)
3. \(11^\circ \text{C}\)
4. \(21^\circ \text{C}\)

A photoelectric surface is illuminated successively by the monochromatic light of wavelength \(\lambda\) and \(\frac{\lambda}{2}\). If the maximum kinetic energy of the emitted photoelectrons in the second case is \(3\) times that in the first case, the work function of the surface of the mineral is:
[\(h\) = Plank’s constant, \(c\) = speed of light]
1. \(\frac{hc}{2\lambda}\)
2. \(\frac{hc}{\lambda}\)
3. \(\frac{2hc}{\lambda}\)
4. \(\frac{hc}{3\lambda}\)

In an astronomical telescope in normal adjustment, a straight line of length \(L\) is drawn on the inside part of the objective lens. The eye-piece forms a real image of this line. The length of this image is \(l.\) The magnification of the telescope is:
1. \(\frac{L}{l}+1\)
2. \(\frac{L}{l}-1\)
3. \(\frac{L+1}{l-1}\)
4. \(\frac{L}{l}\)