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

1.	Acceleration is along \((\text{-}\vec R )\).
2.	Magnitude of the acceleration vector is \(\frac{v^2}{R}\), where \(v\) is the velocity of the particle.
3.	Magnitude of the velocity of the particle is \(8\) m/s.
4.	Path of the particle is a circle of radius \(4\) m.

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. \(V_a = V_b\)

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]

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:

Two slits in Young’s experiment have widths in the ratio of \(1:25.\) The ratio of intensity at the maxima and minima in the interference pattern \(\dfrac{I_{max}}{I_{min}}\) is:

Water rises to height '\(h\)' in a capillary tube. If the length of capillary tube above the surface of the water is made less than \('h'\), then:

A circuit contains an ammeter, a battery of \(30~\text{V},\) and a resistance \(40.8~\Omega\)$$ all connected in series. If the ammeter has a coil of resistance \(480~\Omega\)$$ and a shunt of \(20~\Omega,\)$$ then the reading in the ammeter will be:
1. \(0.5~\text{A}\)
2. \(0.02~\text{A}\)
3. \(2~\text{A}\)
4. \(1~\text{A}\)