Liquid oxygen at \(50~\text K\) is heated up to \(300~\text K\) at a constant pressure of \(1~\text{atm}.\) The rate of heating is constant. Which one of the following graphs represents the variation of temperature with time?

1.		2.
3.		4.

An alternating electric field of frequency $\mathrm{\nu }$, is applied across the dees (radius=R) of a cyclotron that is being used to accelerate protons (mass=m). The operating magnetic field B, used in the cyclotron and the kinetic energy (K) of the proton beam, produced by it, are given by:

1. $\mathrm{B}=\frac{\mathrm{m\nu }}{\mathrm{e}}$ $\mathrm{and}$ $\mathrm{K}=2{\mathrm{m\pi }}^2{\mathrm{\nu }}^2{\mathrm{R}}^2$

2. $\mathrm{B}=\frac{2\mathrm{\pi m\nu }}{\mathrm{e}}$ $\mathrm{and}$ $\mathrm{K}={\mathrm{m}}^2{\mathrm{\pi \nu R}}^2$

3. $\mathrm{B}=\frac{2\mathrm{\pi m\nu }}{\mathrm{e}}$ $\mathrm{and}$ $\mathrm{K}=2{\mathrm{m\pi }}^2{\mathrm{\nu }}^2{\mathrm{R}}^2$

4. $\mathrm{B}=\frac{\mathrm{m\nu }}{\mathrm{e}}$ $\mathrm{and}$ $\mathrm{K}={\mathrm{m}}^2{\mathrm{\pi \nu R}}^2$

A ray of light is incident at an angle of incidence, \(i\), on one face of a prism of angle \(A\) (assumed to be small) and emerges normally from the opposite face. If the refractive index of the prism is \(\mu,\) the angle of incidence \(i\), is nearly equal to:

A spherical planet has a mass \(M_p\) and diameter \(D_p\)${\mathrm{}}_{}$. A particle of mass \(m\) falling freely near the surface of this planet will experience acceleration due to gravity equal to:

The damping force of an oscillator is directly proportional to the velocity. The units of the constant of proportionality are:
1. kg-msec^-1
2. kg-msec^-2
3. kg-sec^-1
4. kg-sec

A concave mirror of the focal length \(f_1\) is placed at a distance of \(d\) from a convex lens of focal length \(f_2\)${\mathrm{}}_{}$. A beam of light coming from infinity and falling on this convex lens-concave mirror combination returns to infinity. The distance \(d\) must be equal to:

1. \(f_1+f_2\)

2. \(-f_1+f_2\)

3. \(2f_1+f_2\)

4. \(-2f_1+f_2\)

A geostationary satellite is orbiting the earth at a height of \(5R\) above the surface of the earth, \(R\) being the radius of the earth. The time period of another satellite in hours at a height of \(2R\) from the surface of the earth is:

1. \(5\)

2. \(10\)

3. \(6\sqrt2\)

4. \(\dfrac{6}{\sqrt{2}}\)

Transfer characteristics [output voltage (${\mathrm{V}}_{\mathrm{o}}$) vs input voltage (${\mathrm{V}}_{\mathrm{i}}$)] for a base biased transistor in CE configurations are as shown in the figure. For using the transistor as a switch, it is used:

1. In region III

2. Both in the region (I) and (III)

3. In region II

4. In region I

If the voltage across a bulb rated \((220~\text{V}\text-100~\text{W})\) drops by \(2.5\%\) of its rated value, the percentage of the rated value by which the power would decrease is:
1. \(20\%\)
2. \(2.5\%\)
3. \(5\%\)
4. \(10\%\)

A particle has initial velocity \(\left(2 \hat{i} + 3 \hat{j}\right)\) and acceleration \(\left(0 . 3 \hat{i} + 0 . 2 \hat{j}\right)\). The magnitude of velocity after \(10\) s will be: