A thin prism having refracting angle \(10^\circ\) is made of glass of a refractive index \(1.42\). This prism is combined with another thin prism of glass with a refractive index \(1.7\). This combination produces dispersion without deviation. The refracting angle of the second prism should be:
1. \(6^{\circ}\)
2. \(8^{\circ}\)
3. \(10^{\circ}\)
4. \(4^{\circ}\)

The acceleration due to gravity at a height \(1~\text{km}\) above the earth's surface is the same as at a depth \(d\) below the surface of the earth. Then:

A potentiometer is an accurate and versatile device to make electrical measurements of E.M.F. because the method involves:

A spherical black body with a radius of \(12\) cm radiates \(450\) W power at \(500\) K. If the radius were halved and the temperature is doubled, the power radiated in watts would be:
1. \(450\)
2. \(1000\)
3. \(1800\)
4. \(225\)

The figure shows a circuit that contains three identical resistors with resistance \(R = 9.0~\Omega\)$$ each, two identical inductors with inductance \(L = 2.0~\text{mH}\) each, and an ideal battery with emf \(\varepsilon = 18~\text{V}\). The current \('i'\) through the battery just after the switch is closed will be:
  
1. \(0.2~\text{A}\)
2. \(2~\text{A}\)
3. \(4~\text{A}\)
4. \(2~\text{mA}\)

Radioactive material 'A' has decay constant '8\(\lambda\)' and material 'B' has a decay constant '\(\lambda\)'. Initially, they have the same number of nuclei. After what time, the ratio of the number of nuclei of material 'A' to that of 'B' will be \(\frac{1}{e}\)?

\(1 .   \frac{1}{7 \lambda}\)
\(2 .   \frac{1}{8 \lambda}\)
\(3 .   \frac{1}{9 \lambda}\)
\(4 .   \frac{1}{\lambda}\)

The diagrams below show regions of equipotential. 
      
A positive charge is moved from \(\mathrm{A}\) to \(\mathrm{B}\) in each diagram. Choose the correct statement from the options given below:

Two astronauts are floating in gravitation-free space after having lost contact with their spaceship. The two will:

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:

One end of the string of length \(l\) is connected to a particle of mass \(m\) and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in a circle with speed \(v\), the net force on the particle (directed towards the center) will be: (\(T\) represents the tension in the string)
1. \(T+\frac{m v^2}{l}\)
2. \(T-\frac{m v^2}{l}\)
3. zero
4. \(T\)