A rectangular block of mass m and area of cross-section A floats in a liquid of density ρ. If it is given a small vertical displacement from equilibrium, it undergoes oscillation with a time period T. Then:
1. $T\propto \sqrt{\rho }$
2. $T\propto \frac{1}{\sqrt{A}}$
3. $T\propto \frac{1}{\rho }$
4. $T\propto \frac{1}{\sqrt{m}}$

Two cells having the same emf, are connected in series through an external resistance R. Cells have internal resistance r₁ and r₂ respectively. When the circuit is closed, the potential difference across the first cell is zero. The value of R is:

1. $r_1-r_2$

2. $\frac{r_1+r_2}{2}$

3. $\frac{r_1-r_2}{2}$

4. $r_1+r_2$

A black body at \(1227^\circ\text{C}\) emits radiations with maximum intensity at a wavelength of \(5000~\mathring {A}\). If the temperature of the body is increased by \(1000^\circ\text{C},\) the maximum intensity will be observed at:
1. \(4000~\mathring {A}\)
2. \(5000~\mathring {A}\)
3. \(6000~\mathring {A}\)
4. \(3000~\mathring {A}\)

Two circular coils \(1\) and \(2\) are made from the same wire but the radius of the \(1\)^st coil is twice that of the \(2\)^nd coil. What is the ratio of the potential difference applied across them so that the magnetic field at their centres is the same?
1. \(3\)
2. \(4\)
3. \(6\)
4. \(2\)

A transistor-oscillator using a resonant circuit with an inductance \(L\) (of negligible resistance) and a capacitance \(C\) has a frequency \(f.\) If \(L\) is doubled and \(C\) is changed to \(4C,\) the frequency will be:
1. \(f/4\)
2. \(8f\)
3. \(f/2\sqrt2\)
4. \(f/2\)

The binding energy of deuteron is \(2.2~\text{MeV}\) and that of \(_2\mathrm{He}^{4}\) is \(28~\text{MeV}\). If two deuterons are fused to form one \(_{2}\mathrm{He}^{4}\), ${\mathrm{}}^{}$then the energy released is:
1. \(25.8~\text{MeV}\)
2. \(23.6~\text{MeV}\)
3. \(19.2~\text{MeV}\)
4. \(30.2~\text{MeV}\)