A vessel of depth \(t\) is half filled with a liquid having a refractive index \(n_1\) and the other half is filled with water having a refractive index \(n_2.\) The apparent depth of the vessel as viewed from the top is:
1. \(\frac{2t(n_1+n_2)}{n_1n_2}\)
2. \(\frac{tn_1n_2}{(n_1+n_2)}\)
3. \(\frac{t(n_1+n_2)}{2n_1n_2}\)
4. \(\frac{n_1n_2}{(n_1+n_2)t}\)

The de-Broglie wavelength of electrons falling on the target in an X-ray tube is 'A. The cut-off wavelength of the emitted X-ray is:

1.  ${\mathrm{\lambda }}_0=\frac{{\left(\mathrm{mc\lambda }\right)}^2}{\mathrm{h}}$

2.  ${\mathrm{\lambda }}_0=\frac{{\mathrm{m}}^2\mathrm{c\lambda }}{{\mathrm{h}}^2}$

3.  ${\mathrm{\lambda }}_0=\frac{2\mathrm{m} {\mathrm{c\lambda }}^2}{\mathrm{h}}$

4.  ${\mathrm{\lambda }}_0=\frac{2\mathrm{m} {\mathrm{c\lambda }}^2}{{\mathrm{h}}^2}$

If M₀ is the mass of an oxygen isotope ₈O¹⁷, M_P and M_n are the masses of a proton and a neutron, respectively, the nuclear binding energy of the isotope is:

1.  ${\mathrm{M}}_{\mathrm{o}}{\mathrm{c}}^2$

2.  $\left({\mathrm{M}}_{\mathrm{o}}-17{\mathrm{M}}_{\mathrm{c}}\right) {\mathrm{c}}^2$

3.  $\left({\mathrm{M}}_{\mathrm{o}}-8{\mathrm{M}}_{\mathrm{p}}\right) {\mathrm{c}}^2$

4.  $\left(8{\mathrm{M}}_{\mathrm{p}}+9{\mathrm{M}}_{\mathrm{n}}-{\mathrm{M}}_{\mathrm{o}}\right) {\mathrm{c}}^2$

A nucleus disintegrates into two nuclear parts which have their velocities in the ratio \(2:1\). The ratio of their nuclear size will be:
1. \( 2^{1 / 3}: 1 \)
2. \( 1: 3^{1 / 2} \)
3. \( 3^{1 / 2}: 1 \)
4. \( 1: 2^{1 / 3}\)