IIT JAM 2007 Physics Question Paper with Answer Key PDF

IIT JAM Questions

• 1.

  The shortest distance between an object and its real image formed by a thin convex lens of focal length 20 cm is _____ cm. (in integer)
  

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• 2.

  Consider a chamber at room temperature (27 \(^\circ\)C) filled with a gas having a molecular diameter of 0.35 nm. The pressure (in Pascal) to which the chamber needs to be evacuated so that the molecules have a mean free path of 1 km is \rule{1cm{0.15mm} \(\times 10^{-5}\) Pa. (up to two decimal places)
  (Boltzmann constant \(k_B = 1.38 \times 10^{-23}\) J/K)}
  

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• 3.

  Consider a volume V enclosed by a closed surface S having unit surface normal \(\hat{n}\). For \(\mathbf{r} = x\hat{i} + y\hat{j} + z\hat{k}\), the value of the surface integral \(\frac{1}{9} \oint_{S} \mathbf{r} \cdot \hat{n} \,dS\) is

  • \(V\)
  • \(3V\)
  • \(\frac{V}{3}\)
  • \(\frac{V}{9}\)
    
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• 4.

  In a two-level atomic system, the excited state is 0.2 eV above the ground state. Considering the Maxwell-Boltzmann distribution, the temperature at which 2% of the atoms will be in the excited state is _____ K. (up to two decimal places)
  (Boltzmann constant \(k_B = 8.62 \times 10^{-5}\) eV/K)
  

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• 5.

  At a particular temperature T, Planck's energy density of black body radiation in terms of frequency is \(\rho_T(\nu) = 8 \times 10^{-18} \text{ J/m}^3 \text{ Hz}^{-1}\) at \(\nu = 3 \times 10^{14}\) Hz. Then Planck's energy density \(\rho_T(\lambda)\) at the corresponding wavelength (\(\lambda\)) has the value \rule{1cm}{0.15mm} \(\times 10^2 \text{ J/m}^4\). (in integer) 
  [Speed of light \(c = 3 \times 10^8\) m/s] 
  (Note: The unit for \(\rho_T(\nu)\) in the original problem was given as J/m³, which is dimensionally incorrect for a spectral density. The correct unit J/(m³·Hz) or J·s/m³ is used here for the solution.)

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• 6.

  The packing fraction for a two-dimensional hexagonal lattice having sides 2r with atoms of radii r placed at each vertex and at the center is _____. (up to two decimal places)
  

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