IIT JAM 2006 Computer Applications Question Paper with Answer Key PDF (March 26)

IIT JAM Questions

• 1.

  One kg of water at 27\(^\circ\)C is brought in contact with a heat reservoir kept at 37\(^\circ\)C. Upon reaching thermal equilibrium, this mass of water is brought in contact with another heat reservoir kept at 47\(^\circ\)C. The final temperature of water is 47\(^\circ\)C. The change in entropy of the whole system in this entire process is \rule{1cm{0.15mm} cal/K. (up to two decimal places)
  Take specific heat at constant pressure of water as 1 cal/(g K)}
  

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• 2.

  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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• 3.

  A light beam given by \(\mathbf{E}(z, t) = E_{01} \sin(kz - \omega t)\hat{i} + E_{02} \sin(kz - \omega t + \frac{\pi}{6})\hat{j}\) passes through an ideal linear polarizer whose transmission axis is tilted by 60\(^\circ\) from x-axis (in x-y plane). If \(E_{01} = 4\) V/m and \(E_{02} = 2\) V/m, the electric field amplitude of the emerging light beam from the polarizer is ______ V/m. (up to two decimal places)
  

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• 4.

  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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• 5.

  A NPN bipolar junction transistor (BJT) is connected in common emitter (CE) configuration as shown in the circuit diagram below. The amplifier is operating in the saturation regime. The collector-emitter saturation voltage (\(V_{CE,sat}\)) is 0.2 V. The current gain \(\beta = 100\). The maximum value of base resistance \(R_{BB}\) is \rule{1cm{0.15mm} k\(\Omega\). (in integer)}
  

  

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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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