GATE 1997 Civil Engineering (CE) Question Paper with Answer Key PDFs

GATE Questions

• 1.

  Consider two infinitely long fins made of the same material and exposed to the same convective environment. One fin has a square cross-section of side \(a\), and the other has a circular cross-section of diameter \(d\). Assume \(a = d\). The ratio of the steady-state heat transfer rate from the square fin to that from the circular fin, \(\frac{\dot{Q}_{\text{square}}}{\dot{Q}_{\text{circular}}}\), is:

  • \(\frac{\pi}{4}\)
    
  • \(\frac{4}{\pi}\)
    
  • \(\frac{2}{\sqrt{\pi}}\)
    
  • \(\frac{\sqrt{\pi}}{2}\)
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• 2.

  A cantilever beam of length \(L\) is fixed at the left end (\(x=0\)). It is subjected to a concentrated downward point load \(P\) and a concentrated clockwise moment \(M = \frac{PL}{2}\) at the midpoint (\(x = L/2\)). Which of the following descriptions correctly represents the Shear Force Diagram (SFD) for the beam?

  • A rectangular block of constant positive height \(P\) from \(x=0\) to \(x=L/2\), and zero shear force from \(x=L/2\) to \(x=L\).
    
  • A rectangular block of constant positive height \(P\) from \(x=0\) to \(x=L/2\), followed by another rectangular block of height \(P/2\) from \(x=L/2\) to \(x=L\).
    
  • A triangular shape increasing linearly from \(x=0\) to \(x=L/2\).
    
  • A rectangular block from \(x=0\) to \(x=L\), unaffected by the point load.
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• 3.

  Two cars, P and Q, start from a point X in India at 10 AM. Car P travels North with a speed of 25 km/h and car Q travels East with a speed of 30 km/h. Car P travels continuously but car Q stops for some time after traveling for one hour. If both cars are at the same distance from X at 11:30 AM, for how long (in minutes) did car Q stop?

  • 10
    
  • 12
    
  • 15
    
  • 18
    
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• 4.

  For the differential equation given below, which one of the following options is correct? \[ \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0, \quad 0 \leq x \leq 1, 0 \leq y \leq 1 \]

  • \( u = e^{x + y} \) is a solution for all \(x\) and \(y\)
    
  • \( u = e^{x} \sin y \) is a solution for all \(x\) and \(y\)
    
  • \( u = \sin x \sin y \) is a solution for all \(x\) and \(y\)
    
  • \( u = \cos x \cos y \) is a solution for all \(x\) and \(y\)
    
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• 5.

  Two metal parts (a cylinder and a cube) of same volume are cast under identical conditions. The diameter of the cylinder is equal to its height. The ratio of the solidification time of the cube to that of the cylinder is _______________ (rounded off to 2 decimal places).
  Assume that solidification time follows Chvorinov's rule with an exponent of 2.
  

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• 6.

  Let A and B be real symmetric matrices of same size. Which one of the following options is correct?

  • \( (AB)^T = B^T A^T \)
    
  • \( AB = BA \)
    
  • \( A^T = A^{-1} \)
    
  • \( A = A^{-1} \)
    
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