GATE 2020 Civil Engineering (CE) Exam

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.

  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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• 3.

  A vibrating system has a critical damping coefficient \(C_c = 350 \, \text{N}\cdot\text{s/m}\) and an actual damping coefficient \(C = 35 \, \text{N}\cdot\text{s/m}\). The logarithmic decrement of the system is approximately:

  • 0.10
    
  • 0.31
    
  • 0.63
    
  • 3.14
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• 4.

  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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• 5.

  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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• 6.

  The values of a function \( f \) obtained for different values of \( x \) are shown in the table below.

  

  Using Simpson’s one-third rule, approximate the integral \[ \int_0^1 f(x) \, dx \quad \text{(rounded off to 2 decimal places)}. \]

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