GATE 1992 Electrical Engineering (EE) Question Paper with Answer Key PDF

GATE Questions

• 1.

  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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• 2.

  The welding process commonly used for fabricating tailor-welded blanks of dissimilar thickness for automotive applications is

  • arc welding
    
  • laser welding
    
  • gas welding
    
  • friction welding
    
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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.

  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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• 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.

  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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