GATE 2026 Production and Industrial Engineering Question Paper with Solution 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.

  If two unbiased coins are tossed, then what is the probability of having at least one head?
  

  • 0.25
    
  • 0.5
    
  • 0.675
    
  • 0.75
    
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• 3.

  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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• 4.

  A plate of 30 mm thickness is fed through a rolling mill with two powered rolls. Each roll has a diameter of 500 mm. The plate thickness is to be reduced to 27 mm in a single pass. Assume no change in width. The process feasibility and the maximum draft (in mm) can be represented, respectively, as
  Use the coefficient of friction as 0.12

  • NOT feasible and 6.0
    
  • NOT feasible and 2.6
    
  • feasible and 3.6
    
  • feasible and 3.0
    
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• 5.

  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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• 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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