GATE 2026 CH Question Paper with Solutions (Available)- Download Pdf

GATE Questions

• 1.

  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 \(y\)
    
  View Solution

  ---

• 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.
  View Solution

  ---

• 3.

  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.
  

  View Solution

  ---

• 4.

  Consider two identical tanks with a bottom hole of diameter \( d \). One tank is filled with water and the other tank is filled with engine oil. The height of the fluid column \( h \) is the same in both cases. The fluid exit velocity in the two tanks are \( V_1 \) and \( V_2 \). Neglecting all losses, which one of the following options is correct?

  

  
   

  • \( V_2>V_1 \)
    
  • \( V_2 = V_1 \)
    
  • \( V_2<V_1 \)
    
  • Insufficient data to definitively conclude the relationship between \( V_1 \) and \( V_2 \)
    
  View Solution

  ---

• 5.

  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
  View Solution

  ---

• 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 \[ \int_0^1 f(x) \, dx \quad \text{(rounded off to 2 decimal places)}. \]

  View Solution