Model exam

When solving a 1-Dimensional wave equation using variable separable method, we get the solution if _____________

• k is positive

• k is negative

• k is 0

• k can be anything

When solving a 1-Dimensional heat equation using a variable separable method, we get the solution if ______________

• k is positive

• k is negative

• k is 0

• k can be anything

The partial differential equation of 1-Dimensional heat equation is ___________

• u_t = c²u_xx

• u_t = pu_xx

• u_tt = c²u_xx

• u_t = – c²u_xx

Howmany possible solutions are derived for one dimensional wave equation

• 0

• 1

• 2

• 3

Find the nature of one dimensional heat equation

• Hyperbolic

• Parabolic

• Eliptic

• None of these

Howmany different solutions are derived for Laplace's equation in cartesian co-ordinates

• 0

• 1

• 2

• 3

What is the nature of Lagrange’s linear partial differential equation?

• First-order, Third-degree

• Second-order, First-degree

• First-order, Second-degree

• First-order, First-degree

Find the general solution of the linear partial differential equation, yzp+zxq=xy.

• $φ(x^2-y^2,\ x^2–z^2)=0$
  

• $φ(x^2-y^2,\ y^2-z^2)=0$
  

• $φ(x^2-y^2,\ y^2-x^2)=0$
  

• $φ(x^2-z^2,\ z^2-x^2)=0$
  

Which of the following is true with respect to formation of differential equation by elimination of arbitrary constants?

• The given equation should be differentiated with respect to independent variable

• Elimination of the arbitrary constant by replacing it using derivative

• If ‘n’ arbitrary constant is present, the given equation should be differentiated ‘n’ number of times

• To eliminate the arbitrary constants, the given equation must be integrated with respect to the dependent variable

Find the singular solution of z=px+qy+p²

• 4z+x²

• 4x+z²

• 4x=z²

• x=4