Partial Differential Equations MCQ

Test your knowledge with important Partial Differential Equations MCQ and their applications. These MCQs are beneficial for competitive exams too. Explore 30 + more Partial Differential Equations MCQs at Bissoy

• Wave equation is a linear elliptical partial differential equation.
  ক

  False

  খ

  True
• The wave equation is known as d’Alembert’s equation.
  ক

  True

  খ

  False
• In which of the following fields, does the wave equation not appear?
  ক

  Acoustics

  খ

  Electromagnetics

  গ

  Pedology

  ঘ

  Fluid Dynamics
• Wave equation is a third-order linear partial differential equation.
  ক

  True

  খ

  False
• Who discovered the one-dimensional wave equation?
  ক

  Jean d’Alembert

  খ

  Joseph Fourier

  গ

  Robert Boyle

  ঘ

  Isaac Newton
• What is the half-interval method in numerical analysis is also known as?
  ক

  Newton-Raphson method

  খ

  Regula Falsi method

  গ

  Taylor’s method

  ঘ

  Bisection method
• Heat Equation is an example of elliptical partial differential equation.
  ক

  True

  খ

  False
• What is another name for heat equation?
  ক

  Induction equation

  খ

  Condenser equation

  গ

  Diffusion equation

  ঘ

  Solar equation
• In mathematics, an initial condition (also called a seed value), is a value of an evolving variable at some point in time designated as the initial time (t=0).
  ক

  False

  খ

  True
• Under ideal assumptions, what is the two-dimensional heat equation?
  ক

  ut = c∇2 u = c(uxx + uyy)

  খ

  ut = c2 uxx

  গ

  ut = c2 ∇2 u = c2 (uxx + uyy)

  ঘ

  ut = ∇2 u = (uxx + uyy)
• Which of the following is not a field in which heat equation is used?
  ক

  Probability theory

  খ

  Histology

  গ

  Financial Mathematics

  ঘ

  Quantum Mechanics
• Who was the first person to develop the heat equation?
  ক

  Joseph Fourier

  খ

  Galileo Galilei

  গ

  Daniel Gabriel Fahrenheit

  ঘ

  Robert Boyle
• While solving any partial differentiation equation using a variable separable method which is of order 1 or 2, we use the formula of fourier series to find the coefficients at last.
  ক

  True

  খ

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

  k is positive

  খ

  k is negative

  গ

  k is 0

  ঘ

  k can be anything
• When solving a 1-Dimensional wave equation using variable separable method, we get the solution if _____________
  ক

  k is positive

  খ

  k is negative

  গ

  k is 0

  ঘ

  k can be anything
• While solving a partial differential equation using a variable separable method, we equate the ratio to a constant which?
  ক

  can be positive or negative integer or zero

  খ

  can be positive or negative rational number or zero

  গ

  must be a positive integer

  ঘ

  must be a negative integer
• While solving a partial differential equation using a variable separable method, we assume that the function can be written as the product of two functions which depend on one variable only.
  ক

  True

  খ

  False
• Separation of variables was first used by L’Hospital in 1750.
  ক

  False

  খ

  True
• u (x, t) = e − 2π*2t*sin πx is the solution of the two-dimensional Laplace equation.
  ক

  True

  খ

  False
• For a partial differential equation, in a function φ (x, y) and two variables x, y, what is the form obtained after separation of variables is applied?
  ক

  Φ (x, y) = X(x)+Y(y)

  খ

  Φ (x, y) = X(x)-Y(y)

  গ

  Φ (x, y) = X(x)Y(y)

  ঘ

  Φ (x, y) = X(x)/Y(y)
• The matrix form of the separation of variables is the Kronecker sum.
  ক

  True

  খ

  False
• Which of the following equations cannot be solved by using the method of separation of variables?
  ক

  Laplace Equation

  খ

  Helmholtz Equation

  গ

  Alpha Equation

  ঘ

  Biharmonic Equation
• Separation of variables, in mathematics, is also known as Fourier method.
  ক

  False

  খ

  True
• By using the method of separation of variables, the determination of solution to P.D.E. reduces to determination of solution to O.D.E.
  ক

  True

  খ

  False
• Elliptic equations have no characteristic curves.
  ক

  True

  খ

  False
• The condition that a second order partial differential equation should satisfy to be parabolic is b2-ac=0.
  ক

  True

  খ

  False
• Which of the following represents the family of the characteristic curves for parabolic equations?
  ক

  aζx+bζy=0

  খ

  aζx+b=0

  গ

  a+ζy=0

  ঘ

  a(ζx+ζy)=0
• The condition which a second order partial differential equation must satisfy to be elliptical is b2-ac=0.
  ক

  True

  খ

  False
• Which of the following represents the canonical form of a second order parabolic PDE?
  ক

  \(\frac{∂^2 z}{∂η^2}+⋯=0 \)

  খ

  \(\frac{∂^2 z}{∂ζ∂η}+⋯=0\)

  গ

  \(\frac{∂^2 z}{∂α^2}+\frac{∂^2 z}{∂β^2}…=0\)

  ঘ

  \(\frac{∂^2 z}{∂ζ^2}+⋯=0\)
• Which of the following is the condition for a second order partial differential equation to be hyperbolic?
  ক

  b2-ac<0

  খ

  b2-ac=0

  গ

  b2-ac>0

  ঘ

  b2-ac=<0