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Latest GATE Physics Exam Question (Objective Questions), MCQ in English

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Question Bank GATE Physics Exam (Only MCQ) - English
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Physics

Question 1Single Answer
What is the physical interpretation of the gradient of a scalar field in the context of electrostatics?
  1. A
    Rate of change of electric field strength
  2. B
    Magnitude of electric field divergence
  3. C
    Direction of maximum increase in electric potential
  4. D
    Curl of the electric field
Question 2Single Answer
What is the divergence of a vector field representing an incompressible fluid flow?
  1. A
    Positive
  2. B
    Zero
  3. C
    Negative
  4. D
    Infinite
Question 3Single Answer
What is the curl of a conservative vector field, such as the electric field in electrostatics?
  1. A
    Zero
  2. B
    Non-zero constant
  3. C
    Divergent vector
  4. D
    Scalar field
Question 4Single Answer
What does Stokes’ theorem relate in the context of magnetostatics?
  1. A
    Volume integral of magnetic field to its gradient
  2. B
    Surface integral of magnetic field to volume integral of its divergence
  3. C
    Line integral of electric field to surface integral of its divergence
  4. D
    Line integral of magnetic field to surface integral of its curl
Question 5Single Answer
What is the value of the surface integral of a vector field over a closed surface if its divergence is zero everywhere?
  1. A
    Positive
  2. B
    Negative
  3. C
    Zero
  4. D
    Infinite
Question 6Single Answer
The energy levels of a one-dimensional harmonic oscillator are:
  1. A
    (n + 1)hw
  2. B
    nhw
  3. C
    (n + 1/2)hw
  4. D
    n²hw
Question 7Single Answer
The zero-point energy of a one-dimensional harmonic oscillator is:
  1. A
    hw/2
  2. B
    hw
  3. C
    hw/4
  4. D
    0
Question 8Single Answer
The transmission coefficient for a particle tunneling through a potential barrier is:
  1. A
    Exponentially small for thick barriers
  2. B
    Exponentially large for thick barriers
  3. C
    Constant for all barriers
  4. D
    Zero for all barriers
Question 9Single Answer
The wave function for a particle in a one-dimensional infinite potential well is:
  1. A
    Constant at the boundaries
  2. B
    Non-zero at the boundaries
  3. C
    Infinite at the boundaries
  4. D
    Zero at the boundaries
Question 10Single Answer
What is the conserved quantity for a Hamiltonian that is invariant under translation in the z-direction in a three-dimensional system?
  1. A
    Angular momentum about the z-axis
  2. B
    Linear momentum in the z-direction
  3. C
    Total energy
  4. D
    Kinetic energy
Question 11Single Answer
What is the phase space volume for a system with a Hamiltonian that includes a velocity-dependent force?
  1. A
    Not conserved
  2. B
    Conserved
  3. C
    Increases with time
  4. D
    Decreases with time
Question 12Single Answer
What is the phase space trajectory for a particle in a potential V(x, y) = kxy?
  1. A
    An ellipse
  2. B
    A hyperbola
  3. C
    A parabola
  4. D
    A straight line
Question 13Single Answer
What is the conserved quantity for a Hamiltonian that is invariant under translation in the y-direction?
  1. A
    Kinetic energy
  2. B
    Angular momentum
  3. C
    Total energy
  4. D
    Linear momentum in the y-direction
Question 14Single Answer
What is the phase space density for a system with a non-conservative force?
  1. A
    Conserved
  2. B
    Not conserved
  3. C
    Increases with time
  4. D
    Zero everywhere
Question 15Single Answer
What is the conserved quantity for a Hamiltonian that is invariant under rotation about the x-axis?
  1. A
    Total energy
  2. B
    Linear momentum
  3. C
    Angular momentum about the x-axis
  4. D
    Kinetic energy
Question 16Single Answer
What is the phase space volume for a system with a conservative Hamiltonian?
  1. A
    Decreases with time
  2. B
    Increases with time
  3. C
    Conserved
  4. D
    Zero everywhere
Question 17Single Answer
What is the phase space trajectory for a particle in a central potential with a fixed radius?
  1. A
    A straight line
  2. B
    An ellipse
  3. C
    A circle
  4. D
    A parabola
Question 18Single Answer
What is the conserved quantity for a Hamiltonian that does not depend on the generalized coordinate z?
  1. A
    Angular momentum
  2. B
    Linear momentum in the z-direction
  3. C
    Total energy
  4. D
    Kinetic energy
Question 19Single Answer
What is the phase space trajectory for a particle in a three-dimensional harmonic oscillator?
  1. A
    A hyperbola
  2. B
    A sphere
  3. C
    A parabola
  4. D
    An ellipsoid
Question 20Single Answer
What is the conserved quantity for a Hamiltonian that is invariant under translation in the x-direction?
  1. A
    Angular momentum
  2. B
    Linear momentum in the x-direction
  3. C
    Total energy
  4. D
    Kinetic energy
Question 21Single Answer
What is the phase space density for a system with a time-dependent Hamiltonian?
  1. A
    Zero everywhere
  2. B
    Conserved
  3. C
    Increases with time
  4. D
    Not conserved
Question 22Single Answer
The energy levels of a particle in a one-dimensional finite potential well are:
  1. A
    Continuous and infinite
  2. B
    Discrete and finite
  3. C
    Discrete and infinite
  4. D
    Continuous and finite
Question 23Single Answer
The wave function for a particle in a finite potential well:
  1. A
    Decays exponentially outside the well
  2. B
    Oscillates outside the well
  3. C
    Is zero outside the well
  4. D
    Is constant outside the well
Question 24Single Answer
The tunneling probability through a rectangular potential barrier depends on:
  1. A
    The barrier width and height
  2. B
    The barrier width only
  3. C
    The barrier height only
  4. D
    The particle’s mass only
Question 25Single Answer
What is the conserved quantity for a Hamiltonian that is invariant under rotation about the z-axis?
  1. A
    Linear momentum
  2. B
    Angular momentum about the z-axis
  3. C
    Total energy
  4. D
    Kinetic energy
Question 26Single Answer
What is the phase space volume for a system with a dissipative force according to Liouville’s theorem?
  1. A
    Conserved
  2. B
    Not conserved
  3. C
    Increases with time
  4. D
    Zero everywhere
Question 27Single Answer
What is the conserved quantity for a Hamiltonian that does not depend on time?
  1. A
    Angular momentum
  2. B
    Linear momentum
  3. C
    Total energy
  4. D
    Kinetic energy
Question 28Single Answer
What is the phase space density for a system with a time-independent Hamiltonian?
  1. A
    Constant along trajectories
  2. B
    Increasing with time
  3. C
    Decreasing with time
  4. D
    Zero everywhere
Question 29Single Answer
What is the conserved quantity for a Hamiltonian that does not depend on the generalized coordinate y?
  1. A
    Kinetic energy
  2. B
    Angular momentum
  3. C
    Total energy
  4. D
    Linear momentum in the y-direction
Question 30Single Answer
What is the phase space trajectory for a particle in a two-dimensional harmonic oscillator?
  1. A
    A hyperbola
  2. B
    A circle
  3. C
    A parabola
  4. D
    An ellipse
Question 31Single Answer
The Fourier series of an odd function contains:
  1. A
    No trigonometric terms
  2. B
    Only cosine terms
  3. C
    Both sine and cosine terms
  4. D
    Only sine terms
Question 32Single Answer
The Fourier transform is used to solve:
  1. A
    Non-linear equations
  2. B
    Wave equations
  3. C
    Algebraic equations
  4. D
    Matrix equations
Question 33Single Answer
The convergence of a Fourier series depends on:
  1. A
    Cauchy conditions
  2. B
    Dirichlet conditions
  3. C
    Riemann conditions
  4. D
    Euler conditions
Question 34Single Answer
The Fourier transform of a Gaussian function is:
  1. A
    A delta function
  2. B
    Another Gaussian function
  3. C
    A sine function
  4. D
    A cosine function
Question 35Single Answer
The Laplace transform of a unit step function u(t) is:
  1. A
    1/s
  2. B
    s
  3. C
    1/s²
  4. D
    s²
Question 36Single Answer
The Laplace transform of sin(at) is:
  1. A
    a/(s² - a²)
  2. B
    s/(s² + a²)
  3. C
    a/(s² + a²)
  4. D
    s/(s² - a²)
Question 37Single Answer
The Laplace transform is used to convert a differential equation into:
  1. A
    A non-linear equation
  2. B
    A partial differential equation
  3. C
    An algebraic equation
  4. D
    A matrix equation
Question 38Single Answer
The Fourier series of a function that is neither even nor odd contains:
  1. A
    No trigonometric terms
  2. B
    Only sine terms
  3. C
    Only cosine terms
  4. D
    Both sine and cosine terms
Question 39Single Answer
The Fourier transform of a function f(x) is related to its:
  1. A
    Spatial domain representation
  2. B
    Time domain representation
  3. C
    Frequency domain representation
  4. D
    Energy domain representation
Question 40Single Answer
The Laplace transform of a second derivative f''(t) is:
  1. A
    sF(s) + sf(0) + f'(0)
  2. B
    s²F(s) + sf(0) + f'(0)
  3. C
    sF(s) - sf(0) - f'(0)
  4. D
    s²F(s) - sf(0) - f'(0)
Question 41Single Answer
Parseval’s theorem for Fourier series relates:
  1. A
    The frequency in the time domain to the frequency in the frequency domain
  2. B
    The amplitude in the time domain to the amplitude in the frequency domain
  3. C
    The phase in the time domain to the phase in the frequency domain
  4. D
    The energy in the time domain to the energy in the frequency domain
Question 42Single Answer
The Laplace transform of cos(at) is:
  1. A
    a/(s² - a²)
  2. B
    a/(s² + a²)
  3. C
    s/(s² - a²)
  4. D
    s/(s² + a²)
Question 43Single Answer
The Laplace transform is used in solving the heat conduction equation to:
  1. A
    Transform the spatial variable
  2. B
    Transform the time variable
  3. C
    Transform the temperature variable
  4. D
    Transform the boundary conditions
Question 44Single Answer
The Fourier series of a periodic function converges to:
  1. A
    Zero at discontinuities
  2. B
    The function’s maximum value at discontinuities
  3. C
    The function’s minimum value at discontinuities
  4. D
    The function’s average value at discontinuities
Question 45Single Answer
The Fourier transform of a rectangular pulse is:
  1. A
    A sinc function
  2. B
    A delta function
  3. C
    A Gaussian function
  4. D
    A cosine function
Question 46Single Answer
The Fourier transform is used in solving the wave equation to:
  1. A
    Transform the boundary conditions
  2. B
    Transform the time variable
  3. C
    Transform the wave amplitude
  4. D
    Transform the spatial variable
Question 47Single Answer
The Fourier series expansion of a square wave contains:
  1. A
    Only odd harmonics
  2. B
    Only even harmonics
  3. C
    Both odd and even harmonics
  4. D
    No harmonics
Question 48Single Answer
The Laplace transform of a periodic function with period T can be expressed using:
  1. A
    The transform of the derivative
  2. B
    The transform of the entire function
  3. C
    The transform of one period
  4. D
    The transform of the integral
Question 49Single Answer
The Fourier series of a function converges if the function is:
  1. A
    Differentiable everywhere
  2. B
    Continuous everywhere
  3. C
    Piecewise continuous and has a finite number of discontinuities
  4. D
    Integrable everywhere
Question 50Single Answer
The Laplace transform is used to solve initial value problems because it:
  1. A
    Incorporates initial conditions automatically
  2. B
    Eliminates initial conditions
  3. C
    Requires boundary conditions
  4. D
    Requires final conditions
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