List of top Questions asked in CUET (PG)

If the resonance frequency of an acoustic system is 300Hz and the half-power frequencies are 150Hz and 450Hz, the quality factor is:

Which of the following statements are true for ideal PN junction current voltage relationship?
(A) The abrupt depletion layer approximation applies.
(B) The Maxwell-Boltzmann approximation applies to carrier statistics.
(C) The concept of low injection applies.
(D) The total current is not constant throughout the entire pn structure.
Choose the correct answer from the options given below:

	LIST I		LIST II
A.	∇ ⋅ E = ρ/ε₀		I. Gauss's Law in magnetostatics
B.	∇ ⋅ B = 0		II. Faraday's Law of electromagnetic Induction
C.	∇ × E = - ∂B/∂t		III. Gauss's Law in electrostatics
D.	∇ × B = μ₀J + μ₀ε₀ ∂E/∂t		IV. Modified Ampere's Law

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Higher-energy photons are scattered from electrons initially at rest. Assume the photons are backscattered ($\theta = 180^\circ$) and their energies are much higher than the electron's rest mass energy. The wavelength shift will be \[ \frac{h}{m_e c} = 2.43 \times 10^{-12} \, \text{m}: \]

For Fresnel half period zones:
(A) The amplitude of disturbance is directly proportional to the area of the zone.
(B) The radii of half period zones are directly proportional to the square root of the natural number.
(C) The area of each zone is directly proportional to the wavelength of the light.
(D) The radii of half period zones are directly proportional to the square root of the wavelength of the light.
Choose the correct answer from the options given below:

In an LCR circuit, the current and emf differ in phase by $\Phi$. The value of $\Phi$ is:

Let f(x) be a differentiable function for all values of x with f′(x) ≤ 32 and f(3) = 21, then the maximum value of f(8) is:

The principal value of \( i^i \) is:

Match List I with List II:

List I	List II
A. Fraunhofer Diffraction	I. Interaction of the light waves from two different wave fronts.
B. Fresnel Diffraction	II. The distance between the source and the screen are effectively at infinite distance.
C. Interference of Light	III. It’s a phenomenon in which the wave vibrations are restricted to a particular direction in a plane.
D. Polarization of Light	IV. The source and screen or both are at finite distances from the aperture or obstacle.

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Statement (I): The determinant of a matrix A and its transpose A^T are equal.
Statement (II): The determinant of the product of two matrices A and B is the product of their determinants.
In light of the above statements, choose the most appropriate answer from the options given below:

In order to introduce a phase difference of $\pi/2$ in a Quarter wave plate, the thickness of the crystal should have a value of... (Given: wavelength = $5893 \times 10^{-10} \, \text{m}$, refractive index for O-ray is $1.65836$ and refractive index for E-ray is $1.48641$)

The asymptote of the spiral \( r = \frac{\theta}{\sin \theta} \) is:

Let P and Q be two matrices such that P Q = 0 and P is non-singular, then
(a) Q is also non-singular
(b) Q = 0
(c) Q is singular
(d) P = Q
Choose the correct answer from the options given below:

Given below are two statements:
Statement (I): The nth derivative of the function \( e^x \cos x \cos 2x \) is:
\[\frac{e^x}{2} \big[ (10^n) \cos(3x + n \tan^{-1} 3) + (2^n) \cos(x + \frac{n \pi}{4}) \big]\]
Statement (II): The nth derivative of the function \( x \cos 2x \cos 3x \) is:
\[\frac{1}{2} \big[ (2^n) \cos(2x + \frac{n \pi}{2}) + (4^n) \cos(4x + \frac{n \pi}{2}) + (6^n) \cos(6x + \frac{n \pi}{2}) \big]\]
In light of the above statements, choose the most appropriate answer from the options given below:

Statement (I): If a given component of the total applied force vanishes, the corresponding component of the linear momentum is not conserved.
Statement (II): If the component of applied torque along the axis of rotation vanishes, then the component of total angular momentum along the axis of rotation is conserved.
Choose the most appropriate answer:

Solve the following differential equation by the method of Laplace transform: \[ y''' + 2y'' - y' - 2y = 0 \] given that $y(0) = 0$, $y'(0) = 0$, and $y''(0) = 6$.
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Let \( a \) be the magnitude of the directional derivative of the function: \[\phi(x, y) = \frac{x}{x^2 + y^2}\] along a line making an angle of \( 45^\circ \) with the positive x-axis at the point \( (0, 2) \). Then, the value of \( 1/a^2 \) is:

	LIST I		LIST II
A.	Bipolar npn transistor operate in the cut-off mode.		I. The base-emitter is reverse biased and
B.	Bipolar npn transistor operate in the saturation mode.		II. Both the base-emitter and base
C.	Bipolar npn transistor operate in the inverse active mode.		III. The base-emitter is forward biased
D.	Bipolar npn transistor operate in the forward active mode.		IV. Both the base-emitter and bas

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	LIST I (Name of the surface)		LIST II
A.	Ellipsoid		I. x²/a² + y²/b² + z²/c² = 1
B.	Hyperboloid of one sheet		II. x²/a² - y²/b² - z²/c² = 1
C.	Hyperboloid of two sheets		III. -x²/a² + y²/b² + z²/c² = 1
D.	Central conicoid		IV. x²/a² + y²/b² + z = 1

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Match List I with List II:

LIST I	LIST II
A. Maxwell's First Equation	I. Modified Ampere's Law
B. Maxwell's Second Equation	II. Faraday's Laws of Electromagnetic Induction
C. Maxwell's Third Equation	III. Gauss Law in Electrostatics
D. Maxwell's Fourth Equation	IV. Gauss Law in Magnetostatics

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If A is a skew-symmetric matrix of odd order, then the determinant of A is:

If \( (\sqrt{3} + 1)^n + (\sqrt{3} - 1)^n = 4 \), then the value of \( n \) is:

Given below are two statements:
{Statement (I):} Two families of curves such that every member of either family cuts each member of the other family at right angles are called orthogonal trajectories of each other.
{Statement (II):} The orthogonal trajectories of the curve \( xy = c \) is \( y = \frac{1}{x} \).
Choose the most appropriate answer from the options given below: