List of top Questions asked in CUET (PG)

Given below are two statements:
Assertion (A): Lyapunov direct method states that the equilibrium point of a system is asymptotically stable if there exists a positive definite function whose derivative is negative definite.
Reason (R): The equilibrium point of \(\dfrac{dx}{dt}=-y,\ \dfrac{dy}{dt}=x\) is asymptotically stable.

The equation of line passing through \((-3,5)\) and perpendicular to the line through the points \((2,5)\) and \((-3,6)\) is:

Given below are two statements:
Assertion (A): If a function \(f(x)\) is continuous in \([a,b]\) and differentiable in \((a,b)\), then there exists a point \(c\in(a,b)\) such that \(\dfrac{f(b)-f(a){b-a}=f'(c)\).
Reason (R): This is the statement of Cauchy's mean value theorem.}

Which of the following are indeterminate forms?
A. \(0^0\),
B. \(1^\infty\),
C. \(\infty^0\),
D. \(0\times\infty\), E. \(1\cdot\infty\).

Which of the following quantity is not conserved in inelastic collision?

Consider the following differential equations which are obtained by successive differentiations. Choose the correct answer from the options given below.

The volume of the solid of revolution of the cardioid \(r=a(1+\cos\theta)\) about the initial line is:

Which motion is simple harmonic motion?

Evaluate \(\iint_S \vec{A}\cdot \hat{n}\,dS\), where \(\vec{A}=2y\hat{i}+yz\hat{j}+xz\hat{k}\) and \(S\) is the surface of the region bounded by \(x=0,\ y=0,\ z=0,\ y=3\) and \(x+2z=6\).

Given below are two statements:
Assertion (A): In photoelectric effect there is no time lag \((\sim10^{-9}s)\) between incidence of photon and emission of photoelectrons.
Reason (R): This is because electromagnetic wave energy is concentrated in photons and not spread out, so there should be no delay in the emission of electrons.

Which of the following is correct in Compton effect?
A. X-ray photon strikes an electron which is at rest,
B. Maximum Compton shift is few metres,
C. Maximum Compton shift is \(0.0484\ \text{\AA}\),
D. An electron strikes on metal surface.

Calculate the entropy change in the following. Given latent heat of steam is \(540\ \text{cal/g}\), latent heat of ice is \(80\ \text{cal/g}\).
A. \(10g\) of water at \(100^\circ C\) converted to steam at same temperature,
B. \(20g\) of water at \(100^\circ C\) converted to steam at same temperature,
C. \(1g\) of ice at \(0^\circ C\) converted into water at \(0^\circ C\),
D. \(10g\) of ice at \(0^\circ C\) converted into water at \(0^\circ C\).

Which of the following is/are correct \(Tds\) equation?

An iron furnace radiates \(42.5\) calories per second through an opening of cross-section \(1\ \text{cm}^2\). If the relative emittance of the furnace is \(0.80\), the temperature of furnace is given Stefan's constant \(\sigma=1.36\times10^{-8}\ \text{cal/m}^2\text{s K}^4\):

Which of the following is incorrect thermodynamical relation of Maxwell?

In Newton's Ring experiment with reflected light, the correct vertically downward arrangement of equipments is:
A. Microscope, Glass plate at \(45^\circ\), Plano-convex lens, Plane glass plate.
B. Plano-convex lens, Microscope, Plane glass plate.
C. Glass plate at \(60^\circ\), Microscope, Plano-convex lens.
D. Microscope, Plane glass plate, Plano-convex lens.

Which of the following is reversible process?

One mole of an ideal gas expands isothermally to ten times its initial volume. The change in entropy in terms of \(R\) is:

Which of the following holds for coherence of light?
A. Coherence is mainly divided into temporal and spatial coherence,
B. Temporal coherence is directly related to finite bandwidth of source,
C. Spatial coherence is related to finite size of the source,
D. Spatial coherence is related to finite bandwidth of the source.

The direction in a uniaxial crystal along which the e-ray and o-ray travel with same speed is:

In a Michelson interferometer, \(100\) fringes cross the field of view when the movable mirror is moved through \(29.48\ \mu m\). The wavelength of light used is:

For a wave train of wavelength \(\lambda\) having \(N\) number of wave oscillations, the coherence length is:

Newton's Rings are formed when a plano-convex lens of large radius of curvature placed on a plane glass plate is illuminated with monochromatic light.

Given below are two statements:
Assertion (A): The Fraunhofer diffraction is produced by the interference between parallel rays. The Fraunhofer diffraction can be observed using two convex lenses.
Reason (R): The two convex lenses are used to observe Fraunhofer diffraction, one to make light from the source parallel and other to focus the light after diffraction on to the screen.

Which of the following are correct form of Maxwell's equation?
A. \(\vec{\nabla}\cdot\vec{B}=0\),
B. \(\vec{\nabla}\cdot\vec{E}=\dfrac{\rho}{\epsilon_0}\),
C. \(\vec{\nabla}\times\vec{E}=-\dfrac{\partial \vec{B}}{\partial t}\),
D. \(\dfrac{1}{2}\left(\epsilon_0E^2+\dfrac{B^2}{\mu_0}\right)=U\). Choose the correct answer from the options given below: