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Topic:- DU_J18_PHD_PHY_Topic01
- An infinite long wire carries a time independent current I=1 Ampere. The wire is bent and a semi-circle detour of radius R = 1 cm is made with the centre at the origin. The magnitude of magnetic field at the origin is [Question ID = 19633]
- 25 μο Τ / 4π [Option ID = 48525]
- 2.5 μο Τ [Option ID = 48523]
- 25 μο Τ / π [Option ID = 48524]
- 2.5 μο Τ / 4π [Option ID = 48526]
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- In a rotational structure of electronic bands (the transition between rotational levels of the different electronic levels) having larger rotational constant of the upper electronic level than the lower one, [Question ID = 19617]
- band head appears in R-branch [Option ID = 48460]
- band head appears in P-branch [Option ID = 48459]
- band head appears in Q-branch [Option ID = 48461]
- no band head appears [Option ID = 48462]
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- In a bistable multivibrator, commutating capacitors are used to [Question ID = 19610]
- change the frequency of the output [Option ID = 48433]
- provide a.c. coupling [Option ID = 48432]
- increase the base storage output [Option ID = 48434]
- increase the speed of response [Option ID = 48431]
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- In the Geiger Muller (GM) region, when the applied voltage is increased, which of the following happens: [Question ID = 19623]
- The pulse amplitude increases but the counting rate remains nearly constant. [Option ID = 48483]
- The pulse amplitude remains nearly constant and the counting rate increases. [Option ID = 48484]
- Both the pulse amplitude and the counting rate increases. [Option ID = 48485]
- Both the pulse amplitude and counting rate remain nearly constant. [Option ID = 48486]
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- In the absorption spectra of harmonic vibrating diatomic oscillator, only one spectral line is observed. It is because [Question ID = 19618]
- Separation between any two adjacent E-level is same [Option ID = 48465]
- All other lines are very weak in intensity [Option ID = 48466]
- Only one molecule is present in a particular E-level [Option ID = 48464]
- Only one transition is possible from ground E level to higher E level [Option ID 48463]
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- Magnetic field required to bend a non-relativistic charge particle of energy E in an arc of radius R is [Question ID = 19632]
- inversely proportional to √E and directly proportional to R. [Option ID = 48520]
- directly proportional to E and inversely proportional to R². [Option ID = 48521]
- directly proportional to √E and inversely proportional to R. [Option ID = 48519]
- inversely proportional to √E and directly proportional to R². [Option ID = 48522]
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- The number of ways in which two particles can be distributed in six states, if the particles are indistinguishable and only one particle can occupy any one state, is [Question ID = 19612]
- 31 [Option ID = 48440]
- 36 [Option ID = 48439]
- 21 [Option ID = 48442]
- 25 [Option ID = 48441]
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- Consider a 2-D harmonic oscillator with mass m and frequency w. A perturbation H' = bxy is applied to the system, where x and y are the two spatial coordinates. The first order correction to the ground state energy is [Question ID = 19635]
- 0 [Option ID = 48531]
- bħ / 2mw [Option ID = 48534]
- bħ / 2mw [Option ID = 48532]
- bħ / 2mw [Option ID = 48533]
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- An electron of charge -e is decelerated at a constant rate from an initial velocity vo to rest over a distance d (vo << c). The energy lost to radiation is given by [Question ID = 19630]
- μο e² vo³ / 6 πcd [Option ID = 48512]
- μο e² vo³ / 3 πcd [Option ID = 48511]
- Cannot be determined from the information supplied. [Option ID = 48514]
- μο e² vo³ / 12 πcd [Option ID = 48513]
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- The lattice constant and saturation magnetization of BCC iron at 0 K are 2.87 Å and 1950 kAm⁻¹, respectively. The net magnetic moment per iron atom in the crystal is [Question ID = 19597]
- 2.30 x 10⁻²³ A m² [Option ID = 48380]
- 0.67 x 10⁻²¹ A m² [Option ID = 48382]
- 7.30 x 10⁻²⁵ A m² [Option ID = 48379]
- 1.87 x 10⁻²² A m² [Option ID = 48381]
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- Consider the density matrix of a two level system given by p= |1⟩⟨1| + |2⟩⟨2|. Then [Question ID = 19615]
- The expectation value of the operator O₂ = |1⟩⟨2| + |2⟩⟨1| is ħ / 2 [Option ID = 48452]
- The expectation value of the operator O₁ = |1⟩⟨1| - |2⟩⟨2| is ħ / 2 [Option ID = 48451]
- The system is in a pure state. [Option ID = 48453]
- (O₁) = 0, where O₁ = |1⟩⟨1| - |2⟩⟨2|. [Option ID = 48454]
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- A quantum-mechanical particle of mass m and charge q is subjected to a potential of the form V(x) = ½ mw²x², where w is a constant. An electric field E = E₀x is now switched on (E₀ being a constant). What is the consequent change, upto second order in E₀, in the energy of the second excited state? [Question ID = 19594]
- qE₀ / mħω [Option ID = 48368]
- q²E₀ ⟨x²⟩ / (mħω)² [Option ID = 48370]
- q²E₀ / 2mw² [Option ID = 48367]
- 2q²E₀ / mω [Option ID = 48369]
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- For the infinite square well potential the unperturbed wave functions are ψ(x) = √(2/a) sin(nπ/a x) If the floor of the well is raised by V₀, the first order correction to the energy is [Question ID = 19591]
- V₀ / 4 [Option ID = 48358]
- V₀ / 2 [Option ID = 48356]
- V₀ / 3 [Option ID = 48357]
- V₀ [Option ID = 48355]
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- Lead (Pb) starts superconducting at 7.19 K when the applied magnetic field is zero. When a magnetic field of 0.074 Tesla is applied at 2 K, superconductivity disappears. The critical magnetic field for Lead (Pb) is [Question ID = 19599]
- 0.04 T [Option ID = 48388]
- 0.08 T [Option ID = 48390]
- 0.034 T [Option ID = 48387]
- 0.068 T [Option ID = 48389]
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- If A and B are two linear operators, then the commutator bracket [A, B⁻¹] is equal to [Question ID = 19586]
- A⁻¹[A, B] B⁻¹ [Option ID = 48335]
- -A⁻¹[A, B] A⁻¹ [Option ID = 48336]
- B⁻¹[A, B] A⁻¹ [Option ID = 48337]
- -B⁻¹[A, B] B⁻¹ [Option ID = 48338]
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- For a simple harmonic oscillator of mass m and angular frequency w, let |n⟩ represent the n-th energy eigenstate so that H |n⟩ = ħω (n + ½) |n⟩. The physical state at time t = 0 is represented by |ψ(0)⟩ = |2⟩ - |3⟩ - |1⟩. If one makes a measurement of the energy of the system at any subsequent time t, the probability of finding the energy to be 3ħω/2: [Question ID = 19589]
- depends on time t. [Option ID = 48350]
- is ½ [Option ID = 48348]
- is 1/6. [Option ID = 48349]
- is 0. [Option ID = 48347]
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- For temperatures 10 K and 20 K, a superconductor has the critical magnetic field as 0.15 Tesla and 0.60 Tesla, respectively. The transition temperature for this superconductor in Kelvin is [Question ID = 19596]
- 23.3 [Option ID = 48378]
- 15.0 [Option ID = 48376]
- 22.4 [Option ID = 48377]
- 4.2 [Option ID = 48375]
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- A theory has equally spaced nondegenerate energy levels starting from Emin = E₀ all the way upto E∞. The system of many such particles is at equilibrium at a temperature T. If the average energy-squared of the particles is given by ⟨E²⟩ = 5E₀², What is T? [Question ID = 19614]
- T = E₀/2kʙ [Option ID = 48449]
- T = 2E₀/kʙ [Option ID = 48448]
- T = 3E₀/2kʙ [Option ID = 48450]
- T = E₀/kʙ [Option ID = 48447]
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- The Hamiltonian for a spin ½ particle of mass m in an external field is given by H = p²/2m + g(t)σ.p where g(t) is a time-dependent coupling constant and σ are the Pauli matrices. Which of the following statements is true? [Question ID = 19590]
- The energy and all the components of the spin angular momentum of the particle are conserved. [Option ID = 48351]
- The linear momentum and all the components of the spin angular momentum of the particle are conserved. [Option ID = 48354]
- The linear momentum and the magnitude of the spin angular momentum of the particle are conserved.
- The linear momentum and the energy of the particle are conserved. [Option ID = 48352]
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- A solid contains N spin-half magnetic atoms. At sufficiently high temperatures, the atoms are randomly oriented, while at sufficiently low temperatures, they are perfectly aligned. The heat capacity is given by C(T) = C₀(e^(T₀/T) - 1)⁻¹, T₀ ≤ T ≤ 3T₀, 0, Otherwise where C₀ and T₀ are constants. Determine the maximum value of C₀. [Question ID = 19613]
- NkB ln2 / (2-ln3) [Option ID = 48445]
- NkB ln2 / 2 [Option ID = 48443]
- 2NkB ln2 / (2+ln3) [Option ID = 48446]
- NkB ln2 / ln3 [Option ID = 48444]
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- Green's function corresponding to the Laplacian operator ∇² is G(r, r') = 1 / (4π|r - r'|) The value of φ(0) corresponding to the solution of the inhomogeneous differential equation ∇²φ = A exp(-βr) / r (where A and β are positive numbers) is equal to, [Question ID = 19625]
- 0 [Option ID = 48491]
- A / 4πβ [Option ID = 48494]
- A / β [Option ID = 48492]
- A / πβ [Option ID = 48493]
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- A star is pulsating isotropically. Its gravitational force on any body, at distances much larger than its own mean radius, is given by F(r) = (k/r) + (a/r²) r̂ where k and a are positive constants. Which of the following is true about the motion of the body? [Question ID = 19604]
- Any bounded motion is described by a precessing ellipse. [Option ID = 48407]
- No bounded motion exists at all. [Option ID = 48410]
- Any bounded motion is described by a pulsating ellipse. [Option ID = 48408]
- Any bounded motion is still in an elliptical path, but the parameters of the ellipse are shifted from those in the Newtonian case. [Option ID = 48409]
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- The Hamiltonian for a particle in one dimension is given by H(x, p) = p²/2m + λpx + ½λ²x² where m, λ are constants. The corresponding Lagrangian is [Question ID = 19603]
- L = ½m(ẋ)² - λmẋx - ½λ²x² [Option ID = 48405]
- L = ½m(ẋ - λx)² - λmẋx - ½λ²x² [Option ID = 48406]
- L = ½m(ẋ - λx)² - ½λ²x² [Option ID = 48404]
- L = ½m(ẋ)² - ½λ²x² [Option ID = 48403]
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- Consider the 2π -periodic function f(x) defined as f(x) = x(π - x), x ∈ [0,π] x(x - π), x ∈ [π,0] Which of the following is true? [Question ID = 19627]
- f(x) = - Σ(k=0 to ∞) 4π / (2k+1)³ sin[(2k+1)x] [Option ID = 48502]
- f(x) = Σ(k=0 to ∞) 8 / πk sin(kx) [Option ID = 48500]
- f(x) = Σ(k=0 to ∞) 4 / πk² sin(kx) + cos(kx) [Option ID = 48499]
- f(x) = Σ(k=0 to ∞) 4π / (2k+1)⁸ sin[(2k+1)x] [Option ID = 48501]
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- In 3-dimensional space, a particle of mass m moves in a potential A cos²βr where r is the distance of the particle from the origin, A and β are real constants. Which of the following statements are correct? [Question ID = 19600]
- The motion is periodic in r with an oscillation distance π/β. [Option ID = 48394]
- The motion is periodic in r with an oscillation distance 2π/β. [Option ID = 48392]
- The trajectory of the particle is always confined to some plane passing through the origin. [Option ID = 48391]
- The radial momentum pᵣ is conserved because of the periodic nature of the potential. [Option ID = 48393]
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- The ⁹⁰Sr → ⁹⁰Y → ⁹⁰Zr chain decays with a half-life of 28 years and 64 hours, respectively. If 1g of pure ⁹⁰Sr is allowed to decay, then the ratio (Nsr/Ny) after 1 hour is [Question ID = 19621]
- 3.56 × 10⁴ [Option ID = 48477]
- 3.56 × 10⁵ [Option ID = 48475]
- 4.56 × 10⁴ [Option ID = 48478]
- 4.56 × 10⁵ [Option ID = 48476]
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- For the electronic configuration 2p3d, the complete spectroscopic terms in Russel-Saunders coupling scheme are [Question ID = 19587]
- ¹P, ¹D, ¹F, ¹G, ¹H, ³P, ³D, ³F, ³G, ³H [Option ID = 48339]
- ²P, ²D, ²F, ⁴P, ⁴D, ⁴F [Option ID = 48342]
- ²S, ²P, ²D, ²F, ⁴S, ⁴P, ⁴D, ⁴F [Option ID = 48340]
- ¹P, ¹D, ¹F, ³P, ³D, ³F [Option ID = 48341]
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- The Hamiltonian of a two-level system is given by H = ½ħωσz. At time t = 0 the system is in the eigenstate of σz having the largest eigenvalue. The expectation values ⟨σx⟩(t), ⟨σy⟩(t) and ⟨σz⟩(t) (where σᵢ are Pauli matrices) are respectively [Question ID = 19592]
- sin(ωt/2), 0, and cos(ωt/2) [Option ID = 48361]
- cos(ωt/2), sin(ωt/2) and 0 [Option ID = 48359]
- 0, cos(ωt/2) and sin(ωt/2) [Option ID = 48360]
- cos(ωt/2), 0, and sin(ωt/2) [Option ID = 48362]
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- The Lagrangian for a system is given by L = q₁q₂ - ω²q₁q₂ where ω is a constant and qᵢ = d/dt qᵢ. L is invariant under the following transformations q₁ → e^(α)q₁ and q₂ → e^(α)q₂, α is a constant. The conserved quantity corresponding to this symmetry transformation is [Question ID = 19601]
- q₁q₁ + q₂q₂ [Option ID = 48398]
- q₁q₂ - q₂q₁ [Option ID = 48395]
- q₁q₂ + q₂q₁ [Option ID = 48396]
- q₁q₁ - q₂q₂ [Option ID = 48397]
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- An integral is defined to be, I = ∫(0 to ∞) sinx / x dx. Then I is equal to: [Question ID = 19628]
- π / cos√2 [Option ID = 48506]
- π / 2 [Option ID = 48503]
- 2 / π cos√2 [Option ID = 48505]
- π / cos√2 [Option ID = 48504]
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- In the given astable multivibrator, the frequency of the square wave generated is [Question ID = 19607]
- 32.4 kHz [Option ID = 48421]
- 3.5 kHz [Option ID = 48419]
- 324 Hz [Option ID = 48422]
- 3.5 Hz [Option ID = 48420]
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- A point mass m is attached, through a massless incompressible rod of length l, to a fixed point. The mass is allowed to have any motion consistent with the above. If θ be the instantaneous angle of the rod with the vertical, which of the following is necessarily true? (Here κ ≥ 0 is an arbitrary constant) [Question ID = 19605]
- θ̈ + κ/l sinθ = 0 [Option ID = 48412]
- θ̈ + (κ sinθ) / (ml²) + (g/l) sinθ = 0 [Option ID = 48413]
- θ̈ + (g/l) sinθ = 0 [Option ID = 48411]
- θ̈ + (κcosθ) / (ml²) + (g/l) sinθ = 0 [Option ID = 48414]
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- Neutrons are captured by ¹⁰B to form ¹¹B, which breaks into an alpha particles and the ⁷Li nucleus. Then, the kinetic energy of the ⁷Li and the Q value of the reaction are (Given M(¹⁰B) = 10.01611 amu; M(n) = 1.008987 amu; M(⁷Li) = 7.01822 amu; M(⁴He)= 4.003879 amu) [Question ID = 19620]
- 1.01 MeV and 2.59 MeV [Option ID = 48473]
- 1.78 MeV and 2.79 MeV [Option ID = 48472]
- 1.01 MeV and 2.79 MeV [Option ID = 48471]
- 1.78 MeV and 2.59 MeV [Option ID = 48474]
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- An ultrafast laser produces a sequence of pulses with a repetition time of T. The pulse is a wavepacket of energy E and a central wavelength of λ. The laser beam hits a mirror at an angle θ to the normal and is reflected. The average force on the mirror is [Question ID = 19629]
- None of these [Option ID = 48510]
- 2 E cos θ / cT [Option ID = 48509]
- E cos θ / cT [Option ID = 48507]
- E cos 2θ / cT [Option ID = 48508]
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- The canonical partition function for a system of N non interacting particles is given by (αkT)³ᴺ, where α and k are constants. The internal energy of the system is (large N) [Question ID = 19616]
- 3NkT [Option ID = 48457]
- NkT / 2 [Option ID = 48455]
- 2NkT [Option ID = 48456]
- 6NkT [Option ID = 48458]
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- The acceleration of the system given in the figure, where k is the spring constant and x is the displacement relative to the relaxed length of the spring, is [Question ID = 19626]
- (-kx + m₁g) / (m₁ + m₂) [Option ID = 48497]
- (kx - m₂g) / (m₁ + m₂) [Option ID = 48496]
- (-kx + m₂g) / (m₁ + m₂) [Option ID = 48495]
- (kx - m₁g) / (m₁ + m₂) [Option ID = 48498]
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- A system, in three dimensions, is described by the Lagrangian L = ½m(ẋ² + ẏ² + ż²) + ẋ sin(t) - ½k(x² + y²) + x cos(t) where k is constant. Of energy (E), linear momentum (p) and angular momentum (J), which are conserved? [Question ID = 19602]
- p₂ alone [Option ID = 48399]
- E, p, and J. alone. [Option ID = 48402]
- E, p, J [Option ID = 48401]
- p alone [Option ID = 48400]
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- For a simple harmonic oscillator of mass m and angular frequency w, if |n⟩ represents the n-th energy eigenstate, then the expectation value ⟨n|p²|n⟩ is equal to: [Question ID = 19588]
- mħnw [Option ID = 48345]
- mħw (n + ½) [Option ID = 48343]
- mħw (2n + 1) [Option ID = 483
This download link is referred from the post: DUET Last 10 Years 2011-2021 Question Papers With Answer Key || Delhi University Entrance Test conducted by the NTA
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