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A two-state quantum system has energy eigenvalues ±𝜖 corresponding to the normalized states |𝜓±⟩. At time 𝑡=0, the system is in quantum state 1√2[|𝜓+⟩+ |𝜓−⟩]. The probability that the system will be in the same state at 𝑡=ℎ/(6𝜖) is ________ (up to two decimal places).0 AnswerLet |ψ1 〉 = ( 1 0 ), |ψ2 〉 = ( 0 1 ) represent two possible states of a two-level quantum system. The state obtained by the incoherent superposition of |ψ1 〉 and |ψ2 〉 is given by a density matrix that is defined as ρ ≡ c1 |ψ1 〉〈ψ1| + c2 |ψ2 〉〈ψ2|. If c1 = 0.4 and c2 = 0.6, the matrix element ρ22 (rounded off to one decimal place) is _________0 AnswerConsider a causal second-order system with the transfer function G(s) = 1/ (1 + 2s + s 2) with a unit-step R(s) = 1/ s as an input. Let C(s) be the corresponding output. The time taken by the system output c(t) to reach 94% of its steady-state value lim t→∞ c(t), rounded off to two decimal places, is:0 AnswerThe Hamiltonian of a system is H. The fourth order contribution to the ground state energy of H is γε 4 . The value of γ (rounded off to three decimal places) is _________0 AnswerConsider two systems A and B each having two distinguishable particles. In both the systems, each particle can exist in states with energies 0, 1, 2 and 3 units with equal probability. The total energy of the combined system is 5 units. Assuming that the system A has energy 3 units and the system B has energy 2 units, the entropy of the combined system is kB ln λ. The value of λ is________________0 AnswerIn a closed piston-cylinder system, methane was observed to obey the following equation of state P V nb nRT ( ) where b = 0.029 m3 /mol. The temperature and volume are 500 oC and 5 m3 respectively for 100 moles of methane. At this state of the system, the isobaric rate of change of temperature with volume (in oC/m3 ) is __________ (rounded off to second decimal place).0 AnswerA microcanonical ensemble consists of 12 atoms with each taking either energy 0 state, or energy 𝜖 state. Both states are non-degenerate. If the total energy of this ensemble is 4𝜖, its entropy will be ________ 𝑘𝐵 (up to one decimal place), where 𝑘𝐵 is the Boltzmann constant.1 AnswerIn a given year in India, official poverty lines are higher in some States than in others because0 AnswerIn a given year in India, official poverty lines are higher in some States than in others because0 AnswerIn a system, there are three types of resources: 0 E, F and G. Four processes P0, P1, P2 and P3 execute concurrently. At the outset, the processes have declared their maximum resource requirements using a matrix named Max as given below. For example, Max[P2,F] is the maximum number of instances of F that P2 would require. The number of instances of the resources allocated to the various processes at any given state is given by a matrix named Allocation.0 Answer In a given year in India, official poverty lines are higher some States than in others because 0 AnswerLet the state-space representation of an LTI system be ẋ(t) = A x(t) + B u(t), y(t) = C x(t) + d u(t) where A, B, C are matrices, d is a scalar, u(t) is the input to the system, and y(t) is its output. Let B = [0 0 1]^T and d = 0. Which one of the following options for A and C will ensure that the transfer function of this LTI system is:0 AnswerName and state the aspect of financial management that enables to foresee the fund requirements both in terms of the quantum and the timings. -CBSE business studies 2016 class 111 AnswerConsider a two-state system at thermal equilibrium having energies 0 and 2kBT for which the degeneracies are 1 and 2, respectively. The value of the partition function at the same absolute temperature T is_______. (Round off to two decimal places) (kB is the Boltzmann constant)0 AnswerThe Hamiltonian for a quantum harmonic oscillator of mass m in three dimensions is H = p^2/2m + 1/2 mω^2 r^2 where ω is the angular frequency. The expectation value of r^2 in the first excited state of the oscillator in units of ħ/mω (rounded off to one decimal place) is __________0 AnswerThe Head of State in the Parliamentary System of government is called - CBSE class 8 civics 1 Answer(Gate 2018 Mechanical engineering)An ideal gas undergoes a process from state 1 ( T1 = 300 K, 1 p = 100 kPa) to state 2 ( T2 = 600 K, 2 p = 500 kPa). The specific heats of the ideal gas are : cp = 1 kJ/kg-K and cv = 0.7 kJ/kg-K. The change in specific entropy of the ideal gas from state 1 to state 2 (in kJ/kg-K) is ___________0 AnswerThe Hamiltonian operator for a two-level quantum system is:0 AnswerConsider an arbitrary set of CPU-bound processes with unequal CPU burst lengths submitted at the same time to a computer system. Which one of the following process scheduling algorithms would minimize the average waiting time in the ready queue? Gate1 AnswerGive an example of a general resource graph that cannot be completely reduced, but which represents a system state that is free from deadlock?.1 Answer
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