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Delhi University Entrance Test (DUET) 2020 Previous Year Question Paper With Answer Key

This post was last modified on 27 December 2020

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DUET Last 10 Years 2011-2021 Question Papers With Answer Key || Delhi University Entrance Test conducted by the NTA

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Topic:- PHY MSC S2

An atomic transition line with wavelength 350 nm is observed to be split into three components in a spectrum of light from a sunspot. Adjacent components are separated by 1.7 pm. Determine the strength of the magnetic field in the sunspot
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[Question ID = 6662]
1. 3 T [Option ID = 26642]
2. 0.03 T [Option ID = 26643]
3. 3.3 T [Option ID = 26644]
4. 0.3 T [Option ID = 26645]
Correct Answer :-

• 0.3 T [Option ID = 26645]
which one of the following is correct in respect of an electron and a proton having a same de-Broglie wavelength of 2 Å

[Question ID = 6663]
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1. Both have same kinetic energy [Option ID = 26646]
2. Both have same velocity [Option ID = 26647]
3. Both have same momentum [Option ID = 26648]
4. The kinetic energy of proton is more than that of electron [Option ID = 26649]
Correct Answer :-
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• Both have same momentum [Option ID = 26648]
If rp & rh are the radius and Ep & EH are the energy of an electron in the nth orbit of positronium atom and hydrogen atom respectively, then

[Question ID = 6664]
1. ? = 2 r? and Ep = ?/2 [Option ID = 26650]
2. ? = 2 r? and Ep = 2 ? [Option ID = 26651]
3. ? = 2 r? and Ep = ?/4 [Option ID = 26652]
4. ? = r and Ep = 2 ? [Option ID = 26653]
Correct Answer :-

• ?p = 2 r and Ep? = ?/2 [Option ID = 26650]
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An X-ray beam of wavelength 0.16 nm is incident on a set of planes of a certain crystal. The first Bragg reflection is observed for an incidence angle of 30°. What is the corresponding inter planar spacing?

[Question ID = 6669]
1. 0.16 nm [Option ID = 26670]
2. 0.67 nm [Option ID = 26671]
3. 1.02 nm [Option ID = 26672]
4. 0.89 nm [Option ID = 26673]
Correct Answer :-

• 0.16 nm [Option ID = 26670]

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What is the velocity of conduction electron of silver having Fermi energy 5.52 eV

[Question ID = 6670]
1. 1.39 x 10⁶ m/s [Option ID = 26674]
2. 2.39 x 10⁶ m/s [Option ID = 26675]
3. 0.89 x 10⁶ m/s [Option ID = 26676]
4. 0 [Option ID = 26677]
Correct Answer :-

• 1.39 x 10⁶ m/s [Option ID = 26674]
Given that a piece of n-type silicon contains impurity atoms, calculate the carrier concentration of silicon at room temperature. Given that the intrinsic electron concentration of silicon at room temperature is 1.6 × 10¹⁶ m^-3
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1. 3.2 x 10¹⁰ m^-3 [Option ID = 26678]
2. 2.5 x 10¹⁰ m^-3 [Option ID = 26679]
3. 1.5 x 10¹⁰ m^-3 [Option ID = 26680]
4. 3.2 x 10¹¹ m^-3 [Option ID = 26681]
Correct Answer :-

• 3.2 x 10¹⁰ m^-3 [Option ID = 26678]
The dispersion relation for a one-dimensional monoatomic lattice chain is given by the equation, w = vs|sin(^K/₂)|, where, 'a' is the interatomic spacing, K = ^2p/_? and vs has the dimension of velocity. The relation between the phase velocity Vp and group velocity Vg in the long wavelength limit is given by

[Question ID = 6674]
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1. Vp = Vg [Option ID = 26690]
2. Vp = 2Vg [Option ID = 26691]
3. Vp = Vg/2 [Option ID = 26692]
4. Vp ? Vg [Option ID = 26693]
Correct Answer :-
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• Vp = Vg [Option ID = 26690]
The largest wavelength of light falling on double slits separated by 1.5 µm, for which there is a first order maximum is in the,

[Question ID = 6676]
1. ultraviolet range [Option ID = 26698]
2. visible range [Option ID = 26699]
3. infrared range [Option ID = 26700]
4. X-ray range [Option ID = 26701]
Correct Answer :-

• infrared range [Option ID = 26700]
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In a multi-stage R-C coupled amplifier, the coupling capacitor

[Question ID = 6680]
1. limits the low frequency response [Option ID = 26714]
2. limits the high frequency response [Option ID = 26715]
3. reduces the amplitude of input signal [Option ID = 26716]
4. blocks d.c. component without affecting the frequency response [Option ID = 26717]
Correct Answer :-

• blocks d.c. component without affecting the frequency response [Option ID = 26717]

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An AM transmitter is coupled to an aerial. The input current is found to be 5 A. With modulation the current value increases to 5.9 A. The depth of modulation is

[Question ID = 6681]
1. 83.4% [Option ID = 26718]
2. 88.6% [Option ID = 26719]
3. 78.2% [Option ID = 26720]
4. 74.3% [Option ID = 26721]
Correct Answer :-

• 88.6% [Option ID = 26719]
Hexadecimal equivalent of a digital number 10011101 is
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[Question ID = 6683]
1. H913 [Option ID = 26726]
2. 9D [Option ID = 26727]
3. AE [Option ID = 26728]
4. 157 [Option ID = 26729]
Correct Answer :-

• 9D [Option ID = 26727]
If the doping concentration in a Si-Zener diode is increased, the Zener breakdown voltage

[Question ID = 6684]
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1. Decreases [Option ID = 26730]
2. Increases [Option ID = 26731]
3. Remains unchanged [Option ID = 26732]
4. Becomes broader [Option ID = 26733]
Correct Answer :-
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• Decreases [Option ID = 26730]
Which one of the following is an example of doubly magic nuclei

[Question ID = 6685]
1. ¹⁶O [Option ID = 26734]
2. ⁴⁸Ca [Option ID = 26735]
3. ¹²⁴Sn [Option ID = 26736]
4. ²⁰⁴pb [Option ID = 26737]
Correct Answer :-

• ⁴⁸Ca [Option ID = 26735]
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Which radiation has maximum ionization power?

[Question ID = 6686]
1. Alpha [Option ID = 26738]
2. Beta [Option ID = 26739]
3. Neutron [Option ID = 26740]
4. Gamma [Option ID = 26741]
Correct Answer :-

• Alpha [Option ID = 26738]

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For beta-minus decay, which statement is TRUE?

[Question ID = 6688]
1. Daughter nuclide atomic mass (AD) is more than that of the parent nuclide atomic mass (Ap) [Option ID = 26746]
2. Daughter nuclide atomic number (ZD) is same that of the parent nuclide atomic number (Zp) [Option ID = 26747]
3. Daughter nuclide neutron number (ND) is less than that of the parent nuclide neutron number (Np) [Option ID = 26748]
4. Daughter nuclide neutron number (ND) is same that of the parent nuclide neutron number (Np) [Option ID = 26749]
Correct Answer :-

• Daughter nuclide neutron number (ND) is less than that of the parent nuclide neutron number (Np) [Option ID = 26748]
The probability that student A solves the problem is 1/2, and that of B is 2/3. What is the probability that the problem is solved?
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[Question ID = 6689]
1. 4/6 [Option ID = 26750]
2. 1/3 [Option ID = 26751]
3. 5/6 [Option ID = 26752]
4. none of these [Option ID = 26753]
Correct Answer :-

• 5/6 [Option ID = 26752]
Are the three points whose position vectors are 2i+3j-4k, i-2j+3k and -7j+10k collinear?

[Question ID = 6690]
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1. Yes [Option ID = 26754]
2. No [Option ID = 26755]
3. Has both [Option ID = 26756]
4. None of these [Option ID = 26757]
Correct Answer :-
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• Yes [Option ID = 26754]
The number of independent fundamental solutions in n-th order ordinary differential equation is

[Question ID = 6692]
1. n-1 [Option ID = 26762]
2. n [Option ID = 26763]
3. n+1 [Option ID = 26764]
4. 2n [Option ID = 26765]
Correct Answer :-

• n [Option ID = 26763]
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If z1 = 2-3i and z2 = 4 + 6i then find ^z1/_z2

[Question ID = 6693]
1. -5/26-6i/13 [Option ID = 26766]
2. -5/26+6i/13 [Option ID = 26767]
3. 8+18i [Option ID = 26768]
4. 8-18i [Option ID = 26769]
Correct Answer :-

• -5/26-6i/13 [Option ID = 26766]

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The rank of the following matrix
| 1 2 2 |
| 2 1 1 |
| 3 6 6 | is

[Question ID = 6699]
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1. 1 [Option ID = 26790]
2. 2 [Option ID = 26791]
3. 3 [Option ID = 26792]
4. 4 [Option ID = 26793]
Correct Answer :-
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• 2 [Option ID = 26791]
Two Carnot engines X and Y are operating in series. The engine X receives heat at 1200 K and rejects to a reservoir at a temperature T. The second engine Y receives the heat rejected by X and in turn rejects to a heat reservoir at 300 K. Calculate the temperature T (in Kelvin) for the situation when the efficiency of the engines is same

[Question ID = 6704]
1. 600 K [Option ID = 26810]
2. 750 K [Option ID = 26811]
3. 0 [Option ID = 26812]
4. 450 K [Option ID = 26813]
Correct Answer :-

• 600 K [Option ID = 26810]
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A square conducting loop of mass m, side l and resistance R is dropped into a region with a uniform horizontal magnetic field B. B's direction is perpendicular to the plane of the falling loop. The loop will reach a terminal velocity v given by

[Question ID = 7330]
1. v = ^mgR/_(Bl)² [Option ID = 29314]
2. v = ^2mgR/_B²l² [Option ID = 29315]
3. v = ^mgR/_2B²l² [Option ID = 29316]
4. None of these [Option ID = 29317]
Correct Answer :-

• v = ^mgR/_(Bl)² [Option ID = 29314]

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An ideal inductor, a resistor of resistance R Ohms and a capacitor with adjustable capacitance are connected in series to an alternating voltage with an effective value of V Volts and with frequency of f Hz. The current flowing through the circuit when the capacitance of the capacitor is set to C₁ is the same as when the capacitance of the capacitor is set to C₂, C₂ > C₁. The inductance of the inductor L is given by

[Question ID = 7331]
1. ¹/_8p²f² ^C1+C2/_C1C2 [Option ID = 29318]
2. ¹/_8p²f² ^C1C2/_C1+C2 [Option ID = 29319]
3. ¹/_2pf ^C1C2/_C1-C2 [Option ID = 29320]
4. ¹/_2p²f²R (^C1C2/_(C1-C2)) / ^C1+C2 [Option ID = 29321]
Correct Answer :-

• ¹/_8p²f² ^C1+C2/_C1C2 [Option ID = 29318]
A cylinder of length L is made up of an inner core of steel of radius r1 and an outer sheath of copper of thickness r1. The resistivities of steel and copper are p₁ and p₂ respectively. The total resistance of the cylinder is
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[Question ID = 7332]
1. ^(P₁P₂)L/_{pr₁² (3P₁ + P₂)} [Option ID = 29322]
2. ^{(3P₁ + P₂)L}/_pr₁² [Option ID = 29323]
3. ^(P₁+P₂)L/_4pr₁² [Option ID = 29324]
4. Cannot be determined from the information provided above [Option ID = 29325]
Correct Answer :-

• ^(P₁P₂)L/_{pr₁² (3P₁ + P₂)} [Option ID = 29322]
A meter stick is at an angle of 45° to the x' axis in its rest frame. The rod moves with a speed of ^c/₂ along the +x direction w.r.t. a frame S. The length of the rod in S is

[Question ID = 7333]
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1. ^v3/₂ meters [Option ID = 29326]
2. ^v5/₃ meters [Option ID = 29327]
3. ^v2/₃ meters [Option ID = 29328]
4. ²/₃ meters [Option ID = 29329]
Correct Answer :-
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• ^v3/₂ meters [Option ID = 29326]
An AC generator with output V and frequency f is connected to the plates of an air filled parallel plate capacitor of plate area A and plate separation d. The maximum value of the displacement current is

[Question ID = 7334]
1. ^{2p e_o fVA}/_d [Option ID = 29330]
2. ^e_ofV/_d [Option ID = 29331]
3. ^{2p?e_o A}/_Vd [Option ID = 29332]
4. Cannot be determined from the information provided [Option ID = 29333]
Correct Answer :-

• ^{2p e_o fVA}/_d [Option ID = 29330]
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An electron enters a uniform magnetic field of flux density 1.2 Wb/m². Find the energy difference in (eV), between electrons having spins parallel and anti-parallel to the field. (Given: µ_B = 9.3 x 10^-24 J/T)

[Question ID = 7335]
1. 3.95 x 10^-5 eV [Option ID = 29334]
2. 13.95 x 10^-5eV [Option ID = 29335]
3. 23.95 x 10^-5 eV [Option ID = 29336]
4. 33.95 x 10^-5 eV [Option ID = 29337]
Correct Answer :-

• 13.95 x 10^-5eV [Option ID = 29335]

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Using the vector atom model, determine the possible values of the angular momentum of an electron in f- shell

[Question ID = 7336]
1. ^3v7/₂ h ^v35/₂h [Option ID = 29338]
2. ^2v7/₂ h ^v25/₂ h [Option ID = 29339]
3. ^5v7/₂ h ^v15/₂ h [Option ID = 29340]
4. ^7v5/₂h ^v7/₂ h ^v5/₂ [Option ID = 29341]
Correct Answer :-

• ^3v7/₂ h ^v35/₂h [Option ID = 29338]
The two eigenvalues of the matrix
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| 1 1 |
| 1 1 | are

[Question ID = 7337]
1. 2,0 [Option ID = 29342]
2. 1,1 [Option ID = 29343]
3. 1,2 [Option ID = 29344]
4. 0,1 [Option ID = 29345]
Correct Answer :-

• 2,0 [Option ID = 29342]

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The commutator, [x², p_x], is equal to

[Question ID = 7338]
1. ihx [Option ID = 29346]
2. 2ihx [Option ID = 29347]
3. 2ihp_x [Option ID = 29348]
4. Zero [Option ID = 29349]
Correct Answer :-

• ihx [Option ID = 29346]
A particle of mass m is confined in the ground state of a one dimensional box extending from x = -^l/₂ to x = +^l/₂. The wave function of the particle in this state is h. The energy eigenvalue corresponding to
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[Question ID = 7339]
1. ^{h² p²}/_32mL² [Option ID = 29350]
2. ^{h² p²}/_{2 mL²} [Option ID = 29351]
3. ^{h² p²}/_{4 mL²} [Option ID = 29352]
4. ^2p²/_16mL² [Option ID = 29353]
Correct Answer :-

• ^{h² p²}/_32mL² [Option ID = 29350]
The normalized wave functions ?₁ and ?₂, correspond to the ground state and the first excited states of a particle in a potential. The operator Â acts on the wave functions as Â?₁ = ?₂ and Â?₂ = ?₁. The expectation value of the operator Å for the state ? = (3?₁ + 4?₂)/5 is

[Question ID = 7340]
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1. 0.96 [Option ID = 29354]
2. 0.32 [Option ID = 29355]
3. 0 [Option ID = 29356]
4. 0.75 [Option ID = 29357]
Correct Answer :-
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• 0.96 [Option ID = 29354]
The primitive translation vector of a two-dimensional lattice are a = 2î + î, b = 2j. The primitive translation vector of its reciprocal lattice in x-direction is given by

[Question ID = 7341]
1. a* = pî [Option ID = 29358]
2. a* = 2pî [Option ID = 29359]
3. a* = î [Option ID = 29360]
4. a* = p? [Option ID = 29361]
Correct Answer :-

• a* = pî [Option ID = 29358]
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The mean drift speed v_d of an electron in an applied electric field E with electron density ‘n’ can be expressed as

[Question ID = 7342]
1. v_d = |sE/ne| [Option ID = 29362]
2. v_d = |sE/el [Option ID = 29363]
3. v_d = |sE/nl [Option ID = 29364]
4. none of these [Option ID = 29365]
Correct Answer :-

• v_d = |sE/ne| [Option ID = 29362]

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An un-damped oscillator has time period t_o = 1.0 sec. Now a little damping is added so that its time period changes to t₁ = 1.001 sec. By what factor will the amplitude of oscillation decrease after 10 cycles?

[Question ID = 7343]
1. ˜ 17 [Option ID = 29366]
2. ˜ 1 [Option ID = 29367]
3. ˜ 1/17 [Option ID = 29368]
4. None of these [Option ID = 29369]
Correct Answer :-

• ˜ 17 [Option ID = 29366]
A kilogram of water has a constant heat capacity of 4.2 kJ/K/kg over the temperature range 0°C to 100° C. The water was initially at 0° C and is brought into contact with a heat reservoir at 100° C. When the water is in thermal equilibrium with the heat reservoir calculate the change in entropy of the universe (Water + Reservoir).
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[Question ID = 7344]
1. 184.8 J/K [Option ID = 29370]
2. 2437.8 J/K [Option ID = 29371]
3. 0 J/K [Option ID = 29372]
4. 1310.8 J/K [Option ID = 29373]
Correct Answer :-

• 184.8 J/K [Option ID = 29370]
Two identical finite bodies of constant volume and of constant heat capacity at constant volume C_v, are used to drive a heat engine. Their initial temperatures are T₁ and T₂. The maximum amount of work which can be obtained from the system is

[Question ID = 7345]
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1. C_v {2 (T₁T₂)^1/2 - (T₁ + T₂)} [Option ID = 29374]
2. C_v (T₁ + T₂) [Option ID = 29375]
3. C_v (T₁T₂)^1/2 [Option ID = 29376]
4. 0 [Option ID = 29377]
Correct Answer :-
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• C_v {2 (T₁T₂)^1/2 - (T₁ + T₂)} [Option ID = 29374]
For a system of bosons, we can write the Bose-Einstein distribution function as f(E_i) = ¹/_{exp(a+ßE_i)-1}, Where, ß = ¹/_{k_B T} and a = µ/k_BT (K_B = Boltzmann constant). If µ represents the chemical potential, then which one of the following is true?

[Question ID = 7346]
1. µ = 0 [Option ID = 29378]
2. µ = 0 [Option ID = 29379]
3. µ = 1 [Option ID = 29380]
4. µ = 1 [Option ID = 29381]
Correct Answer :-

• µ = 0 [Option ID = 29379]
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An ideal capacitor C is charged to a voltage V_o and connected at t = 0 across an ideal inductor L (The circuit now consists of a capacitor and an inductor only). If the resonant frequency ?_o = ¹/_vLC, the voltage across the capacitor at time t > 0 is given by

[Question ID = 7347]
1. V_o [Option ID = 29382]
2. V_o cos(?_ot) [Option ID = 29383]
3. V_o sin(?_ot) [Option ID = 29384]
4. V_oe^-?_otcos (?_ot) [Option ID = 29385]
Correct Answer :-

• V_o cos(?_ot) [Option ID = 29383]

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Magnetic moment of proton (µ_p) in terms of nuclear magneton (µ_N) is

[Question ID = 7348]
1. µ_p = 1.9µµ [Option ID = 29386]
2. µ_p = 2.7 µ_N [Option ID = 29387]
3. µ_p = 3.8µµ [Option ID = 29388]
4. µ_p = 5.4µµ [Option ID = 29389]
Correct Answer :-

• µ_p = 2.7 µ_N [Option ID = 29387]
Find the eigenvalues of A+4I where I is identity matrix and A = | 1 2 | | 1 2 |
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[Question ID - 7349]
1. 1,3 [Option ID = 29390]
2. 5,7 [Option ID = 29391]
3. None of these [Option ID = 29392]
4. None of these [Option ID = 29393]
Correct Answer :-

• 5,7 [Option ID = 29391]
The limit lim _n?8 (¹/_n)ⁿ is

[Question ID = 7350]
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1. 1 [Option ID = 29394]
2. ¹/_e [Option ID = 29395]
3. 0 [Option ID = 29396]
4. e [Option ID = 29397]
Correct Answer :-
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• ¹/_e [Option ID = 29395]
((1+i)/v2)⁴⁹ is equal to

[Question ID = 7351]
1. (1+i)/v2 [Option ID = 29398]
2. (2+98i)/v2 [Option ID = 29399]
3. v2 [Option ID = 29400]
4. (2-98i)/v2 [Option ID = 29401]
Correct Answer :-

• (1+i)/v2 [Option ID = 29398]
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sin (^p/₄+i) is equal to

[Question ID = 7352]
1. ^v2/₄ (e+e^-¹/₄) + i ^v2/₄(e^¹/₄-e^-¹/₄) [Option ID = 29402]
2. ^v2/₄ (e^¹/₄+e^-¹/₄) + i ^v2/₄(e^¹/₄-e^-¹/₄) [Option ID = 29403]
3. ^v2/₄ (e+e^-)+ i ^v2/₄(e-e^-) [Option ID = 29404]
4. ^v2/₄ (e^¹/₄+e^-) + i ^v2/₄(e^¹/₄+e^-¹/₄) [Option ID = 29405]
Correct Answer :-

• ^v2/₄ (e^¹/₄+e^-¹/₄) + i ^v2/₄(e^¹/₄-e^-¹/₄) [Option ID = 29403]

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Two students are working on a math problem. The first student has probability 1/2 of solving it and the second student has probability 3/4 of solving it. What is the probability that at least one of them solves the problem?

[Question ID = 7353]
1. ³/₈ [Option ID = 29406]
2. ⁵/₈ [Option ID = 29407]
3. ⁷/₈ [Option ID = 29408]
4. ⁹/₈ [Option ID = 29409]
Correct Answer :-
<
• ⁷/₈ [Option ID = 29408]
Expansion of the function f(z) = ¹/_z²-3z+2 in the region defined by |z| > 2 is
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[Question ID = 7354]
1. z^-2+3z^-4+7z^-6+... [Option ID = 29410]
2. z^-2+3z^-3+7z^-4+... [Option ID = 29411]
3. z^-1+3z^-2+7z^-3+... [Option ID = 29412]
4. z^-3+3z^-4+7z^-5+... [Option ID = 29413]
Correct Answer :-

• z^-2+3z^-3+7z^-4+... [Option ID = 29411]
The Fourier transformation of the function f(x) = 1 for |x| < a = 0 for |x| > a is

[Question ID = 7355]
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1. ²/_p ^{sin sa}/_S [Option ID = 29414]
2. ^p/₂ ^{sin sa}/_S [Option ID = 29415]
3. ^p/₂ ^{sin sa}/_S [Option ID = 29416]
4. ^p/₂ ^{cos sa}/_S [Option ID = 29417]
Correct Answer :-
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• ²/_p ^{sin sa}/_S [Option ID = 29414]
The Laplace transformation of the function f(t) = 2^t is

[Question ID = 7356]
1. ^{ln 2}/_{s - ln 2} [Option ID = 29418]
2. ¹/_{s - ln 2} [Option ID = 29419]
3. ^{ln 2}/_sln2-1 [Option ID = 29420]
4. ^{ln 2}/_{s ln 2-1} [Option ID = 29421]
Correct Answer :-

• ¹/_{s - ln 2} [Option ID = 29419]
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Consider a collection of non-interacting particles, each of mass m in a volume where the gravitational force is a -ve (z- direction). Consider the system is in thermal equilibrium at a temperature T. Find the partition function

[Question ID = 7357]
1. Q_N = ^(kT)³/_2pmgh² [Option ID = 29422]
2. Q_N = ...

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This post was last modified on 27 December 2020

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