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Past Questions — 2010
Among the configurations the lowest input impedance is obtained by
A)
CE
B)
CC
C)
CB
D)
both CB and CC
Based on Mizo customary knowledge / general exam pattern.
The moderators are required
A)
for thermalization of fast neutrons
B)
to increase the energy of the neutrons
C)
to increase the number of neutrons
D)
to decrease the number of delayed neutrons
In a nuclear reactor, the fission of Uranium-235 produces 'fast neutrons' which have very high kinetic energy. However, the probability (cross-section) of these fast neutrons inducing further fission in U-235 is very low. To sustain a chain reaction, these fast neutrons must be slowed down to 'thermal energies' (energies comparable to the ambient temperature of the medium). This process of slowing down neutrons is called 'thermalization'. A moderator (such as graphite, heavy water, or light water) is a material composed of light nuclei that slows down neutrons through successive elastic collisions.
Analysis of other options:
- Option (b) is incorrect because moderators decrease the kinetic energy of neutrons, they do not increase it.
- Option (c) is incorrect because moderators do not create new neutrons; that is the role of the fission process itself.
- Option (d) is incorrect because delayed neutrons are a result of radioactive decay of fission fragments and are not managed or decreased by the moderator.
The half life of a substance is 20 minutes. What is the time interval between 33% decay and 67% decay?
A)
40 minutes
B)
20 minutes
C)
30 minutes
D)
25 minutes
Based on Mizo customary knowledge / general exam pattern.
Full wave rectifier is preferred over half wave rectifier because of the difference in
A)
the output level
B)
frequency
C)
ripples
D)
construction
A rectifier converts alternating current (AC) to direct current (DC). The 'ripple' refers to the residual AC component remaining in the DC output.
1. **Half-Wave Rectifier**: Only one half-cycle of the AC input is used, while the other is blocked. This results in large gaps between pulses, leading to a high ripple factor (1.21). This makes the output very 'un-smooth' and difficult to filter.
2. **Full-Wave Rectifier**: Both half-cycles of the AC input are converted to DC. This results in a continuous series of pulses with no gaps, significantly reducing the ripple factor (0.482).
Because the ripple is much lower in a full-wave rectifier, it is far easier to smooth the output using a filter capacitor to obtain a steady DC voltage. While full-wave rectifiers have a higher output level (average voltage) and higher ripple frequency, the primary technical reason they are 'preferred' in power supply design is the significant reduction in the ripple factor, which improves efficiency and output quality.
In the first excited state of a one-dimensional harmonic oscillator with angular frequency w, the energy eigen value is given by
A)
ħω
B)
ħω/2
C)
3ħω/2
D)
2ħω
The energy eigenvalues of a one-dimensional quantum harmonic oscillator are given by the formula: E_n = (n + 1/2)ħω, where n is the quantum number (n = 0, 1, 2, ...).
1. Ground State: The lowest energy state occurs when n = 0.
E_0 = (0 + 1/2)ħω = ħω/2.
2. First Excited State: The first excited state occurs when n = 1.
E_1 = (1 + 1/2)ħω = (3/2)ħω = 3ħω/2.
Evaluating the options:
- Option (a) ħω: Incorrect. This does not correspond to any eigenvalue of the harmonic oscillator.
- Option (b) ħω/2: Incorrect. This is the energy of the ground state (n=0).
- Option (c) 3ħω/2: Correct. This is the energy of the first excited state (n=1).
- Option (d) 2ħω: Incorrect. This does not match the (n + 1/2) formula for any integer n.
The nuclear fusion can be explained by
A)
optical model of the nucleus
B)
shell model of the nucleus
C)
collective model of the nucleus
D)
liquid drop model of the nucleus
The Liquid Drop Model (LDM), proposed by George Gamow and further developed by Niels Bohr and John Wheeler, treats the nucleus as a drop of incompressible nuclear fluid. This model is particularly effective in explaining the energetics of nuclear processes involving the bulk properties of the nucleus, such as binding energy and the process of nuclear fission and fusion. In nuclear fusion, two light nuclei merge to form a heavier, more stable nucleus; the LDM explains this through the concept of surface tension and the Coulomb barrier, where the reduction in surface area (relative to volume) upon merging leads to a more stable configuration and the release of energy.
Why other options are incorrect:
- a. Optical Model: This is used primarily to describe the scattering of nucleons (like neutrons) from a nucleus by treating the nucleus as a complex refractive medium.
- b. Shell Model: This model explains the 'magic numbers' and the spin/parity of ground states by treating nucleons as moving in independent energy shells, similar to electrons in an atom. It is not used to explain the bulk process of fusion.
- c. Collective Model: This model combines the shell model and the liquid drop model to explain the rotational and vibrational excitations of nuclei, rather than the fundamental process of fusion.
The rate of radioactive disintegration is
A)
affected by pressure
B)
affected by temperature
C)
affected by the number of original kind atoms present at any time
D)
affected by the daughter nucleus
The rate of radioactive decay (disintegration) is governed by the law of radioactive decay, which states that the number of nuclei disintegrating per unit time (Activity, A) is directly proportional to the number of radioactive nuclei (N) present in the sample at that instant. Mathematically, this is expressed as: A = λN, where λ is the decay constant.
1. Why option (c) is correct: Since A ∝ N, the rate of disintegration depends solely on the quantity of the parent (original kind) atoms present. As the number of atoms decreases over time, the rate of disintegration also decreases.
2. Why options (a) and (b) are incorrect: Radioactive decay is a nuclear process, not a chemical one. It is independent of external physical conditions such as temperature, pressure, or the chemical state of the atom. These factors affect electron shells, but not the stability of the nucleus.
3. Why option (d) is incorrect: The decay of a parent nucleus is a spontaneous process. The nature or presence of the daughter nucleus does not influence the probability of the parent nucleus decaying.
The dielectric between the conductors reduces the electric intensity
A)
to zero
B)
between them
C)
with no charge
D)
None of these
When a dielectric material is inserted between two charged conductors, the electric field (electric intensity) within the dielectric is reduced. This happens because the external electric field polarizes the molecules of the dielectric, creating an induced internal electric field that opposes the original external field. The net electric field (E_net) is given by E_net = E_0 / K, where E_0 is the original field and K is the dielectric constant. Therefore, the dielectric reduces the electric intensity specifically in the region 'between them' (the space occupied by the dielectric). Option (a) is incorrect because the field is reduced, not necessarily to zero (unless it is a perfect conductor). Option (c) is irrelevant to the mechanism of field reduction.
N-type semiconductor is obtained by doping germanium or silicon with an impurity like
A)
Aluminium
B)
Phosphorus
C)
Indium
D)
Gallium
To create an N-type (negative-type) semiconductor, a pure intrinsic semiconductor like Silicon (Si) or Germanium (Ge), which belong to Group IV of the periodic table (4 valence electrons), must be doped with a pentavalent impurity (Group V elements). Pentavalent impurities have 5 valence electrons; four form covalent bonds with the surrounding semiconductor atoms, leaving one extra electron free to move, thereby increasing the conductivity of the material via negative charge carriers.
1. Phosphorus (P) is a Group V element (pentavalent), making it the correct dopant for N-type semiconductors.
2. Aluminium (Al), Indium (In), and Gallium (Ga) are all Group III elements (trivalent). Doping with these elements creates 'holes' (absence of electrons), resulting in a P-type (positive-type) semiconductor.
The continuous X-ray spectrum at constant voltage will have
A)
a minimum wavelength
B)
a maximum wavelength
C)
a minimum frequency
D)
a maximum frequency
In the production of X-rays (Bremsstrahlung), electrons are accelerated by a constant voltage (V) and strike a target. The maximum energy an electron can transfer to a photon occurs when the electron loses all its kinetic energy in a single collision. This energy is given by E = hν = eV, where h is Planck's constant, ν is frequency, e is the charge of an electron, and V is the accelerating voltage. Since wavelength (λ) is inversely proportional to frequency (λ = c/ν), the maximum energy corresponds to the shortest possible wavelength. This is known as the Duane-Hunt law, expressed as λ_min = hc/eV. Therefore, for a constant voltage, the continuous X-ray spectrum is characterized by a distinct 'cutoff' or minimum wavelength (λ_min), below which no X-rays are emitted. There is no theoretical maximum wavelength or maximum frequency for the continuous spectrum in this context, as electrons can lose any fraction of their energy, leading to longer wavelengths.
The critical mass of a fissionable material can be reduced by
A)
heating it
B)
cooling it
C)
adding impurities to it
D)
surrounding it with a shield that will reflect neutrons
Critical mass is the minimum amount of fissionable material (like Uranium-235 or Plutonium-239) required to maintain a self-sustaining nuclear chain reaction. The primary factor that determines whether a mass is critical is the rate of neutron leakage from the surface of the material.
1. **Neutron Reflection (Option d):** When a fissionable mass is surrounded by a 'neutron reflector' (a shield made of materials like beryllium or graphite), neutrons that would otherwise escape the system are reflected back into the core. This increases the neutron flux within the material, allowing a smaller mass to achieve criticality. Therefore, a reflector reduces the required critical mass.
2. **Heating/Cooling (Options a & b):** While temperature can affect the cross-section of neutron absorption (Doppler broadening), it is not the primary method used to reduce the critical mass of a material in a fundamental sense; in many cases, heating can actually increase the critical mass due to thermal expansion (decreasing density).
3. **Adding Impurities (Option c):** Impurities generally act as 'neutron poisons' (materials with high neutron absorption cross-sections). Adding impurities increases the number of neutrons absorbed without causing fission, which increases the amount of material needed to sustain a reaction, thereby increasing the critical mass.
Which of the following are not electromagnetic waves?
A)
Cosmic rays
B)
γ-rays
C)
β-rays
D)
X-rays
Beta rays are electrons (particles), not EM waves; gamma and X-rays are EM. Cosmic rays also particles but beta is textbook non-EM example.
The photoelectric current in a photoelectric cell depends upon
A)
The nature of the metal used as the counter
B)
The wavelength of the incident light
C)
The intensity of the incident light
D)
All the above parameters
In the photoelectric effect, the photoelectric current is defined as the rate of flow of photoelectrons from the cathode to the anode. According to Einstein's photoelectric equation and experimental observations: 1. Photoelectric current is directly proportional to the intensity of the incident light (provided the frequency of the light is above the threshold frequency). This is because higher intensity means more photons striking the surface per unit time, which results in more electrons being ejected. 2. The wavelength (or frequency) of the incident light determines whether electrons are ejected at all (threshold frequency) and determines the maximum kinetic energy of the ejected electrons, but it does not determine the quantity of current once the threshold is exceeded. 3. The nature of the metal (work function) determines the threshold frequency, but not the current magnitude for a given intensity. Therefore, the current depends specifically on the intensity of the incident light.
The work function is
A)
the same for all metal surfaces
B)
the same for all type of surfaces
C)
different for different metal surfaces
D)
dependent on the frequency of the incident light
Work function depends on material composition and surface conditions, varies between metals.
When the speed of electrons increases, the specific charge
A)
increases
B)
decreases
C)
remains unchanged
D)
increase and then decreases
The 'specific charge' of a particle is defined as the ratio of its electric charge (q) to its mass (m), expressed as q/m. For an electron, the charge (e ≈ 1.602 × 10⁻¹⁹ C) and the rest mass (m₀ ≈ 9.109 × 10⁻³¹ kg) are fundamental physical constants. In the context of classical physics and standard competitive exam questions of this level, the specific charge is treated as a constant property of the particle, regardless of its velocity. While relativistic mass increases as speed approaches the speed of light, the term 'specific charge' in general physics refers to the intrinsic property of the particle. Since the charge of the electron does not change with speed and the intrinsic mass remains constant, the specific charge remains unchanged. Therefore, option (c) is the correct answer.
Crystalline solids are
A)
anistropic
B)
isotropic
C)
amporphus
D)
None of these
Step-by-step reasoning: 1. Definition of Crystalline Solids: Crystalline solids are materials in which the constituent particles (atoms, ions, or molecules) are arranged in a highly ordered, repeating three-dimensional lattice structure. 2. Understanding Anisotropy: Anisotropy refers to the property of a material where its physical properties (such as electrical conductivity, refractive index, or thermal expansion) vary depending on the direction in which they are measured. Because the arrangement of atoms in a crystal lattice differs along different axes, the physical properties also differ. Therefore, crystalline solids are anisotropic. 3. Evaluating other options: (b) Isotropic: Isotropic materials have the same properties in all directions. This is a characteristic of amorphous solids (like glass), not crystalline solids. (c) Amorphous: This is a different category of solids characterized by a lack of long-range order; crystalline solids are the opposite of amorphous solids. (d) None of these: Incorrect, as option (a) is correct.
Even though we can get X-ray by the bombardment of any charged particles on a target, what is the reason for using electrons to produce X-rays?
A)
Electrons have smallest possible charge
B)
Electrons are common constituents of all matter
C)
Electron mass is very small
D)
Electrons can be produced very easily
To produce X-rays (specifically Bremsstrahlung or 'braking radiation'), a charged particle must be decelerated rapidly upon hitting a target. According to classical electromagnetism, the acceleration (or deceleration) of a charged particle is inversely proportional to its mass (F = ma, so a = F/m). Because electrons have an extremely small mass compared to other charged particles like protons or alpha particles, they undergo much more violent acceleration/deceleration when interacting with the electric fields of the target nuclei. This high rate of deceleration results in the emission of high-energy photons in the X-ray spectrum. While electrons are common (option b) and easy to produce (option d), these are practical conveniences rather than the physical reason why they are the most efficient particles for generating X-rays. The fundamental physical reason is their low mass, which allows for the necessary high acceleration to emit X-ray photons.
Suppose each state voltage gain is about 100, then the theoretical maximum voltage gain from a R. C coupled two stage transistor amplifier is
A)
100
B)
greater than 100 but less than 200
C)
200
D)
10,000
In a multi-stage amplifier, the total voltage gain (Av_total) is the product of the individual voltage gains of each stage. This is because the output of the first stage serves as the input to the second stage.
Given:
- Voltage gain of the first stage (Av1) = 100
- Voltage gain of the second stage (Av2) = 100
The theoretical maximum voltage gain for a two-stage RC coupled amplifier is calculated as:
Av_total = Av1 × Av2
Av_total = 100 × 100 = 10,000
Analysis of options:
- Option (a) 100: This is the gain of only one stage.
- Option (b) and (c): These assume additive gain (100 + 100), which is incorrect for cascaded amplifiers.
- Option (d) 10,000: This correctly applies the multiplicative property of cascaded gain.
The difference between an amplifier and an oscillator is that an oscillator
A)
needs no external input signal
B)
needs no d.c. power supply
C)
delivers a reshaped version of the input signal
D)
delivers output signal without amplification of input signal
An amplifier is a device that increases the amplitude of an existing external input signal. It requires an input signal to function. In contrast, an oscillator is a circuit that generates its own periodic signal (such as a sine wave or square wave) without requiring an external AC input signal. It achieves this by using a feedback loop (positive feedback) and a frequency-determining network to convert DC power from a power supply into an AC signal.
Evaluating the options:
- Option (a) is correct because an oscillator is a self-starting signal generator.
- Option (b) is incorrect because both amplifiers and oscillators require a DC power supply (biasing) to operate the active components (transistors/op-amps).
- Option (c) is incorrect because reshaping a signal is typically the function of a wave-shaping circuit or a comparator, not the defining difference between an amplifier and an oscillator.
- Option (d) is incorrect because an oscillator actually involves amplification (the loop gain must be at least 1) to sustain oscillations; it does not 'deliver output without amplification'.
The Schrödinger wave equation is
A)
the general differential equation of wave motion
B)
tatisfying the Broglie relation
C)
satisfying the uncertainty relation
D)
to obtain the energy state of the harmonic oscillator
The Schrödinger equation is the fundamental equation of quantum mechanics. It describes how the quantum state of a physical system (represented by the wave function Ψ) changes with time. Mathematically, it is a linear partial differential equation that serves as the 'general differential equation of wave motion' for matter waves, analogous to how the classical wave equation describes sound or light waves.
Evaluating the other options:
- Option (b): While the Schrödinger equation is consistent with the de Broglie relation (p = h/λ), it is not 'defined' as satisfying it; rather, the de Broglie relation is a prerequisite for the formulation of the equation.
- Option (c): The Heisenberg Uncertainty Principle is a consequence of the mathematical properties of the wave function (Fourier transforms), not the definition of the equation itself.
- Option (d): Obtaining the energy states of a harmonic oscillator is a specific application (a boundary value problem) of the Schrödinger equation, not the definition of the equation itself.
An electric dipole of moment p is placed in the position of stable equilibrium in a uniform electric field of intensity E. The torque required to rotate, when the dipole makes an angle q with the initial position is
A)
zero
B)
π/4
C)
π
D)
π/2
At stable equilibrium p∥E, θ=0, torque pE sinθ=0; maximum at 90°.
In nuclear reaction there is conservation of
A)
mass only
B)
energy only
C)
momentum only
D)
mass, energy and momentum
In nuclear reactions, several fundamental conservation laws must be obeyed:
1. **Conservation of Momentum**: Linear momentum is conserved in all nuclear reactions, as there are no external forces acting on the system.
2. **Conservation of Energy**: While 'rest mass' is not conserved (mass is converted to energy via E=mc²), the total energy (including rest mass energy and kinetic energy) is strictly conserved.
3. **Conservation of Mass (Mass Number)**: In the context of nuclear physics, the total number of nucleons (protons + neutrons) remains constant before and after the reaction. This is often referred to as the conservation of mass number.
Therefore, while mass-energy is interconvertible, the total quantity of mass-energy, the total nucleon count (mass number), and the momentum are all conserved. Option (d) is the most comprehensive and correct answer.
Bohr magneton is the unit of moment of electron which has spin angular momentum equal to
A)
zero
B)
ħ/2
C)
3ħ/2
D)
5ħ/2
Bohr magneton corresponds to orbital moment with ħ; spin ħ/2 gives 1μB.
When transistor is operating in active region, collector junction is
A)
reverse biased of NPN transistor
B)
reverse biased for PNP transistor
C)
forward biased in both NPN and PNP transistor
D)
reverse biased in both NPN and PNP transistor
To operate a Bipolar Junction Transistor (BJT) in the 'Active Region' (which is the required region for linear amplification), specific biasing conditions must be met for its two junctions: the Emitter-Base (EB) junction and the Collector-Base (CB) junction.
1. Emitter-Base Junction: This junction must be Forward Biased to allow majority carriers to be injected from the emitter into the base.
2. Collector-Base Junction: This junction must be Reverse Biased. This creates a depletion region and a strong electric field that sweeps the carriers (electrons in NPN, holes in PNP) from the base into the collector.
This rule applies regardless of the transistor type:
- For an NPN transistor: The EB junction is forward biased (P-type base positive relative to N-type emitter) and the CB junction is reverse biased (N-type collector positive relative to P-type base).
- For a PNP transistor: The EB junction is forward biased (N-type base negative relative to P-type emitter) and the CB junction is reverse biased (P-type collector negative relative to N-type base).
Therefore, in the active region, the collector junction is reverse biased for both NPN and PNP transistors.
According to Bohr’s theory of the Hydrogen atom, the speed v of the electron in a stationary orbit n is related to the principal quantum number n as (C is a constant)
A)
v = C/n²
B)
v = C/n
C)
v = C x n
D)
v = C × n²
According to Bohr's model of the hydrogen atom, the electron moves in circular orbits where the angular momentum is quantized. The quantization condition is given by: mvr = nh/(2π), where m is the mass of the electron, v is the velocity, r is the radius of the orbit, and n is the principal quantum number (n = 1, 2, 3...).
Additionally, for a stable orbit, the centripetal force is provided by the electrostatic attraction between the nucleus and the electron:
(mv²/r) = (Ze²)/(4πε₀r²), where Z is the atomic number (for Hydrogen, Z=1).
By solving these two equations simultaneously for velocity (v), we find that:
v = (Ze²)/(2ε₀nh)
In this expression, Z, e, ε₀, n, and h are constants except for n. Therefore, we can group the constants as C = (Ze²)/(2ε₀h).
This simplifies the relationship to: v = C/n.
This means the velocity of the electron is inversely proportional to the principal quantum number n. As n increases (the electron moves to a higher energy level), the velocity of the electron decreases.
Comparing this to the options:
- Option (a) v = C/n² is incorrect (this describes the energy levels, where E ∝ 1/n²).
- Option (b) v = C/n is correct.
- Option (c) v = C x n is incorrect.
- Option (d) v = C x n² is incorrect.