← MES Jr. Grade
Past Questions
In a circuit with more number of loops, which law can be best suited for the analysis?
A)
KCL
B)
Ohm’s law
C)
KVL
D)
None of the mentioned
In network analysis, the choice between Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL) typically depends on the topology of the circuit to minimize the number of simultaneous equations required for a solution.
1. **KVL (Kirchhoff's Voltage Law)** is the foundation for **Mesh Analysis**. Mesh analysis is specifically designed for planar circuits with multiple loops. When a circuit has a high number of loops (meshes), defining loop currents allows the analyst to systematically solve for all currents using KVL equations.
2. **KCL (Kirchhoff's Current Law)** is the foundation for **Nodal Analysis**. Nodal analysis is generally more efficient when the number of nodes is smaller than the number of loops.
3. **Ohm's Law** is a fundamental relationship between voltage, current, and resistance, but it is a component-level law, not a system-level analysis method for complex multi-loop circuits.
Therefore, for a circuit characterized by a 'more number of loops,' KVL (via Mesh Analysis) is the most suited tool for systematic analysis.
Prove that the power of an energy signal is zero.
A _____________ shift register can convert serial to parallel data:
A)
SISO
B)
SIPO
C)
PISO
D)
PIPO
A shift register is a sequential logic circuit used for the storage and transfer of data. The classification of shift registers is based on how data enters (input) and exits (output) the register:
1. **SIPO (Serial-In, Parallel-Out):** Data is fed into the register one bit at a time (serially) through a single input line. Once the register is filled, all stored bits are available simultaneously at the output pins (parallelly). Therefore, it converts serial data to parallel data.
2. **SISO (Serial-In, Serial-Out):** Data enters serially and exits serially. It acts as a delay line and does not perform data conversion.
3. **PISO (Parallel-In, Serial-Out):** Data is loaded into the register all at once (parallelly) and then shifted out one bit at a time (serially). This converts parallel data to serial data.
4. **PIPO (Parallel-In, Parallel-Out):** Data is loaded parallelly and retrieved parallelly. It is used primarily for temporary data storage (buffer) and does not perform conversion.
Which of the following is also known as the dual of Norton’s theorem?
A)
Thevenin’s theorem
B)
Superposition theorem
C)
Maximum power transfer theorem
D)
Millman’s theorem
In network theory, duality refers to the relationship between two circuits where the mesh equations of one are identical to the nodal equations of the other. Thevenin's Theorem and Norton's Theorem are duals of each other because they describe the same linear network from two different perspectives:
1. Thevenin's Theorem represents a complex network as an equivalent circuit consisting of a single voltage source (Vth) in series with a resistance (Rth). This is a voltage-source representation.
2. Norton's Theorem represents the same complex network as an equivalent circuit consisting of a single current source (In) in parallel with a resistance (Rn). This is a current-source representation.
Mathematically, they are linked by Ohm's Law: Vth = In * Rth, and the equivalent resistances are identical (Rth = Rn).
Why other options are incorrect:
- Superposition theorem: Deals with the linear addition of responses from multiple independent sources; it is not a dual of Norton's theorem.
- Maximum power transfer theorem: Describes the condition under which a load extracts maximum power from a source; it is an application of Thevenin/Norton theorems, not a dual.
- Millman's theorem: A method to simplify multiple parallel voltage sources into a single voltage source; while related to simplification, it is not the formal dual of Norton's theorem.
What about the stability of system in H(z) = z(3z-4) / ((z-0.4)(z-2))
A)
system is stable
B)
unstable
C)
stable at 0.4
D)
can’t say
To determine the stability of a discrete-time system given its transfer function H(z), we must examine the locations of its poles in the z-plane.
1. **Identify the Poles**: The poles of the system are the values of z for which the denominator of H(z) equals zero.
The denominator is (z - 0.4)(z - 2).
Setting this to zero gives:
z₁ = 0.4
z₂ = 2
2. **Stability Criterion**: For a causal LTI (Linear Time-Invariant) system to be stable (specifically BIBO stable), all poles of the transfer function must lie strictly inside the unit circle in the z-plane. This means the magnitude of every pole must be less than 1 (|z| < 1).
3. **Evaluate the Poles**:
- For the first pole: |z₁| = |0.4| = 0.4. Since 0.4 < 1, this pole is inside the unit circle.
- For the second pole: |z₂| = |2| = 2. Since 2 > 1, this pole lies outside the unit circle.
4. **Conclusion**: Because there is at least one pole (z = 2) located outside the unit circle, the system is unstable.
- Option (a) is incorrect because not all poles are inside the unit circle.
- Option (c) is incorrect because stability is a property of the system as a whole, not a property 'at' a specific pole value.
- Option (d) is incorrect because the stability can be definitively determined from the given transfer function.
In an n-p-n transistor circuit the collector current is 18 mA. If 90% of the electrons emitted reach the collector, than the emitter current is:
A)
1.6 mA
B)
16.4 mA
C)
18 mA
D)
20 mA
Step-by-step solution:
1. **Identify given values**:
- Collector current ($I_C$) = 18 mA.
- Transport factor (the percentage of electrons emitted by the emitter that successfully reach the collector) = 90% or 0.90.
2. **Understand the physics**: In an n-p-n transistor, the emitter emits electrons. Some of these electrons recombine in the base (base current, $I_B$), and the rest reach the collector (collector current, $I_C$). The total emitter current ($I_E$) is the sum of the electrons that reach the collector and those that are lost in the base.
3. **Apply the formula**:
The relationship between collector current and emitter current based on the transport efficiency is:
$I_C = \text{Transport Factor} \times I_E$
$18\text{ mA} = 0.90 \times I_E$
4. **Calculate $I_E$**:
$I_E = \frac{18\text{ mA}}{0.90}$
$I_E = \frac{180}{9}\text{ mA}$
$I_E = 20\text{ mA}$
5. **Verification**: If $I_E = 20\text{ mA}$ and 90% reach the collector, then $20 \times 0.9 = 18\text{ mA}$ (which matches $I_C$). The remaining 10% (2 mA) constitutes the base current ($I_B$).
Comparing this result to the options:
- a. 1.6 mA (Incorrect)
- b. 16.4 mA (Incorrect)
- c. 18 mA (Incorrect - this is the collector current)
- d. 20 mA (Correct)
State and prove Tellegen’s theorem.
Find the initial value and final value of X(z) = 1 / (1 + 2z-1 - 3z-2).
For a Band Pass Filter, the slope of the filter is given as 40dB/decade. The order of the Band Pass Filter is __________.
A)
2
B)
3
C)
4
D)
6
Step-by-step reasoning:
1. **Understanding Filter Slope**: The slope (or roll-off rate) of a filter indicates how quickly the gain decreases as the frequency moves away from the passband.
2. **Standard Roll-off Rate**: For a first-order filter (n=1), the roll-off rate is 20 dB/decade (or 6 dB/octave) per pole.
3. **Formula for Slope**: The slope of a filter is given by the formula:
Slope = n × 20 dB/decade
where 'n' is the order of the filter.
4. **Calculation**: Given that the slope is 40 dB/decade:
40 dB/decade = n × 20 dB/decade
n = 40 / 20
n = 2
5. **Application to Band Pass Filters**: A Band Pass Filter (BPF) is essentially a combination of a High Pass Filter (HPF) and a Low Pass Filter (LPF). The 'order' of the BPF refers to the order of the individual filters that define the transition bands. A 2nd-order BPF provides a roll-off of 40 dB/decade on both the lower and upper stopbands.
Therefore, the order of the filter is 2.
What happens when a P-type semiconductor is joined with an N-type semiconductor?
A)
They repel each other
B)
They form an insulator
C)
They create a diode
D)
They have no interaction
When a P-type semiconductor (rich in holes) is joined with an N-type semiconductor (rich in electrons), a PN junction is formed. At the interface, electrons from the N-side diffuse into the P-side and holes from the P-side diffuse into the N-side, creating a 'depletion region'. This structure allows current to flow easily in one direction (forward bias) while blocking it in the opposite direction (reverse bias). This one-way conduction property is the fundamental characteristic of a diode.
Why other options are incorrect:
- (a) They do not repel each other; they are physically joined to form a crystal lattice.
- (b) While the depletion region has high resistance, the overall device is a semiconductor, not an insulator, as it can conduct under specific bias conditions.
- (d) There is a significant interaction involving charge carrier diffusion and the creation of a built-in potential barrier.
In a semiconductor diode, the barrier offers opposition to:
A)
Majority as well as minority carriers in both regions
B)
Free electrons in N region only
C)
Majority carriers in both regions
D)
Holes in P region only
In a semiconductor P-N junction, a depletion region is formed where mobile charge carriers are absent, creating a built-in potential barrier.
1. **Majority Carriers**: In the P-region, the majority carriers are holes; in the N-region, they are electrons. The internal electric field of the barrier is directed from the N-region to the P-region. This field opposes the diffusion of holes from P to N and electrons from N to P. Therefore, the barrier specifically opposes the movement of majority carriers across the junction.
2. **Minority Carriers**: Conversely, the barrier actually *assists* the movement of minority carriers (electrons in P-region and holes in N-region), as the electric field sweeps them across the junction (this is the mechanism behind reverse saturation current).
3. **Analysis of Options**:
- Option (a) is incorrect because the barrier does not oppose minority carriers; it facilitates them.
- Option (b) is incorrect because it only mentions one region and one carrier type, ignoring the holes in the P-region.
- Option (c) is correct because it encompasses both majority carriers (holes in P and electrons in N) which are the ones hindered by the potential barrier.
- Option (d) is incorrect because it ignores the electrons in the N-region.
Noise generated by an amplifier of radio is an example for?
A)
Discrete signal
B)
Deterministic signal
C)
Random signal
D)
Periodic signal
Step-by-step reasoning: 1. Definition of Noise: In electronic systems, noise refers to unwanted electrical signals that interfere with the desired signal. Noise generated by an amplifier (such as thermal noise or shot noise) is caused by the random motion of electrons. 2. Analyzing the options: (a) Discrete signal: A signal that is defined only at specific points in time. Noise in an amplifier is a continuous-time signal. (b) Deterministic signal: A signal whose value can be predicted exactly at any given time using a mathematical formula (e.g., a sine wave). Noise is unpredictable and cannot be described by a deterministic equation. (c) Random signal: A signal whose value cannot be predicted with certainty; it can only be described using statistical properties (like mean and variance). Since noise is stochastic and unpredictable, it is a classic example of a random signal. (d) Periodic signal: A signal that repeats its pattern at regular intervals. Noise is aperiodic and does not repeat. Therefore, noise generated by an amplifier is a random signal.
The resonant frequency of quartz crystal oscillator is 450kHz. The equivalent inductance and series resistance at resonant frequency are 4.2 H and 9050 ohms respectively. Find the quality factor of the crystal.
In an RLC series circuit having finite values of RLC, the phase difference between applied voltage and current is:
A)
always 0°
B)
between 0 and 180°
C)
between 0 and 90°
D)
always 90°
In a series RLC circuit, the phase difference (φ) between the applied voltage (V) and the current (I) is determined by the impedance triangle. The formula for the phase angle is: tan(φ) = (X_L - X_C) / R, where X_L is inductive reactance, X_C is capacitive reactance, and R is resistance.
1. If the circuit is purely resistive (X_L = X_C), φ = 0°.
2. If the circuit is purely inductive (R = 0, X_C = 0), φ = 90°.
3. If the circuit is purely capacitive (R = 0, X_L = 0), φ = -90°.
However, the question specifies 'finite values of RLC', meaning R > 0, L > 0, and C > 0. Because R is finite and non-zero, the denominator in the tan(φ) expression is always positive and non-zero. This prevents the phase angle from ever reaching exactly 90° or -90° (which only happens when R = 0). Therefore, the phase angle φ must lie strictly between -90° and 90°. In terms of magnitude (phase difference), it is between 0° and 90°.
- Option (a) is incorrect because it only applies at resonance.
- Option (b) is incorrect because the phase difference in a passive RLC circuit cannot exceed 90°.
- Option (d) is incorrect because it only applies if R = 0 (purely reactive circuit).
In photo emissive materials, what is the relationship between the intensity of incident light and the emitted photoelectrons?
A)
Directly proportional
B)
Inversely proportional
C)
No relationship
D)
Nonlinear relationship
This question relates to the Photoelectric Effect. According to the laws of photoelectric emission: 1. The number of photoelectrons emitted per second (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 are striking the surface per unit time, which in turn releases more electrons. 2. The maximum kinetic energy of the emitted electrons depends on the frequency of the incident light, not the intensity. Therefore, since the question asks about the relationship between intensity and the 'emitted photoelectrons' (referring to the quantity/current), the relationship is directly proportional. Option b is incorrect as it implies fewer electrons with more light. Option c is incorrect as there is a well-defined physical relationship. Option d is incorrect because, in the linear region of operation for photo-emissive materials, the relationship is linear.
The time period of continuous-time sinusoidal signal is given by _____.
A)
T = 2π / w
B)
T = 2π / 3w
C)
T = π / w
D)
T = π / 2w
A continuous-time sinusoidal signal is typically represented as x(t) = A sin(ωt + φ) or x(t) = A cos(ωt + φ), where 'ω' is the angular frequency in radians per second.
1. Definition of Periodicity: A signal is periodic if x(t) = x(t + T) for all t, where T is the fundamental period.
2. For a sinusoid: sin(ω(t + T)) = sin(ωt + ωT).
3. For the signal to repeat itself, the phase shift ωT must be an integer multiple of 2π (the period of a basic sine/cosine function).
4. For the fundamental period (the smallest positive value of T), we set ωT = 2π.
5. Solving for T gives: T = 2π / ω.
Comparing this to the options:
- Option (a) T = 2π / ω is the correct mathematical derivation.
- Option (b) T = 2π / 3ω is incorrect as it represents a signal with three times the frequency.
- Option (c) T = π / ω is incorrect; this would be the period of a squared sinusoid or a signal with double the frequency.
- Option (d) T = π / 2ω is incorrect.
The first Indian state to implement the National e-Vidhan Application program to become paperless is:
A)
Kerala
B)
Tripura
C)
Meghalaya
D)
Nagaland
Nagaland was the first state in India to successfully implement the National e-Vidhan Application (NeVA) and make its Legislative Assembly function paperless. NeVA is a digital initiative under the Digital India programme to modernize and digitize legislative functioning. Therefore, option (d) Nagaland is correct. The other states listed were not the first to implement NeVA.
India is regarded as a country with “Demographic Dividend”. This is due to :
A)
its high population in the age group below 15 years
B)
its high population in the age group of 15-64 years
C)
its high population in the age group above 65 years
D)
its high total population
Demographic dividend means the economic growth potential that arises when a country has a larger proportion of working-age population compared to dependents. In India, this dividend is mainly due to the large share of people in the 15-64 years age group, who form the productive labour force. Option (a) refers to dependent children, not the working population. Option (c) refers to the elderly dependent population. Option (d) is incorrect because demographic dividend depends on age structure, not just total population size.
Which one of the following institution was replaced by NITI-Aayog?
A)
National Development Council
B)
Planning Commission
C)
Finance Commission
D)
National Commission for Central Budgetting
The NITI Aayog (National Institution for Transforming India) was established by the Government of India on January 1, 2015, to replace the Planning Commission. While the Planning Commission followed a 'top-down' approach to planning (where the center decided the plans for states), NITI Aayog is designed as a 'think tank' that promotes 'cooperative federalism' through a 'bottom-up' approach, involving state governments more actively in the policy-making process.
Why other options are incorrect:
- a. National Development Council (NDC): While the NDC was closely linked to the Planning Commission, it was not replaced by NITI Aayog in the same structural capacity; it was a body for coordinating plans.
- c. Finance Commission: This is a constitutional body (established under Article 280 of the Indian Constitution) that recommends the distribution of financial resources between the Union and the States. It continues to exist independently.
- d. National Commission for Central Budgetting: This is not a standard primary institution replaced by NITI Aayog; budgeting is primarily handled by the Ministry of Finance.
In the recently concluded 64th Annual Grammy Awards, Jon Batiste won 5 Grammys including Album of the year called :
A)
Sour
B)
We are
C)
Planet Her
D)
Back of My Mind
At the 64th Annual Grammy Awards (2022), Jon Batiste won Album of the Year for "We Are" and received a total of 5 Grammy awards. Hence, option (b) is correct.
Why others are incorrect:
(a) "Sour" is Olivia Rodrigo's album.
(c) "Planet Her" is Doja Cat's album.
(d) "Back of My Mind" is H.E.R.'s album.
In India, the Enforcement Directorate (ED) which is a specialized investigation agency works under which union ministry?
A)
Ministry of Defence
B)
Ministry of External Affairs
C)
Ministry of Finance
D)
Ministry of Public Personnel
The Enforcement Directorate (ED) is a specialized financial investigation agency under the Department of Revenue, which functions under the Union Ministry of Finance. It investigates offences related to money laundering and foreign exchange violations. इसलिए the correct answer is (c) Ministry of Finance. The other options are incorrect because ED does not function under the Ministry of Defence, Ministry of External Affairs, or Ministry of Public Personnel.
What is the Most important Kharif crops in India?
A)
Wheat
B)
Rice
C)
Maize
D)
Barley
Kharif crops are sown with the onset of the monsoon and harvested after the rainy season. Rice is the most important Kharif crop in India because it requires high temperature, abundant rainfall, and standing water conditions that match the monsoon season. Wheat and barley are mainly Rabi crops grown in winter, so options (a) and (d) are incorrect. Maize is also a Kharif crop in many areas, but it is not the most important one compared to rice.
An instrument used for measuring depth of an ocean is called
A)
Hydrometer
B)
Hygrometer
C)
Galvanometer
D)
Fathometer
A fathometer is an instrument used to measure the depth of water bodies such as oceans and seas, usually by echo sounding. Hence option (d) is correct. A hydrometer measures specific gravity of liquids, a hygrometer measures humidity, and a galvanometer detects/measures small electric currents.
Pulitzer prize is awarded for outstanding work in the field of :
A)
Science and Technology
B)
International Understanding
C)
Literature and Journalism
D)
Environmental Studies
The Pulitzer Prize is a prestigious American award primarily given for excellence in journalism, literature, and musical composition. Therefore, the correct answer is Literature and Journalism. The other options are incorrect because the Pulitzer is not mainly awarded for science and technology, international understanding, or environmental studies.
The first country to approve the commercial production of genetically modified golden rice.
A)
Cambodia
B)
Bangladesh
C)
Philippines
D)
Vietnam
The Philippines became the first country to approve the commercial production of genetically modified Golden Rice in 2021. Golden Rice is genetically engineered to produce beta-carotene, a precursor of vitamin A, to help address vitamin A deficiency.
Why others are incorrect:
- Cambodia: No such first approval for Golden Rice commercial production.
- Bangladesh: It approved cultivation of Bt brinjal, but not the first commercial production of Golden Rice.
- Vietnam: Not the first country to approve Golden Rice commercial production.