TANGEDCO AE EE Full Test - 1 - Electrical Engineering (EE) MCQ

Explanation:

Degree of Differential Equation:

• The degree of the differential equation is represented by the power of the highest order derivative in the given differential equation.
• The differential equation must be a polynomial equation in derivatives for the degree to be defined.

Ex:

• Here, the exponent of the highest order derivative is one (i.e. Second-order) and the given differential equation is a polynomial equation in derivatives. Hence, the degree of this equation is 1.

Ex:

• The order of this equation is 3 and the degree is 2 as the highest derivative is of order 3 and the exponent raised to the highest derivative is 2.

Order of Differential Equation:

• Differential Equations are classified on the basis of the order.
• The order of a differential equation is the order of the highest derivative (also known as differential coefficient) present in the equation.

Ex:

• In this equation, the order of the highest derivative is 4 hence this is a fourth-order differential equation.

Ex:

• This equation represents a Third-order differential equation.
• This way we can have higher-order differential equations i.e. nth order differential equations.

Concept:
If a Matrix is singular then its determinant is zero ()
Calculation:
Given:
Matrix is singular

1 (40 - 40) - 3(20 - 24) + (λ + 2)(10 - 12) = 0
|-3(-4) + (λ + 2)(-2) = 0
12 - 2λ - 4 = 0
8 = 2λ
∴ λ = 4.

Let Z = x + iy

f₁(z) = z² = (x + iy)² = x² – y² + i 2xy = u + iv

u = x² – y², v = 2xy

u_x = 2x, u_y = -2y

v_x = 2y, v_y = 2x

u_x = v_y and u_y = -v_x

f₁(z) is satisfying CR equations

Hence, f₁(z) is analytic function.

f₂(z) = z̅ = x – iy = u + iv

u = x, v = -y

u_x = 1, u_y = 0

v_x = 0, v_y = -1

⇒ u_x ≠ v_y

f₂(z) is not satisfying CR equations.

Concept:
Binomial distribution: If a random variable X has binomial distribution as B (n, p) with n and p as parameters, then the probability of random variable is given as:
P( X = k) = ⁿC_k p^k (1 - p)^{(n - k)}
Where, n is number of observations or trials , p is the probability of success & (1 - p) is probability of failure.
Properties:

• Mean of the distribution (μX) = n × p
• The variance (σ²_x) = n × p × (1 - p)
• Standard deviation (σ_x) = √{np(1 - p)}

Calculation:
Given, mean of BD = np = 5
And variance of BD = npq = 10/3 
⇒ np(1 – p) = 10/3  (∵ p + q = 1)

⇒p = 1/3

Concept:
Cauchy's theorem:
If f(z) is an analytic function and f'(z) is continuous at each point within and on a closed curve C, or if the simple closed curve does not contain any singular point of f(z) then,

Analysis:

f(z) exists for all values of z inside the closed curve C.
∴ f(z) is analytic and also f'(z) is continuous at all points.

Important Point
Cauchy's integral formula:
If f(z) be an analytic function within an on the closed curve C and let 'a' is a point inside C then,

We can solve the given problem by this method as follows:
z₀ is enclosed within the closed curve C

∴ f(z) = (z - z₀)²
The value of the integral is
2πi f(z₀) = 2πi (z₀ - z₀)²
= 0

The equivalent circuit of the Transformer:

I₁ = Primary winding current
I₂ ' =Secondary winding current referred to the primary side
I₀ = NO-load current

The no-load current has two components.

I_w = Core loss component
I_m = magnetizing component

• No-load current is almost the same when we apply the load also.
• The magnetizing branch circuit connected in parallel to the supply voltage as No-load current is constant while we apply load also.
• Therefore Core loss also constant as I₀ remains constant.

The correct answer is Bulk modulus.
Explanation

• Bulk modulus is the correct term for the ratio of hydraulic stress to volumetric strain.
• It quantifies the substance's resistance to uniform compression, a fundamental property in understanding how materials deform under stress.

Other Related Points

• Equivalence - This term does not directly relate to the concept of the ratio between hydraulic stress and volumetric strain. Equivalence generally refers to a state of being equal or equivalent in value, function, meaning, etc., but not in this specific physical context.
• Compression - While compression is related to the concept of applying stress and causing strain, it is a process or effect rather than a measure or ratio. Compression refers to the act of pressing together or the state of being compressed.
• Semi Modulus - This term is not standard in the context of material science or physics related to stress and strain. There isn't a defined physical quantity known as ""Semi modulus"" in the study of materials' responses to external forces. -
• Summary - Bulk modulus is the appropriate term for describing the ratio of hydraulic stress to volumetric strain, highlighting the material's resistance to compression. Other options either refer to different concepts or are not directly related to the specific ratio in question."

The correct answer is option 2) i.e.
Concept:

• Adiabatic process: It is a process in which no heat is exchanged between the system and the surrounding i.e. the system is insulated.

It is represented mathematically as:
PVγ = constant
Work done in an adiabatic process is defined by:
​W = P.dV
Where V₁ and V₂ are the initial and final volume after the process.
Calculation:
From ideal gas law, PV = nRT ----(1)
We know, PV^γ = constant = K ⇒ P = KV^-γ ----(2)
​Substituting (2) in W = P.dV

The correct answer is option 2) i.e. will not change.
Concept:

• Archimedes' principle: A body at rest in a fluid is acted upon by a force pushing it upward called the buoyant force, which is equal to the weight of the fluid that the body displaces.

​The buoyant force (F_B) is given by,

Explanation:
The floating ice will displace some volume of the water.
From Archimedes' principle, F_B = ρ_water × g × V_ice ----(1)
Weight of the displaced fluid (water) = mg = ρ_water × V_{dispalced water} × g ----(2)
For an object to stay afloat, the forces acting on it must be balanced ⇒ (1) = (2)
ρ_water × g × V_ice = ρ_water × V_water × g ⇒ V_ice = V_{dispalced water}
Therefore, when the ice melts, there will be no change in the water level as the melted ice will occupy the same volume as that of displaced water.

Concept:
The synchronous speed of a three-phase induction motor is given by:

Where N_s = Synchronous speed in rpm
f = Supply frequency
P = Number of poles
Calculation:
In India, the frequency of supply f = 50 Hz
For maximum speed, the number of poles must be the minimum.
Minimum number of poles (P) = 2
N_s = 120 x 50/2
N_s = 3000 rpm

• Universal Gas Constant, R, is a property of Ideal Gases.
• The ideal gas equation is given by PV = n RT.
• The universal gas constant or molar constant (Ru) of a gas is the product of the specific gas constant (R) and the molecular mass of the gas (M).
• Ru = MR
• The S.I. units of Ru is 8.314 kJ/kg – mol K.
• M.K.S unit of Ru is 848 kgf -m/kg mole - K (Note 1 kgf-m = 9.81 joules).

• Necking is the range on the stress-strain graph from the ultimate stress point to the point of fracture of the material.
• Necking takes place after a material passes through the elastic, yielding, and strain hardening region of a material test.
• The resulting prominent decrease in the local cross-sectional area provides the basis for the name "neck".
• Necking occurs when a tensile force is applied on metals and it occurs when ductile failure is occurring.

The stress-strain curve for ductile material is shown below:

The highest point 'E' of the diagram corresponds to the ultimate strength of a material.
Beyond point E, the bar begins to form the neck. The load falling from the maximum until a fracture occurs at F.

A window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen interval.

It is normally symmetric around the middle of the interval, usually near a maximum in the middle, and usually tapering away from the middle.

Hamming window:

The Hamming window is an extension of the Hann window in the sense that it is a raised cosine window of the form

with a corresponding spectrum of the form

The parameter α permits the optimization of the destructive sidelobe cancellation.

The common approximation to this value of α is 0.54, for which the window is called the Hamming window and is of the form

The window length L = N + 1

Maxwell’s equation for time-varying electromagnetic fields is as shown:

Important Point
Also, for static electric and magnetic fields, the rate of change of both the electric field and the magnetic field will be zero. The modified Maxwell’s equations for static fields will be:

To write the state equation of any signal flow graph at any point or junction, we only consider input response or incoming response at that point or junction.
Hence state equations of a given signal flow diagram can be written as
X₂ = A₂₁ X₁ + A₂₃ X₃
X₄ = A₄₂ X₂ + A₄₃ X₃
X₃ = A₃₁ X₁ + A₃₂ X₂ + A₃₃ X₃

Concept:
Another number system to Decimal
In each and every representation of numbers with different bases, the maximum value in a number system with the
base ‘r’ is r – 1. Since numbers vary from 0 to r – 1.
To convert any number which is in the different base to decimal number system we use binary-weighted
representation.
Eg: let the number be ( abc⋯ ⋯ yz)_r
Now to convert the above number into the decimal number system
a × r^n-1 + b × r^n-2 + ⋯ ⋯ + y × r¹ + z × r⁰
If we convert all numbers into decimal then we can perform normal addition and subtraction etc..
Example:
(16)₁₀ into binary

(10000)₂ in binary
(16)₁₀ into octal

(20)₈ in octal
Calculation:
Given:
(11X1Y)₈ = (12C9)₁₆
Coverting it into decimal number system,
(11X1Y)₈ = 1 x 8⁴ + 1 x 8³ + X x 8² + 1 x 8 + Y x 8⁰
= 4096 + 512 + 64X + 8 + Y
(12C9)₁₆ = 1 x 16³ + 2 x 16² + 12 x 16 + 9 x 16⁰
= 4096 + 512 + 192 + 9
On solving these Equations we'll get:
64X + Y = 193
The possible values of X and Y are:
X = 3 and Y = 1

8085 microprocessor has 8-bit I/O addresses.

The maximum number of input or output devices that can be connected = 2⁸ = 256

Important Points:

The number of address lines required for memory mapped I/O = 16

Hence, we can connect 2¹⁶ = 65536 devices

The number of address lines required for I/O mapped I/O = 8

Modified z-transform:

Advanced or modified z-transform is defined as

Where T is the sampling period

m is a fraction of the sampling period [0, T]

Properties:

If the delay parameter, m, is considered fixed then all the properties of the z-transform hold for the advanced z-transform.

Linearity:

Time shift:

Damping:

Time multiplication:

Concept:

The relation between the line voltages in terms of the symmetrical components of voltages is given below.

Va0 = Zero Sequence Component of Voltage

Va1 = Positive Sequence Component of Voltage

Va2 = Negative Sequence Component of Voltage

a = 1∠120°, which represents the rotation of 120° in the clockwise direction.

a2 = 1∠-120° or 1∠240° in anticlockwise direction or clockwise direction, respectively.

Application:

The above matrix form can be written as

Concept:
8421 is also known as BCD code
BCD is a weighted code.
In weighted codes, each successive digit from right to left represents weights equal to some specified value, and to get the equivalent decimal number to add the products of the weights by the corresponding binary digit.
The following represents the 4-bit binary representation of decimal values:
The following represents the 4-bit binary representation of decimal values: 

Application:
From the above Table:
8 = 1000
From the above Table:
8 = 1000
7 = 0111
4 = 0100
(874)₁₀ ---- (100001110100)BCD
Important Points

• A number with 'n' decimal digit will require 4k bits in BCD.
• Ex- Decimal 396 is represented in BCD with 12 bits as 0011 1001 0110, with each group of 4 bits representing one decimal digit.
• As the decimal digits relating to 1010, 1011, 1100, 1101, 1110, and 1111 do not exist, these are invalid.

Concept:
Emf induced in a coil or inductor is given by

Where,
L = Inductance
di = final value of current - initial value of current
dt = final time - initial time
Calculation:
L = 0.5 H,
di = 1 - (-1) = 2 A
dt = 1 msec
e = (0.5) (2)/(0.001)
e = 1000 V

Concept:
The angle of asymptotes is given as:

Where,
q = 0, 1, 2, … |P – Z| – 1
P = Number of Poles
Z = Number of zeros.
Calculation:
Given:
A unity feedback system has open-loop poles at s = -2 ± j 2, s = -1 and s = 0 and a zero at s = -3
Number of Poles (P) = 4
Number of Zeros (Z) = 1

q = 0, 1, 2
Hence the angle of asymptotes, = 60°, 180°, and 300(or)-60°
Important Point
1. Every branch of a root locus diagram starts at a pole (K = 0) and terminates at a zero (K = ∞) of the open-loop transfer function.
2. Root locus diagram is symmetrical with respect to the real axis.
3. Number of branches of the root locus diagram are:

• N = P if P ≥ Z
• = Z, if P ≤ Z

4. Number of asymptotes in a root locus diagram = |P – Z|
5. Centroid: It is the intersection of the asymptotes and always lies on the real axis. It is denoted by σ.

ΣP_i is the sum of real parts of finite poles of G(s)H(s)
ΣZ_i is the sum of real parts of finite zeros of G(s)H(s)
6. On the real axis to the right side of any section, if the sum of total number of poles and zeros are odd, root locus diagram exists in that section.
7. Break-in/away points: These exist when there are multiple roots on the root locus diagram.
At the breakpoints gain K is either maximum and/or minimum.
So, the roots of  dK/ds are the break points.

MOV A, C; Move the contents to Accumulator from C register

RAR; Rotate right with carry

RAR; Rotate right with carry

RAR; Rotate right with carry

RAR; Rotate right with carry

MOV C, A; Move the contents to C register from Accumulator

HLT; stop the program

Pole placement by state feedback:

• The pole placement by state feedback is a control system design technique, in which the state variables are used for feedback to achieve the desired closed loop poles.
• The state feedback design requires arbitrary pole placement to achieve the desired performance.
• The necessary and sufficient condition to be satisfied for arbitrary pole placement is that the system be completely state controllable.
  

State observer:

• A device (or a computer program) that estimates or observes the state variables is called state observer.
• The Observer estimates the state variables from information it receives from the output vector c(k). The output of the observer is the estimated state vector x(k).
• The state observer can be designed only if the system is completely state observable.

Important Points:

Complete state controllability:

The system described by X(k + 1) = A X(k) + B U(k) and C(k) = D X(k) + E U(k) is said to be completely state controllable if for any initial time (stage) K=0, there exists a set of unconstrained controls u(k), k = 0, 1, 2, …… (N – 1), which transfers each initial state x(D) to any final state x(N) for some finite N.

Complete state observability:

The system described by X(k+1) = A X(k) + B U(k) and C(k) = D X(k) + E U(k) is said to be completely observable if and only if the following n × pN matrix is of rank n:

Let = [ D’ A’D’ (A’)²D’……(A’)^n-1D] where n is the dimension of x(k) and p is the dimension of c(k). The matrix L is known as the observability matrix.

Synchronous motor:
V curves for synchronous motor gives the relation between armature current and field current. The curves are shown below.

A synchronous motor is capable of operating at all types of power factor i.e. either UPF, leading, or lagging power factor.

• Lagging power factor: If field excitation is such that E_b < V the motor is said to be under excited and it has lagging power factor.
• Leading power factor: If field excitation is such that E_b > V the motor is said to be over-excited and it draws leading current. So that the power factor improves.
• Unity power factor: If field excitation is such that E_b = V the motor is said to be normally excited.

Synchronous generator:
A synchronous generator or alternator is capable of operating at all types of power factor i.e. either UPF, leading or lagging power factor.

• Lagging power factor: If field excitation is such that E_b < V the alternator is said to be over-excited and it has leading power factor.
• Leading power factor: If field excitation is such that E_b > V the alternator is said to be under-excited and it draws leading current. So that the power factor improves.
• Unity power factor: If field excitation is such that E_b = V the alternator is said to be normally excited.
• V -curve for synchronous generator or alternator is shown below

Three phase symmetric fault:

From the above figure,

I_a + I_b + I_c = 0 and V_a = V_b = V_c

If I_a is taken as reference I_b = λ²I_a and I_c = λI_a

Positive sequence current

Negative sequence current

Zero sequence current

Therefore, in a symmetrical three-phase fault, both negative and zero sequence currents are zero.

Corona loss:

The power dissipated in the system due to corona discharges is called corona loss. Accurate estimation of corona loss is difficult because of its variable nature. It has been found that the corona loss under fair weather conditions is less than under foul weather conditions.

The corona loss under appropriate weather conditions is given below by the Peek’s formula,

Where Pc – corona power loss

f – Frequency of supply in Hz

δ – Air density factor

En – r.m.s phase voltage in kV

Eo – disruptive critical voltage per phase in kV

r – Radius of the conductor in meters

D – Spacing between conductors in meters

Corona is affected by the following factors:

• The physical state of atmosphere: Corona is formed due to the ionization of air surrounding the conductors. The number of ions is more than normal in the stormy weather.
• The irregular and rough surface cause more corona loss because unevenness of the surface decreases the value of breakdown voltage.
• A larger distance between conductors reduces the electrostatic stresses at the conductor surfaces. It helps in avoiding the formation of the corona.
• The operating voltage
• Air density factor

Corona loss is independent of the height of the conductor.

Concept:

Apply element-wise inversion i.e multiply by the inverse of the same element to make it an identity matrix until the desired objective is reached.

Calculation:

Let (BA)^-1 = K

Multiply by the BA on both sides, in the same order

(BA)(BA)^-1 = (BA)K

I = BAK {∵ (A)(A^-1) = I}

Multiply B^-1 on both the sides

B^-1I = B^-1BAK

B^-1 = AK

Multiply A^-1 on both sides

A^-1B^-1 = A^-1AK

A^-1B^-1 = K

so, (BA)^-1 = A^-1B^-1 {∵ (BA)^-1 = K}

Helium-Neon Laser:
Helium-Neon laser is a type of gas laser in which a mixture of helium and neon gas is used as a gain medium. Helium-Neon laser is also known as He-Ne laser.

• Emits the wavelength of 632.8 nm.
• Consists of a mixture of ~90% Helium gas, ~10% Neon gas
• The gases are enclosed in a glass tube.
• An electrical discharge is established along the bore of the tube
• Two mirrors are bonded to the ends of the discharge tube, one a total reflector, the other having ~1 % transmission

With other cavity mirrors, other wavelengths of laser emission of He-Ne lasers are possible too.

• Green – 543.5 nm
• Yellow – 594 nm
• Orange – 612 nm

char pointer:

A pointer to char points to single char. sizeof() operator is used to find the size of a variable or pointer in the programming language. Char pointer size is 2 bytes (machine-dependent).

far pointer:

This pointer is used to access the complete memory of RAM. Size of the far pointer is 4 bytes of 32 bit.

In an Intel 8086, as well as in later processors running 16-bit code, a far pointer has two parts: a 16-bit segment value and a 16-bit offset value.

Code:

void main ()
{
char far * farther, * farthest;
printf(“%d..%d”, sizeof(farther),
sizeof(farthest));
}

Farther is a far pointer in this. So, sizeof(farther) will return 4 bytes.

sizeof(farthest) will return 2 bytes. As it is only a char pointer.

Important Points:

The answer will vary depending upon the system.

This ambiguous question