In which state was India's indigenous 4G stack officially inaugurated by the Prime Minister in September 2025?
A
Karnataka
B
Gujarat
C
Odisha
D
Telangana
Question 2Single Answer
The indigenous 4G network launched by BSNL in September 2025 was designed to be upgraded to which technology?
A
3G
B
WiMAX
C
5G
D
CDMA
Question 3Single Answer
Which organization developed the core network component of BSNL's indigenous 4G technology?
A
ISRO
B
DRDO
C
C-DOT
D
TRAI
Question 4Single Answer
Which Indian company supplied the Radio Access Network equipment for BSNL's indigenous 4G rollout?
A
Infosys
B
Wipro
C
Tejas Networks
D
HCLTech
Question 5Single Answer
Which company was responsible for systems integration in the indigenous BSNL 4G project announced in September 2025?
A
RailTel Corporation
B
Bharat Electronics Limited
C
Hindustan Aeronautics Limited
D
Tata Consultancy Services
Question 6Single Answer
According to the Ministry of Communications statement dated 5 February 2026, how many indigenous BSNL 4G sites were installed nationwide as of 15 January 2026?
A
85,511
B
75,000
C
97,672
D
91,200
Question 7Single Answer
How many of the installed indigenous BSNL 4G sites were on-air as of 15 January 2026?
A
95,511
B
97,672
C
90,150
D
89,500
Question 8Single Answer
According to the government announcement of September 2025, India's indigenous 4G stack placed India among approximately how many countries possessing such indigenous capabilities?
A
Three
B
Ten
C
Eight
D
Five
Question 9Single Answer
Which Union Minister announced the nationwide rollout of BSNL's Swadeshi 4G network in September 2025?
A
Hardeep Singh Puri
B
Ashwini Vaishnaw
C
Piyush Goyal
D
Jyotiraditya M. Scindia
Question 10Single Answer
What was the approximate number of indigenous BSNL 4G towers included in the inauguration announced on 27 September 2025?
A
One lakh
B
50,000
C
25,000
D
Two lakh
Question 11Single Answer
Which government initiative is directly associated with promoting India's self-reliance in indigenous telecommunications technology?
A
Smart Cities Mission
B
Atmanirbhar Bharat
C
National Food Security Mission
D
Jal Jeevan Mission
Question 12Single Answer
According to the government reply of March 2026, approximately how much additional capital expenditure support was approved for BSNL's 4G rollout in 2025?
A
₹3,500 crore
B
₹10,000 crore
C
₹5,200 crore
D
₹6,982 crore
Question 13Single Answer
The government approved approximately ₹89,000 crore in 2023 for which BSNL-related purpose?
A
Establishment of satellite launch centres
B
Construction of railway networks
C
Allotment of 4G/5G spectrum
D
Expansion of postal infrastructure
Question 14Single Answer
Which government-funded project aims to extend broadband connectivity to Gram Panchayats and villages across India?
A
PM-KUSUM
B
Sagarmala
C
Amended BharatNet Programme
D
National Solar Mission
Question 15Single Answer
What does DBN stand for in the context of funding telecommunications connectivity projects in India?
A
Digital Broadband Network
B
Digital Bharat Nidhi
C
Department of Broadband Networks
D
Digital Banking Network
Question 16Single Answer
The 4G Saturation Project is primarily intended to provide mobile connectivity to which areas?
A
International airport terminals
B
Metropolitan business districts
C
Private industrial estates
D
Villages without 4G mobile coverage
Question 17Single Answer
Which Indian ministry is responsible for the Department of Telecommunications?
A
Ministry of Information and Broadcasting
B
Ministry of Electronics and Information Technology
C
Ministry of Communications
D
Ministry of Science and Technology
Question 18Single Answer
Under which law was the Telecom Regulatory Authority of India established?
A
Information Technology Act, 2000
B
Telecom Regulatory Authority of India Act, 1997
C
Indian Telegraph Act, 1885
D
Companies Act, 2013
Question 19Single Answer
Which organization functions as India's telecommunications regulator?
A
RBI
B
TRAI
C
SEBI
D
CCI
Question 20Single Answer
Which government organization is primarily responsible for telecommunications licensing and spectrum administration in India?
A
National Informatics Centre
B
Department of Telecommunications
C
National Highways Authority of India
D
Central Electricity Authority
Basic Engineering
Question 21Single Answer
What are the roots of the quadratic equation x² - 7x + 12 = 0?
A
2 and 6
B
3 and 4
C
-3 and -4
D
1 and 12
Question 22Single Answer
If the roots of x² - 6x + k = 0 are equal, what is the value of k?
A
6
B
9
C
36
D
12
Question 23Single Answer
What is the sum of the first 20 terms of the arithmetic progression 3, 7, 11, 15, ...?
A
800
B
820
C
840
D
780
Question 24Single Answer
Which expression represents the nth term of a geometric progression with first term a and common ratio r?
A
a + (n - 1)r
B
ar^(n - 1)
C
ar^n
D
a + nr
Question 25Single Answer
If log₁₀x = 2.5, what is the value of x?
A
25
B
100√10
C
250
D
1000√10
Question 26Single Answer
What is the value of sin²30° + cos²30°?
A
1/2
B
√3/2
C
3/4
D
1
Question 27Single Answer
Which identity correctly expresses sin(A + B)?
A
sinA sinB + cosA cosB
B
sinA cosB + cosA sinB
C
sinA cosB - cosA sinB
D
cosA cosB - sinA sinB
Question 28Single Answer
What is the exact value of tan 75°?
A
2 - √3
B
√3
C
2 + √3
D
1 + √3
Question 29Single Answer
If sin θ = 3/5 and θ is acute, what is cos θ?
A
4/5
B
3/4
C
5/4
D
5/3
Question 30Single Answer
Which expression is equivalent to 1 + tan²θ wherever tan θ is defined?
A
sin²θ
B
cos²θ
C
sec²θ
D
cosec²θ
Question 31Single Answer
What is the value of sin 2θ when sin θ = 3/5 and cos θ = 4/5?
A
16/25
B
12/25
C
7/25
D
24/25
Question 32Single Answer
What is the principal value of tan⁻¹(1)?
A
π/4
B
π/3
C
π/6
D
π/2
Question 33Single Answer
If x + 1/x = 5, what is the value of x² + 1/x²?
A
25
B
27
C
23
D
21
Question 34Single Answer
What is the remainder when x³ - 2x² + 3x - 5 is divided by x - 2?
A
5
B
3
C
1
D
0
Question 35Single Answer
For a quadratic equation ax² + bx + c = 0 with real coefficients and a ≠ 0, which condition gives two distinct real roots?
A
b² - 4ac = -1
B
b² - 4ac = 0
C
b² - 4ac < 0
D
b² - 4ac > 0
Question 36Single Answer
What is the distance between points (2, 3) and (8, 11)?
A
10
B
12
C
8
D
14
Question 37Single Answer
What is the midpoint of the line segment joining (-4, 6) and (8, 2)?
A
(4, 2)
B
(2, 4)
C
(-2, 4)
D
(2, 8)
Question 38Single Answer
What is the slope of the straight line passing through (1, 2) and (5, 10)?
A
1
B
4
C
2
D
-2
Question 39Single Answer
Which equation represents a straight line having slope 3 and y-intercept -2?
A
y = -3x + 2
B
y = 3x - 2
C
y = 2x - 3
D
y = 3x + 2
Question 40Single Answer
What is the slope of a line perpendicular to 2x - 3y + 6 = 0?
A
2/3
B
3/2
C
-2/3
D
-3/2
Question 41Single Answer
What is the distance of the point (3, 4) from the line 3x + 4y - 10 = 0?
A
2
B
4
C
3
D
5
Question 42Single Answer
What is the radius of the circle x² + y² - 6x + 4y - 12 = 0?
A
3
B
5
C
√21
D
4
Question 43Single Answer
What is the centre of the circle x² + y² + 8x - 10y + 5 = 0?
A
(8, -10)
B
(4, -5)
C
(-8, 10)
D
(-4, 5)
Question 44Single Answer
Which equation represents a parabola opening toward the positive x-axis with vertex at the origin?
A
x² = -4ay
B
x² = 4ay
C
y² = 4ax, a > 0
D
y² = -4ax, a > 0
Question 45Single Answer
What is the focus of the parabola y² = 12x?
A
(0, 3)
B
(-3, 0)
C
(3, 0)
D
(0, -3)
Question 46Single Answer
What is the eccentricity of a circle?
A
0
B
2
C
1/2
D
1
Question 47Single Answer
Which conic section has eccentricity exactly equal to 1?
A
Parabola
B
Ellipse
C
Circle
D
Hyperbola
Question 48Single Answer
What is the length of the major axis of the ellipse x²/25 + y²/9 = 1?
A
6
B
8
C
12
D
10
Question 49Single Answer
What is the eccentricity of the ellipse x²/25 + y²/9 = 1?
A
3/5
B
5/4
C
4/5
D
2/5
Question 50Single Answer
What are the asymptotes of the hyperbola x²/16 - y²/9 = 1?
A
y = ±4x/3
B
y = ±3x
C
y = ±4x
D
y = ±3x/4
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Basic Engineering
Question 51Single Answer
What is the area of the triangle with vertices (0, 0), (6, 0) and (0, 4)?
A
24 square units
B
10 square units
C
12 square units
D
14 square units
Question 52Single Answer
Which condition indicates that three distinct points in a plane are collinear?
A
Their distances from the origin are equal
B
Their x-coordinates are different
C
The area of the triangle formed by them is zero
D
Their y-coordinates are positive
Question 53Single Answer
What is the x-intercept of the line 3x + 2y = 12?
A
6
B
3
C
4
D
2
Question 54Single Answer
Which equation represents a circle with centre (2, -3) and radius 4?
A
(x + 2)² + (y - 3)² = 16
B
(x - 2)² + (y + 3)² = 16
C
(x + 2)² + (y + 3)² = 16
D
(x - 2)² + (y + 3)² = 4
Question 55Single Answer
What is the angle between two straight lines having slopes 1 and -1?
A
90°
B
45°
C
60°
D
30°
Question 56Single Answer
What is the magnitude of the vector 3i + 4j + 12k?
A
12
B
15
C
13
D
10
Question 57Single Answer
Which operation between two vectors produces a scalar quantity?
A
Cross product
B
Vector addition
C
Dot product
D
Vector subtraction
Question 58Single Answer
What is the dot product of vectors (2i + 3j) and (4i - j)?
A
11
B
8
C
5
D
7
Question 59Single Answer
What is the angle between two non-zero vectors when their dot product is zero?
A
0°
B
90°
C
45°
D
180°
Question 60Single Answer
What is the magnitude of the cross product of two perpendicular vectors having magnitudes 3 and 5?
A
8
B
15
C
12
D
18
Question 61Single Answer
What is the value of i × j in Cartesian unit vector notation?
A
k
B
-k
C
i
D
j
Question 62Single Answer
Which expression represents the unit vector in the direction of vector a = 3i + 4j?
A
4i/5 + 3j/5
B
3i + 4j
C
3i/4 + j
D
3i/5 + 4j/5
Question 63Single Answer
What is the scalar projection of vector a = 3i + 4j on the positive x-axis?
A
3
B
4
C
5
D
7
Question 64Single Answer
What is the resultant of vectors 2i - 3j and 5i + 4j?
A
3i + j
B
7i + j
C
7i - 7j
D
-3i + j
Question 65Single Answer
What is the work done by force F = 2i + 3j N when displacement s = 4i + 5j m?
A
15 J
B
19 J
C
25 J
D
23 J
Question 66Single Answer
Which vector operation is used to determine torque from position vector r and force F?
A
Dot product r · F
B
Cross product r × F
C
Scalar addition r + F
D
Scalar subtraction r - F
Question 67Single Answer
What is the magnitude of the unit vector i + 0j + 0k?
A
0
B
1
C
√2
D
2
Question 68Single Answer
If two vectors have equal magnitude and opposite directions, what is their resultant?
A
Zero vector
B
A vector of twice the magnitude
C
A perpendicular vector
D
A unit vector
Question 69Single Answer
Which condition must hold for two non-zero vectors to be parallel?
A
Their dot product is zero
B
Their sum is necessarily zero
C
Their magnitudes are always equal
D
Their cross product is zero
Question 70Single Answer
What is the angle between vectors i and i + j?
A
90°
B
60°
C
45°
D
30°
Question 71Single Answer
What is the value of (i + j + k) · (i - j + k)?
A
0
B
2
C
1
D
3
Question 72Single Answer
What geometric quantity is represented by the absolute value of a scalar triple product?
A
Volume of a parallelepiped
B
Length of a diagonal
C
Circumference of a circle
D
Area of a triangle
Question 73Single Answer
What is the vector product of (2i) × (3j)?
A
6k
B
-6k
C
5k
D
6i
Question 74Single Answer
What is the order of a matrix containing 3 rows and 4 columns?
A
3 × 4
B
3 × 3
C
4 × 3
D
4 × 4
Question 75Single Answer
What is the determinant of the matrix [[2, 3], [4, 5]]?
A
2
B
-2
C
10
D
-10
Question 76Single Answer
Which matrix has all its non-diagonal elements equal to zero?
A
Symmetric matrix
B
Singular matrix
C
Rectangular matrix
D
Diagonal matrix
Question 77Single Answer
What is the determinant of a triangular matrix with diagonal entries 2, 3 and 4?
A
20
B
9
C
12
D
24
Question 78Single Answer
Which condition must hold for a square matrix to possess an inverse?
A
Its determinant must be non-zero
B
It must be diagonal
C
Its trace must be zero
D
Every element must be positive
Question 79Single Answer
What is the trace of the matrix [[4, 2], [3, 7]]?
A
9
B
11
C
14
D
10
Question 80Single Answer
What is the rank of the identity matrix of order 4?
A
1
B
4
C
3
D
2
Question 81Single Answer
If A is a 2 × 3 matrix and B is a 3 × 4 matrix, what is the order of AB?
A
2 × 4
B
3 × 3
C
4 × 2
D
2 × 3
Question 82Single Answer
Which property correctly describes matrix multiplication in general?
A
AB = BA for all matrices
B
AB = A + B
C
AB always has determinant zero
D
AB need not equal BA
Question 83Single Answer
What is the determinant of [[1, 2], [2, 4]]?
A
4
B
0
C
-4
D
2
Question 84Single Answer
What is the transpose of the matrix [[1, 2], [3, 4]]?
A
[[1, 2], [3, 4]]
B
[[4, 3], [2, 1]]
C
[[1, 3], [4, 2]]
D
[[1, 3], [2, 4]]
Question 85Single Answer
Which matrix equation defines the inverse A⁻¹ of a nonsingular square matrix A?
A
AA⁻¹ = 0
B
AA⁻¹ = I
C
A + A⁻¹ = I
D
A - A⁻¹ = 0
Question 86Single Answer
What is the value of k if the matrix [[k, 2], [8, 4]] is singular?
A
2
B
8
C
4
D
16
Question 87Single Answer
Which property holds for determinants when two rows of a square matrix are interchanged?
A
The determinant is squared
B
The determinant remains unchanged
C
The sign of the determinant changes
D
The determinant becomes zero
Question 88Single Answer
What is the solution of the equations x + y = 7 and x - y = 3?
A
x = 2, y = 5
B
x = 4, y = 3
C
x = 5, y = 2
D
x = 6, y = 1
Question 89Single Answer
Which method uses ratios of determinants to solve a nonsingular system of linear equations?
A
Newton-Raphson method
B
Euler method
C
Simpson's rule
D
Cramer's rule
Question 90Single Answer
What are the eigenvalues of the diagonal matrix [[3, 0], [0, 7]]?
A
0 and 10
B
3 and 7
C
-3 and -7
D
1 and 21
Question 91Single Answer
What is the determinant of the identity matrix of order 5?
A
5
B
0
C
1
D
-1
Question 92Single Answer
Which matrix satisfies Aᵀ = A?
A
Skew-symmetric matrix
B
Symmetric matrix
C
Orthogonal matrix
D
Singular matrix
Question 93Single Answer
What is the determinant of a 2 × 2 matrix [[a, b], [c, d]]?
A
ab - cd
B
ac - bd
C
ad - bc
D
ad + bc
Question 94Single Answer
What is the inverse of the matrix [[2, 0], [0, 5]]?
A
[[2, 0], [0, 5]]
B
[[5, 0], [0, 2]]
C
[[1/2, 0], [0, 1/5]]
D
[[-2, 0], [0, -5]]
Question 95Single Answer
What is the determinant of the matrix [[1, 2, 3], [0, 1, 4], [0, 0, 2]]?
A
4
B
2
C
6
D
8
Question 96Single Answer
For any nonsingular 3 × 3 matrix A, which expression equals det(A⁻¹)?
A
1/det(A)
B
-det(A)
C
det(A)
D
[det(A)]²
Question 97Single Answer
What is the derivative of x⁵ with respect to x?
A
5x⁵
B
x⁴
C
4x⁵
D
5x⁴
Question 98Single Answer
What is the derivative of sin x with respect to x?
A
cos x
B
-cos x
C
-sin x
D
sec²x
Question 99Single Answer
What is the derivative of ln x for x > 0?
A
ln x
B
x
C
1/x
D
e^x
Question 100Single Answer
If y = e^(3x), what is dy/dx?
A
e^(3x)
B
3e^(3x)
C
xe^(3x)
D
3e^x
Question 101Single Answer
What is the derivative of tan x?
A
cot x
B
cosec²x
C
sec²x
D
-sec²x
Question 102Single Answer
Which rule is used to differentiate the product of two differentiable functions?
A
Product rule
B
Quotient rule
C
Chain rule
D
L'Hôpital's rule
Question 103Single Answer
If y = x² sin x, what is dy/dx?
A
2x sin x + x² cos x
B
2x cos x + x² sin x
C
x² cos x
D
2x sin x - x² cos x
Question 104Single Answer
What is the derivative of cos(2x)?
A
2cos(2x)
B
-sin(2x)
C
-2sin(2x)
D
sin(2x)
Question 105Single Answer
What is the derivative of x/(x + 1)?
A
-1/(x + 1)²
B
x/(x + 1)²
C
1/(x + 1)
D
1/(x + 1)²
Question 106Single Answer
What is the second derivative of y = x⁴?
A
4x³
B
12x²
C
8x²
D
24x
Question 107Single Answer
At which value of x does the function f(x) = x² - 6x + 5 attain its minimum?
A
x = 3
B
x = 2
C
x = 5
D
x = 6
Question 108Single Answer
What is the minimum value of f(x) = x² - 4x + 7?
A
7
B
4
C
3
D
2
Question 109Single Answer
What is the derivative of arcsin x for -1 < x < 1?
A
1/√(1 - x²)
B
-1/√(1 - x²)
C
1/(1 + x²)
D
-1/(1 + x²)
Question 110Single Answer
What is the partial derivative of f(x, y) = x²y + 3xy² with respect to x?
A
x² + 6xy
B
2xy + 6xy²
C
2x + 3y
D
2xy + 3y²
Specialization
Question 111Single Answer
In a balanced star-connected three-phase system, how is line voltage related to phase voltage?
A
VL = √3Vph
B
VL = 3Vph
C
VL = Vph
D
VL = Vph/√3
Question 112Single Answer
A balanced star-connected load receives a line voltage of 415 V. What is its approximate phase voltage?
A
415 V
B
240 V
C
718 V
D
208 V
Question 113Single Answer
In a balanced delta-connected load, what is the relationship between line and phase currents?
A
IL = Iph
B
IL = 3Iph
C
IL = Iph/√3
D
IL = √3Iph
Question 114Single Answer
What is the displacement between successive phase voltages of an ideal balanced three-phase supply?
A
90°
B
120°
C
180°
D
60°
Question 115Single Answer
Which expression gives total active power in a balanced three-phase load?
A
√3VLILcosφ
B
3VLIL
C
VLIL
D
√3VLILsinφ
Question 116Single Answer
A three-phase load draws 10 A at 400 V line voltage and unity power factor. What is its approximate active power?
A
4.00 kW
B
6.93 kW
C
2.31 kW
D
12.0 kW
Question 117Single Answer
Which condition indicates a lagging power factor?
A
Current leads voltage
B
Current lags voltage
C
Current has zero RMS value
D
Current and voltage are in phase
Question 118Single Answer
What is the reactive power of a single-phase load rated 10 kVA at 0.8 lagging power factor?
A
6 kvar
B
8 kvar
C
4 kvar
D
10 kvar
Question 119Single Answer
In a balanced three-phase system, what is the instantaneous sum of the three phase currents when no neutral or leakage current flows?
A
Equal to one line current
B
Zero
C
Three times one phase current
D
Equal to the line voltage
Question 120Single Answer
Which arrangement is commonly used to measure power in a three-phase, three-wire system using two instruments?
A
Two-wattmeter method
B
Single-voltmeter method
C
Three-ammeter bridge
D
Wheatstone bridge
Question 121Single Answer
In the two-wattmeter method for a balanced three-phase load, what happens at a power factor of 0.5?
A
Both readings are necessarily zero
B
Both readings become negative
C
Both readings become equal and positive
D
One wattmeter reads zero
Question 122Single Answer
What is the power factor of a balanced three-phase circuit when the phase angle between voltage and current is 60°?
A
0.866
B
1
C
0.707
D
0.5
Question 123Single Answer
Which instrument is commonly used to indicate the direction of phase sequence in a three-phase supply?
A
Megohmmeter
B
Phase-sequence indicator
C
Frequency counter
D
Earth resistance tester
Question 124Single Answer
What occurs when any two line conductors supplying a conventional three-phase induction motor are interchanged?
A
Direction of rotation reverses
B
Synchronous speed doubles
C
Supply frequency becomes zero
D
Motor becomes a DC machine
Question 125Single Answer
Which connection provides a neutral point in a conventional three-phase distribution system?
A
Delta connection
B
Star connection
C
Series-delta connection
D
Open-delta connection
Question 126Single Answer
In a delta-connected load, which voltage relationship is correct?
A
VL = √3Vph
B
VL = Vph/√3
C
VL = 3Vph
D
VL = Vph
Question 127Single Answer
A three-phase star-connected resistive load has three 20 Ω phase resistors and a line voltage of 400 V. What is the approximate line current?
A
20 A
B
6.67 A
C
34.64 A
D
11.55 A
Question 128Single Answer
Which quantity determines the rotation direction of the magnetic field in a balanced three-phase machine?
A
Phase sequence
B
Supply voltage magnitude alone
C
Stator resistance alone
D
Power factor alone
Question 129Single Answer
A balanced three-phase load consumes 12 kW at 0.8 power factor. What is its apparent power?
A
15 kVA
B
12 kVA
C
20 kVA
D
9.6 kVA
Question 130Single Answer
What is the total reactive power for the load described in Question 1719, assuming lagging power factor?
A
6 kvar
B
12 kvar
C
9 kvar
D
15 kvar
Question 131Single Answer
Which electromagnetic principle is responsible for energy transfer between transformer windings?
A
Mutual induction
B
Photoelectric effect
C
Electrostatic induction
D
Thermoelectric effect
Question 132Single Answer
A transformer has 1000 primary turns and 200 secondary turns. What is its ideal voltage transformation ratio V2/V1?
A
10
B
2
C
5
D
0.2
Question 133Single Answer
What is its ideal secondary voltage?
A
46 V
B
115 V
C
230 V
D
23 V
Question 134Single Answer
Which transformer parameter remains unchanged between primary and secondary windings under ideal operation?
A
Current
B
Voltage
C
Frequency
D
Number of turns
Question 135Single Answer
What is the purpose of laminating a transformer core?
A
To increase copper losses
B
To eliminate magnetic flux
C
To reduce eddy-current losses
D
To increase leakage reactance deliberately
Question 136Single Answer
Which losses constitute the principal no-load power loss of a practical power transformer?
A
Full-load copper losses
B
Core losses
C
Mechanical friction losses
D
Windage losses
Question 137Single Answer
Which test is commonly performed to estimate transformer core losses and no-load current?
A
Short-circuit test
B
Open-circuit test
C
Polarity reversal test
D
Load test at rated current only
Question 138Single Answer
Which transformer test is normally used to estimate equivalent series impedance and rated-current copper losses?
A
Open-circuit test
B
Insulation resistance test alone
C
Short-circuit test
D
No-load polarity test
Question 139Single Answer
A transformer supplies 8 kW output while receiving 8.4 kW input. What is its efficiency?
A
Approximately 95.24%
B
92.0%
C
90.0%
D
Approximately 97.5%
Question 140Single Answer
Under what condition does a conventional transformer achieve maximum efficiency?
A
Copper loss equals iron loss
B
Copper loss becomes zero
C
Iron loss becomes infinite
D
Output power becomes zero
Question 141Single Answer
A 10 kVA transformer supplies a load at 0.8 power factor. What is its active output power at rated apparent load?
A
10 kW
B
12.5 kW
C
8 kW
D
6 kW
Question 142Single Answer
Which transformer configuration uses a common winding portion shared between input and output circuits?
A
Isolation transformer
B
Autotransformer
C
Current transformer
D
Pulse transformer with separate windings
Question 143Single Answer
What is the principal disadvantage of an autotransformer compared with a conventional two-winding isolation transformer?
A
It cannot change voltage
B
It requires a rotating magnetic field
C
It does not provide galvanic isolation
D
It operates exclusively on DC
Question 144Single Answer
Which transformer is intended to reduce large primary currents to suitable values for measurement and protection?
A
Audio output transformer
B
Potential transformer
C
Isolation transformer
D
Current transformer
Question 145Single Answer
Why must the secondary of an energized current transformer not be left open-circuited?
A
Its primary voltage becomes zero
B
Its frequency doubles
C
Dangerous secondary voltage may develop
D
Its core loses all flux
Question 146Single Answer
What is the usual function of a potential transformer?
A
Scaling high AC voltage to a lower measurable voltage
B
Increasing load current for heating
C
Converting AC directly into regulated DC
D
Reversing the phase sequence of a motor
Question 147Single Answer
A 1 kVA single-phase transformer has a rated primary voltage of 250 V. What is its rated primary current?
A
2 A
B
4 A
C
3 A
D
5 A
Question 148Single Answer
Which equation gives the RMS induced EMF of a sinusoidal transformer winding?
A
E = 4.44fNΦm
B
E = 2πfN/Φm
C
E = 4.44N/(fΦm)
D
E = fΦm/(4.44N)
Question 149Single Answer
A transformer winding has 100 turns, peak flux 0.01 Wb and frequency 50 Hz. What is its approximate RMS induced EMF?
A
222 V
B
444 V
C
1000 V
D
111 V
Question 150Single Answer
Which condition increases transformer core flux substantially if the applied RMS voltage remains constant?
A
Decreasing frequency
B
Increasing frequency
C
Increasing winding resistance
D
Decreasing load current
Question 151Single Answer
A transformer has 2% resistance drop and 3% reactance drop at rated current. What is the approximate voltage regulation at unity power factor using the usual approximate expression?
A
2%
B
5%
C
3%
D
1%
Question 152Single Answer
Which cooling designation corresponds to an oil-immersed transformer using natural oil circulation and natural air circulation?
A
ONAF
B
ONAN
C
OFAF
D
OFWF
Question 153Single Answer
Which insulating liquid has traditionally been used in many oil-immersed distribution transformers?
A
Distilled water
B
Ethanol
C
Mineral transformer oil
D
Mercury
Question 154Single Answer
What is the purpose of a Buchholz relay in a suitable oil-immersed transformer equipped with a conservator?
A
Controlling secondary frequency
B
Detecting gas generation and oil surges associated with internal faults
C
Measuring power factor
D
Providing normal tap-changing operation
Question 155Single Answer
Which device changes the effective transformer turns ratio to maintain an appropriate output voltage?
A
Overcurrent relay
B
Breather
C
Lightning arrester
D
Tap changer
Question 156Single Answer
Which principle explains the operation of a DC generator?
A
Electrostatic attraction
B
Electromagnetic induction
C
Piezoelectric conversion
D
Semiconductor rectification
Question 157Single Answer
What is the primary purpose of a commutator in a conventional DC generator?
A
To increase field winding resistance
B
To provide unidirectional output at the brushes
C
To eliminate induced armature EMF
D
To prevent rotor rotation
Question 158Single Answer
Which component carries the rotating armature winding in a conventional DC machine?
A
Yoke
B
Field pole
C
Rotor
D
Brush holder
Question 159Single Answer
What is the function of carbon brushes in a conventional DC machine?
A
To generate the main field flux
B
To provide electrical contact with the commutator
C
To mechanically support the shaft
D
To cool the stator by oil circulation
Question 160Single Answer
Which equation gives the generated EMF of a DC generator?
A
Eg = PΦZN/(60A)
B
Eg = 60A/(PΦZN)
C
Eg = PΦA/(60ZN)
D
Eg = ΦZ/(PN)
Question 161Single Answer
In the DC generator EMF equation, what does A represent?
A
Number of parallel armature paths
B
Number of field poles
C
Armature current
D
Armature resistance
Question 162Single Answer
A four-pole wave-wound DC generator has 600 armature conductors, flux per pole 0.02 Wb and speed 1000 rpm. What is its generated EMF?
A
200 V
B
400 V
C
600 V
D
800 V
Question 163Single Answer
Which quantity is directly proportional to the electromagnetic torque of a DC motor under normal operation?
A
Product of flux per pole and armature current
B
Rotor speed alone
C
Terminal voltage squared
D
Field resistance alone
Question 164Single Answer
What is the main purpose of a starter in a conventional DC motor?
A
Increasing the applied supply frequency
B
Limiting the high armature current during starting
C
Eliminating motor back EMF
D
Providing continuous rectification
Question 165Single Answer
Why is starting current high in a DC motor connected directly to a rated-voltage supply?
A
Field flux is necessarily zero
B
Back EMF is initially zero
C
Commutator segments are open-circuited
D
Supply frequency is excessive
Question 166Single Answer
Which expression gives the approximate back EMF of a DC motor with terminal voltage V, armature current Ia and armature resistance Ra?
A
Eb = V - IaRa
B
Eb = V + IaRa
C
Eb = IaRa/V
D
Eb = V/IaRa
Question 167Single Answer
A DC motor operates from 220 V and draws armature current 20 A through armature resistance 0.5 Ω. Neglect brush drop. What is its back EMF?
A
200 V
B
220 V
C
210 V
D
230 V
Question 168Single Answer
Which DC motor is generally preferred for applications requiring nearly constant speed over a moderate load range?
A
DC shunt motor
B
DC series motor
C
Universal motor operated without field
D
Separately excited generator
Question 169Single Answer
What is the principal characteristic of a DC series motor at starting?
A
High starting torque
B
Exactly constant speed
C
Low current under every load
D
Zero torque
Question 170Single Answer
Why should a DC series motor normally not be operated without mechanical load?
A
Its voltage automatically becomes zero
B
It may accelerate to a dangerously high speed
C
Its armature current becomes infinite instantly
D
Its field changes into a capacitor
Question 171Single Answer
Which component helps reduce sparking and improve commutation in many large DC machines?
A
Electrolytic capacitor
B
Interpole
C
Transformer breather
D
Slip ring
Question 172Single Answer
Which effect describes distortion of the main magnetic field caused by armature current in a DC machine?
A
Dielectric polarization
B
Skin effect
C
Armature reaction
D
Transformer inrush
Question 173Single Answer
For a DC motor operating with approximately constant armature voltage and resistance drop, what happens to speed if field flux decreases?
A
Speed tends to increase
B
Speed becomes exactly zero
C
Speed remains unchanged under every load
D
Speed decreases proportionally
Question 174Single Answer
A DC motor develops mechanical power of 5 kW at 1000 rpm. What is its approximate shaft torque?
A
23.9 N·m
B
47.7 N·m
C
95.5 N·m
D
100 N·m
Question 175Single Answer
Which loss in a DC machine is approximately proportional to the square of armature current when resistance is constant?
A
Friction loss
B
Armature copper loss
C
Windage loss
D
Core hysteresis loss
Question 176Single Answer
Which physical principle produces torque in a conventional three-phase induction motor?
A
Electrostatic attraction
B
Direct battery excitation of rotor magnets
C
Electromagnetic interaction between rotating stator field and induced rotor currents
D
Optical radiation pressure
Question 177Single Answer
What is the synchronous speed of a four-pole induction motor supplied at 50 Hz?
A
1000 rpm
B
750 rpm
C
1500 rpm
D
3000 rpm
Question 178Single Answer
Which expression represents the synchronous speed Ns in rpm for a machine with P poles and supply frequency f?
A
Ns = 60P/f
B
Ns = 120f/P
C
Ns = 60f/P
D
Ns = 120P/f
Question 179Single Answer
A four-pole, 50 Hz induction motor operates at 1440 rpm. What is its slip?
A
4%
B
6%
C
2%
D
8%
Question 180Single Answer
Which expression correctly represents induction motor slip in terms of synchronous speed Ns and rotor speed N?
A
s = (Ns - N)/Ns
B
s = N/Ns
C
s = Ns/(Ns - N)
D
s = (Ns + N)/Ns
Question 181Single Answer
What is the rotor-current frequency of an induction motor supplied at 50 Hz and operating at 3% slip?
A
3 Hz
B
1.5 Hz
C
15 Hz
D
50 Hz
Question 182Single Answer
Which rotor construction consists of conductive bars short-circuited by end rings?
A
Salient-pole synchronous rotor
B
Wound DC armature
C
Squirrel-cage rotor
D
Permanent-magnet rotor
Question 183Single Answer
What is the approximate slip of a conventional induction motor rotor at the instant of starting from rest?
A
Zero
B
1
C
0.5
D
Infinite
Question 184Single Answer
Which technique reduces starting current by initially applying reduced voltage to a suitable three-phase induction motor?
A
Increasing supply voltage
B
Short-circuiting the stator terminals
C
Opening one supply phase
D
Star-delta starting
Question 185Single Answer
What is the approximate starting torque of a star-connected induction motor compared with direct delta starting at the same line voltage, assuming the same motor and neglecting saturation?
A
One-half
B
One-third
C
Twice
D
Three times
Question 186Single Answer
Which method provides wide-range induction motor speed control by varying supply frequency and voltage?
A
Fixed-resistance starter alone
B
Mechanical brake
C
Variable-frequency drive
D
Permanent rotor short circuit
Question 187Single Answer
If a four-pole induction motor's supply frequency increases from 50 Hz to 60 Hz, what is its new synchronous speed?
A
1200 rpm
B
1800 rpm
C
1500 rpm
D
2400 rpm
Question 188Single Answer
What happens to rotor frequency as a three-phase induction motor approaches synchronous speed under motoring operation?
A
It approaches zero
B
It rises above supply frequency
C
It becomes twice the supply frequency
D
It remains exactly at supply frequency
Question 189Single Answer
Which condition occurs when an induction machine rotor is driven above synchronous speed while connected to an appropriate AC supply?
A
Generator operation
B
Locked-rotor operation
C
Direct-current excitation
D
Zero air-gap power transfer
Question 190Single Answer
Which loss arises from rotor conductor resistance in a conventional induction motor?
A
Dielectric loss
B
Rotor copper loss
C
Core saturation alone
D
Mechanical windage
Question 191Single Answer
In an induction motor, rotor copper loss is equal to which fraction of the air-gap power Pg?
A
(1 - s)Pg
B
Pg/s
C
(1 + s)Pg
D
sPg
Question 192Single Answer
An induction motor receives 20 kW air-gap power at 5% slip. What is its rotor copper loss?
A
1 kW
B
0.5 kW
C
2 kW
D
5 kW
Question 193Single Answer
What is the mechanical power developed by the motor in Question 1782, before mechanical losses?
A
20 kW
B
18 kW
C
19 kW
D
21 kW
Question 194Single Answer
What is the primary purpose of external rotor resistance in a wound-rotor induction motor during starting?
A
To eliminate slip
B
To improve starting torque characteristics while controlling current
C
To convert the rotor into a permanent magnet
D
To increase synchronous speed
Question 195Single Answer
Which type of motor normally runs at exactly synchronous speed in steady-state operation without losing synchronism?
A
Squirrel-cage induction motor
B
DC series motor
C
Universal motor
D
Synchronous motor
Question 196Single Answer
A synchronous motor is typically excited using which rotor field arrangement?
A
DC field winding or permanent magnets
B
Rotor resistance alone
C
Capacitive rotor bars alone
D
Open-circuited induction cage
Question 197Single Answer
Which characteristic describes a conventional synchronous motor without a special starting arrangement?
A
It requires slip for steady-state torque
B
It always starts at synchronous speed
C
It cannot operate at leading power factor
D
It is not inherently self-starting from a stationary rotor on a fixed-frequency supply
Question 198Single Answer
What happens to the power factor of a synchronous motor as its field excitation is adjusted from underexcitation toward sufficient overexcitation?
A
It always remains zero
B
It cannot change
C
It can change from lagging through unity to leading
D
It becomes lagging under every condition
Question 199Single Answer
Which graphical characteristic shows synchronous motor armature current versus field current at constant mechanical load?
A
V-curve
B
Magnetization curve of a DC generator
C
B-H curve
D
Torque-slip curve
Question 200Single Answer
Which synchronous machine is commonly driven by a turbine to generate three-phase electrical energy?
