Question 754 - GATE Electrical Engineering

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Q#1 Probability and Statistics GATE EE 2025 MCQ +2 marks -0.66 marks

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Let and be continuous random variables with probability density functions and , respectively. Further, let and

Which one of the following options is correct?

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Network Analysis

259

Network Basics

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Network Elements	0	Browse
Kirchhoffs Laws	1	Browse
Nodal and Mesh Analysis	1	Browse
Power and Energy Calculation	1	Browse
Duality	0	Browse
Topic-wide	55	Browse

Network Theorems (DC Circuits)

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Thevenin and Norton Theorem	0	Browse
Maximum Power Transfer Theorem - DC Circuits	0	Browse
Other Theorems - DC Circuits	0	Browse
Topic-wide	27	Browse

Transient Analysis

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Initial and Final Conditions	0	Browse
First Order Circuits	0	Browse
Second Order Circuits	0	Browse
Laplace Transform Method	0	Browse
Topic-wide	47	Browse

Sinusoidal Steady State Analysis

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Phasor Analysis	0	Browse
Maximum Power Transfer Theorem - AC Circuits	0	Browse
Other Theorems - AC Circuits	0	Browse
Power in AC Circuits	0	Browse
Miscellaneous	0	Browse
Resonance	0	Browse
Topic-wide	79	Browse

Two Port Network

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Two Port Network	0	0	0	Browse
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Graph Theory

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Graph Theory	0	0	0	Browse
Topic-wide	7	0	0	Browse

Three Phase Circuits

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Three Phase Circuits	0	0	0	Browse
Topic-wide	12	0	0	Browse

Magnetically Coupled Circuits

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Magnetically Coupled Circuits	0	0	0	Browse
Topic-wide	11	0	0	Browse

Signals and Systems

164

Signals

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Delta Function	0	Browse
Periodic and other Signals	0	Browse
Signal Graphical Representation	0	Browse
Energy and Power Signals	0	Browse
Waveform Synthesis and Parameters	0	Browse
Topic-wide	26	Browse

LTI Systems

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LTI System Properties	0	Browse
Continuous Convolution	0	Browse
Discrete Convolution	0	Browse
Topic-wide	42	Browse

Fourier Series

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Continuous Time Fourier Series	0	Browse
Properties of Fourier Series	0	Browse
Discrete Time Fourier Series	0	Browse
Topic-wide	21	Browse

Fourier Transform

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Continuous Time Fourier Transform Calculation	0	Browse
Continuous Time Transform Properties	0	Browse
Discrete Time Fourier Transform Calculation	0	Browse
Discrete Time Fourier Transform Properties	0	Browse
Discrete Fourier Transform and Fast Fourier Transform	0	Browse
Topic-wide	28	Browse

Laplace Transform

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Laplace Transform Calculation	0	Browse
Laplace Transform Properties	0	Browse
Initial and Final Value Theorem	0	Browse
Topic-wide	22	Browse

Z Transform

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Z-Transform Calculation	0	Browse
Z-Transform Properties	0	Browse
Initial and Final Value Theorem - Z Transform	0	Browse
Topic-wide	18	Browse

Sampling

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Sampling	0	0	0	Browse
Topic-wide	7	0	0	Browse

Digital Filter Design

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Digital Filters	0	0	0	Browse

Control Systems

201

Transfer Function

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Transfer Function	0	Browse
Block Diagram	0	Browse
Signal Flow Graph	0	Browse
Mathematical Modelling and Sensitivity	0	Browse
Topic-wide	28	Browse

Time Response Analysis

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Steady State Analysis	0	Browse
Transient Analysis	0	Browse
Topic-wide	54	Browse

Stability

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Routh Criteria	0	0	0	Browse
Topic-wide	33	0	0	Browse

Root Locus Technique

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Root Locus	0	Browse
Complimentary Root Locus	0	Browse
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Frequency Domain Analysis

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Frequency Response	0	Browse
Polar Plot	0	Browse
Nyquist Plot and Stability Criterion	0	Browse
Gain Margin and Phase Margin	0	Browse
Bode Plot	0	Browse
Topic-wide	63	Browse

State Variable Analysis

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Deriving State Model	0	Browse
State Model Analysis	0	Browse
Controllability and Observability	0	Browse
Topic-wide	2	Browse

Control System Design

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Compensators	0	Browse
Controller	0	Browse
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Analog Electronics

180

Diode and Its Applications

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Diode Basics and Diode Circuit Analysis	0	Browse
Rectifier Circuits	0	Browse
Filter Circuits	0	Browse
Voltage Regulator	0	Browse
Wave Shaping Circuits	0	Browse
Topic-wide	33	Browse

BJT

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DC Analysis and Biasing Circuits of BJT	0	Browse
Small signal analysis of BJT	0	Browse
Single stage BJT Amplifier	0	Browse
Low frequency and High frequency response of BJT Amplifier	0	Browse
Topic-wide	42	Browse

JFET

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DC Analysis and Biasing Circuits of JFET	0	0	0	Browse
Small signal analysis of JFET	0	0	0	Browse
Single stage JFET Amplifier	0	0	0	Browse
Low frequency and High frequency response of JFET Amplifier	0	0	0	Browse

MOSFET

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DC Analysis and Biasing Circuits of MOSFET	0	Browse
Small signal analysis of MOSFET	0	Browse
Single stage MOSFET Amplifier	0	Browse
Low frequency and High frequency response of MOSFET Amplifier	0	Browse
Topic-wide	16	Browse

Amplifiers

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Multistage Amplifiers	0	Browse
Differential Amplifiers	0	Browse
Feedback Amplifiers	0	Browse
Power Amplifiers	0	Browse
Topic-wide	11	Browse

OP-AMP and its Applications

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Op-amp	0	Browse
Positive feedback applications	0	Browse
Negative feedback applications	0	Browse
Topic-wide	78	Browse

Oscillators

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Sinusoidal Oscillator Circuits and 555 timers	0	0	0	Browse

Digital Electronics

148

Number Systems

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Radix Conversion and Addition/Subtraction	0	Browse
Binary Codes	0	Browse
Topic-wide	1	Browse

Boolean Algebra

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Boolean Algebra	0	Browse
Logic Gates	0	Browse
K-Map	0	Browse
Topic-wide	19	Browse

Combinational Circuits

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Multiplexer and Demultiplexer	0	Browse
Encoders and Decoders	0	Browse
Adders and Subtractors	0	Browse
Other Circuits	0	Browse
Topic-wide	28	Browse

Sequential Circuits

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Flip Flops	0	Browse
Counters	0	Browse
Registers	0	Browse
State Machine	0	Browse
Topic-wide	36	Browse

Data Converters

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ADC	0	Browse
DAC	0	Browse
Topic-wide	22	Browse

Logic Family

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Logic Families	0	0	0	Browse
Topic-wide	9	0	0	Browse

Memory

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Memory	0	0	0	Browse

Microprocessor

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Microprocessor	0	0	0	Browse
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Computer Organisation

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Computer Organisation	0	0	0	Browse

Electrical Machines

390

Transformers

109

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Construction of Transformer	0	Browse
Induced EMF - Transformer	0	Browse
Equivalent Circuit - Transformer	0	Browse
Testing of a Transformer	0	Browse
Losses and Efficiency - Transformer	0	Browse
Voltage Regulation - Transformer	0	Browse
Three Phase Transformer	0	Browse
Auto Transformer	0	Browse
Parallel Operation - Transformer	0	Browse
Harmonics in Transformer	0	Browse
Topic-wide	109	Browse

DC Machines

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Construction of DC Machines	0	Browse
EMF and Torque Equation	0	Browse
Equivalent Circuit - DC Machines	0	Browse
Losses and Efficiency - DC Machines	0	Browse
Speed Control of DC Motor	0	Browse
Starting, Braking and Testing of DC Motor	0	Browse
Characteristics of DC machines	0	Browse
Electromechanical Energy Conversion	0	Browse
Topic-wide	80	Browse

Synchronous Machines

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Induced EMF - Synchronous Machines	0	Browse
Voltage Regulation Methods	0	Browse
Equivalent Circuit - Synchronous Machines	0	Browse
Synchronous Impedance	0	Browse
Power Angle Equation	0	Browse
Parallel Operation - Synchronous Machines	0	Browse
Losses and Efficiency - Synchronous Machines	0	Browse
Voltage Regulation - Synchronous Machines	0	Browse
Droop Characteristics	0	Browse
Salient Pole Machines	0	Browse
Synchronous Motor	0	Browse
Cascading of Machines	0	Browse
Contruction and Physical Phenomenon	0	Browse
Topic-wide	82	Browse

Induction Machines

110

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Construction and Rotating Magnetic Field	0	Browse
Equivalent Circuit - Induction Machines	0	Browse
Torque Slip Characteristics	0	Browse
Power and Efficiency	0	Browse
Tests on an Induction Motor	0	Browse
Starting of Induction Motor	0	Browse
Speed Control	0	Browse
Stability of Induction Motor	0	Browse
Singe Phase Induction Motor	0	Browse
Stepper Motor	0	Browse
Topic-wide	110	Browse

Special Machines

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Special Machines	0	0	0	Browse
Topic-wide	9	0	0	Browse

Power Electronics

237

Power Semiconductor Devices

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Switch Characteristics	0	Browse
Triggering and Characteristics of SCR	0	Browse
Protection and Connection of SCR	0	Browse
Other Devices	0	Browse
Topic-wide	47	Browse

Phase Controlled Converter

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Single Phase Converter	0	Browse
Three Phase Converter	0	Browse
Effect of Source Inductance	0	Browse
Dual Converter	0	Browse
Topic-wide	82	Browse

Chopper

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Buck Converter	0	Browse
Boost Converter	0	Browse
Buck Boost Converter	0	Browse
Thyristor Commutation Techniques	0	Browse
Topic-wide	53	Browse

Inverter

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Single Phase Inverter	0	Browse
Three Phase Inverter	0	Browse
PWM Control	0	Browse
Current Source Inverter	0	Browse
Topic-wide	39	Browse

AC and DC Drives

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AC Drives	0	Browse
DC Drives	0	Browse
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AC Voltage Controller

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AC Voltage Regulator	0	Browse
Cycloconverter	0	Browse
Topic-wide	7	Browse

Power Systems

343

Power System Generation

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Power Plants	0	Browse
Economic Power Generation	0	Browse
Topic-wide	9	Browse

Transmission and Distribution

139

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Transmission Line Parameters (L and C)	0	Browse
Short and Medium Transmission Line	0	Browse
Wave Nature of Long Transmission Line	0	Browse
Surges in Transmission Line	0	Browse
Power and ABCD Parameters	0	Browse
Voltage and Frequency Control	0	Browse
Power Factor Correction	0	Browse
UG Cables	0	Browse
Overhead Insulators	0	Browse
Corona	0	Browse
Distribution Systems	0	Browse
HVDC	0	Browse
Topic-wide	139	Browse

Economic Load Dispatch

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Fault Analysis

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Per Unit System	0	Browse
Symmetrical Components	0	Browse
Sequence Network	0	Browse
Symmetrical Fault Analysis	0	Browse
Unsymmetrical Fault Analysis	0	Browse
Zbus Based Fault Analysis	0	Browse
Topic-wide	65	Browse

Power System Stability

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Swing Equation	0	Browse
Steady State Stability	0	Browse
Equal Area Criteria	0	Browse
Topic-wide	33	Browse

Load Flow Analysis

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Power System Matrices	0	Browse
Gauss Seidel Iteration	0	Browse
Newton Raphson Method	0	Browse
Topic-wide	40	Browse

Power System Protection

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Circuit Breakers	0	Browse
Overcurrent Protection	0	Browse
Protection of Alternator	0	Browse
Protection of Transformer	0	Browse
Protection of Transmission Line	0	Browse
Topic-wide	40	Browse

EMFT EE

Electrostatics

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Magnetostatics

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Measurement

152

Error Analysis

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Error Analysis	0	Browse
Units and Dimensions	0	Browse
Topic-wide	15	Browse

Electro-mechanical Instruments

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PMMC Instruments	0	Browse
Moving Iron Instruments	0	Browse
Electrodynamometer Instruments	0	Browse
Ammeter and Voltmeter	0	Browse
Wattmeter	0	Browse
Energy Meter	0	Browse
Other Instruments	0	Browse
Topic-wide	76	Browse

Measurement of R,L and C

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Measurement of Inductance	0	Browse
Measurement of Capacitance	0	Browse
Measurement of Frequency	0	Browse
Measurement of Resistance	0	Browse
Topic-wide	21	Browse

CRO

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CRO	0	Browse
Lissajous Pattern	0	Browse
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Instrument Transformer

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Potential Transformer	0	Browse
Current Transformer	0	Browse
Topic-wide	9	Browse

Potentiometer and Q-Meter

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Potentiometer	0	Browse
Q-Meter	0	Browse
Topic-wide	5	Browse

Digital Instruments

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Digital Instruments	0	0	0	Browse
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Transducers

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Measurement of Displacement	0	Browse
Measurement of Force	0	Browse
Measurement of Pressure	0	Browse
Measurement of Angular Speed	0	Browse
Measurement of Flow Rate	0	Browse
Measurement of Temperature	0	Browse
Topic-wide	4	Browse

Engineering Mathematics

225

Linear Algebra

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Matrices and Determinants	0	Browse
Solution of Linear Equations	0	Browse
Eigen Values and Eigen Vectors	0	Browse
Topic-wide	68	Browse

Calculus

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Differential Calculus	0	Browse
Integral Calculus	0	Browse
Vector Calculus	0	Browse
Topic-wide	63	Browse

Differential Equations

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First Order Differential Equations	0	Browse
Higher Order Differential Equations	0	Browse
Topic-wide	18	Browse

Complex Functions

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Analytic Functions (Cauchy Riemann Equations) and compex numbers	0	Browse
Complex Integral	0	Browse
Topic-wide	23	Browse

Probability and Statistics

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Probability	0	Browse
Statistics	0	Browse
Random Variable	0	Browse
Topic-wide	32	Browse

Numerical Methods

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Solution of Non-Linear Equation	0	Browse
Numerical Integration	0	Browse
Numerical Solution of Differential Equations	0	Browse
Topic-wide	15	Browse

Transform Theory

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Laplace Transform	0	Browse
Fourier Transform	0	Browse
Z-Transform	0	Browse
Topic-wide	6	Browse

General Aptitude

206

Numerical Ability

116

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Analytical Reasoning	0	Browse
Logical Reasoning	0	Browse
Progressions	0	Browse
Numbers	0	Browse
Clocks and Time Sequence	0	Browse
LCM and HCF, Factors and Remainders	0	Browse
Simple and Compound Interest	0	Browse
Venn Diagrams	0	Browse
Direction Sense	0	Browse
Arithmetic Reasoning	0	Browse
Insert Missing Character	0	Browse
Ratio and Proportion	0	Browse
Percentage, Profit, Loss and Partnerships	0	Browse
Stocks and Shares	0	Browse
Average, Mixtures and Allegations	0	Browse
Geometry and Mensuration	0	Browse
Ages	0	Browse
Time and Work	0	Browse
Pipes and Cisterns	0	Browse
Time and Distance	0	Browse
Data Interpretation	0	Browse
Analytical Figures	0	Browse
Blood Relations	0	Browse
Coding and Decoding	0	Browse
Cube and Dice	0	Browse
Ranking	0	Browse
Speed and Relative Speed	0	Browse
Logarithms	0	Browse
Involution and Evolution	0	Browse
Probability	0	Browse
Permutation and Combinations	0	Browse
Quadratic Equations	0	Browse
Miscellaneous - Numerical Ability	0	Browse
Topic-wide	116	Browse

Verbal Ability

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Grammar	0	Browse
Spotting Errors	0	Browse
Objective Comprehension	0	Browse
Sentence Completion	0	Browse
Sentence Improvement	0	Browse
Analogy	0	Browse
Ordering of Sentences	0	Browse
Vocabulary	0	Browse
Critical Reasoning	0	Browse
Miscellaneous - Verbal Ability	0	Browse
Topic-wide	90	Browse