GATE EE 2005 | Differential Equations Question 13 | Engineering Mathematics

GATE EE 2005

MCQ (Single Correct Answer)

-0.3

The solution of the first order differential equation $$\mathop x\limits^ \bullet \left( t \right) = - 3\,x\left( t \right),\,x\left( 0 \right) = {x_0}\,\,\,\,$$ is

$$x\left( t \right) = {x_0}\,{e^{ - 3\,t}}$$

$$x\left( t \right) = {x_0}\,{e^{ - 3\,}}$$

$$x\left( t \right) = {x_0}\,{e^{ - t\,3}}$$

$$x\left( t \right) = {x_0}\,{e^{ - t\,}}$$

GATE EE 1995

MCQ (Single Correct Answer)

-0.3

If at every point of a certain curve , the slope of the tangent equals $${{ - 2x} \over y},$$ the curve is _______.

A straight line

A parabola

A circle

An Ellipse

GATE EE Subjects

Electric Circuits

Three Phase Circuits Transient Response Graph Theory Two Port Networks Sinusoidal Steady State Analysis Network Elements Network Theorems

Electromagnetic Fields

Time Varying Fields Electrostatics Magnetostatics

Signals and Systems

Linear Time Invariant Systems Continuous and Discrete Time Signals Continuous Time Signal Fourier Transform Continuous Time Periodic Signal Fourier Series Discrete Time Signal Z Transformation Miscellaneous Continuous Time Signal Laplace Transform Sampling Theorem

Electrical Machines

Induction Machines D.C Machines Synchronous Machines Transformers

Engineering Mathematics

Calculus Vector Calculus Linear Algebra Differential Equations Probability and Statistics Transform Theory Complex Variable Numerical Methods

General Aptitude

Verbal Ability Logical Reasoning Numerical Ability

Power System Analysis

Parameters and Performance of Transmission Lines Power Generation Cost Power System Stability Symmetrical Components and Symmetrical and Unsymmetrical Faults Circuit Breaker Switch Gear and Protection Per Unit System Load Flow Studies High Voltage Dc Transmission Generating Power Station

Electrical and Electronics Measurement

Basic of Indicating Instruments Error Analysis and Measurement Measurement of Resistance and A.C Bridges Measurement of Energy and Power Digital Voltmeters Questions Potentiometer and Instrument Transformers Cathode Ray Oscilloscope

Analog Electronics

Diode Circuits and Applications Bjt and Mosfet Biasing Small Signal Modeling Feedback Amplifiers and Oscillator Circuits Operational Amplifier Frequency Response 555 Timer

Control Systems

Time Response Analysis Block Diagram and Signal Flow Graph Polar Nyquist and Bode Plot State Variable Analysis Root Locus Techniques Basics of Control System Routh Hurwitz Stability Controller and Compensator

Power Electronics

Choppers and Commutation Techniques Single and Three Phase Rectifier Power Semiconductor Devices Ac Voltage Controllers Inverters

Digital Electronics

Sequential Circuits Microprocessor Boolean Algebra Analog to Digital and Digital to Analog Converter Combinational Circuits Minimization Logic Families and Memories Logic Gates