GATE ECE 2014 Set 3 | Calculus Question 29 | Engineering Mathematics

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GATE ECE 2014 Set 3

MCQ (Single Correct Answer)

-0.3

If $$z=xy$$ $$ln(xy),$$ then

$$x{{\partial z} \over {\partial x}} + y{{\partial z} \over {\partial y}} = 0$$

$$y{{\partial z} \over {\partial x}} = x{{\partial z} \over {\partial y}}$$

$$x{{\partial z} \over {\partial x}} = y{{\partial z} \over {\partial y}}$$

$$y{{\partial z} \over {\partial x}} + x{{\partial z} \over {\partial y}} = 0$$

GATE ECE 2014 Set 2

MCQ (Single Correct Answer)

-0.3

For $$0 \le t < \infty ,$$ the maximum value of the function $$f\left( t \right) = {e^{ - t}} - 2{e^{ - 2t}}\,$$ occurs at

$$t = {\log _e}4$$

$$t = {\log _e}2$$

$$t=0$$

$$t = {\log _e}8$$

GATE ECE 2014 Set 2

MCQ (Single Correct Answer)

-0.3

The value of $$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {1 \over x}} \right)^x}\,\,$$ is

$$ln2$$

$$1.0$$

$$e$$

$$\infty $$

GATE ECE 2010

MCQ (Single Correct Answer)

-0.3

If $$\,{e^y} = {x^{1/x}}\,\,$$ then $$y$$ has a

maximum at $$x=e$$

minimum $$x=e$$

maximum at $$x = {e^{ - 1}}$$

minimum $$x = {e^{ - 1}}$$

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GATE ECE Subjects

Network Theory

Network Elements Network Theorems Transient Response Sinusoidal Steady State Response Two Port Networks Network Graphs State Equations For Networks Miscellaneous

Control Systems

Signal Flow Graph and Block Diagram Time Response Analysis Compensators Basic of Control Systems Frequency Response Analysis Stability Root Locus Diagram State Space Analysis

Electronic Devices and VLSI

Semiconductor Physics PN Junction BJT and FET IC Basics and MOSFET

Analog Circuits

Bipolar Junction Transistor FET and MOSFET Oscillators Operational Amplifier 555 Timer Frequency Response Diodes Feedback Amplifier Power Amplifier

Digital Circuits

Number System and Code Convertions Boolean Algebra Logic Gates Combinational Circuits Sequential Circuits Semiconductor Memories Logic Families Analog to Digital and Digital to Analog Converters

Microprocessors

Pin Details of 8085 and Interfacing with 8085 Instruction Set and Programming with 8085

Signals and Systems

Representation of Continuous Time Signal Fourier Series Discrete Time Signal Fourier Series Fourier Transform Discrete Time Signal Z Transform Continuous Time Linear Invariant System Transmission of Signal Through Continuous Time LTI Systems Discrete Time Linear Time Invariant Systems Sampling Continuous Time Signal Laplace Transform Discrete Fourier Transform and Fast Fourier Transform Transmission of Signal Through Discrete Time Lti Systems Miscellaneous Fourier Transform

Communications

Analog Communication Systems Digital Communication Systems Random Signals and Noise Fundamentals of Information Theory Noise In Digital Communication

Electromagnetics

Waveguides Antennas Miscellaneous Transmission Lines Maxwell Equations Uniform Plane Waves

General Aptitude

Numerical Ability Verbal Ability

Engineering Mathematics

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