GATE ECE 2014 Set 3 | Calculus Question 31 | 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

Signals and Systems

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

Network Theory

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

Control Systems

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

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

General Aptitude

Numerical Ability Logical Reasoning Verbal Ability

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

Engineering Mathematics

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

Microprocessors

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

Communications

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

Electromagnetics

Waveguides Antennas Miscellaneous Transmission Lines Maxwell Equations Uniform Plane Waves