GATE ECE 2014 Set 3 | Calculus Question 32 | Engineering Mathematics

PREVIOUS NEXT

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

PREVIOUS NEXT

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

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

Digital Circuits

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

General Aptitude

Numerical Ability Logical Reasoning Verbal Ability

Electronic Devices and VLSI

PN Junction Semiconductor Physics IC Basics and MOSFET BJT and FET

Analog Circuits

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

Engineering Mathematics

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

Microprocessors

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

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