GATE ECE 2005 | Calculus Question 48 | Engineering Mathematics

GATE ECE 2005

MCQ (Single Correct Answer)

-0.3

The value of the integral $$1 = {1 \over {\sqrt {2\pi } }}\,\,\int\limits_0^\infty {{e^{ - {\raise0.5ex\hbox{$\scriptstyle {{x^2}}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 8$}}}}} \,\,dx\,\,\,$$ is ________.

$$1$$

$${\pi }$$

$$2$$

$${2\pi }$$

GATE ECE 1997

MCQ (Single Correct Answer)

-0.3

The curve given by the equation $${x^2} + {y^2} = 3axy$$ is

Symmetrical about $$x$$-axis

Symmetrical about $$y$$-axis

Symmetrical about the line $$y=x$$

Tangential to $$x=y=a/3$$

GATE ECE 1995

MCQ (Single Correct Answer)

-0.3

By reversing the order of integration $$\int\limits_0^2 {\int\limits_{{x^2}}^{2x} {f\left( {x,y} \right)dy\,dx} } $$ may be represented as ______.

$$\int\limits_0^2 {\int\limits_{{x^2}}^{2x} {f\left( {x,y} \right)dy\,dx} } $$

$$\int\limits_0^2 {\int\limits_y^{\sqrt y } {f\left( {x,y} \right)dy\,dx} } $$

$$\int\limits_0^4 {\int\limits_{y/2}^{\sqrt y } {f\left( {x,y} \right)dy\,dx} } $$

$$\int\limits_{{x^2}}^{2x} {\int\limits_0^2 {f\left( {x,y} \right)dy\,dx} } $$

GATE ECE 1995

MCQ (Single Correct Answer)

-0.3

The third term in the taylor's series expansion of $${e^x}$$ about $$'a'$$ would be ________.

$${e^a}\left( {x - a} \right)$$

$${{{e^a}} \over 2}{\left( {x - a} \right)^2}$$

$${{{e^a}} \over 2}$$

$${{{e^a}} \over 6}{\left( {x - a} \right)^3}$$

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GATE ECE Subjects

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

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

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

Semiconductor Physics PN Junction BJT and FET IC Basics and MOSFET

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 Complex Variable Probability and Statistics Differential Equations Numerical Methods Transform Theory

Microprocessors

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

Communications

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

Electromagnetics

Maxwell Equations Transmission Lines Uniform Plane Waves Waveguides Antennas Miscellaneous