GATE ECE 2005 | Calculus Question 45 | 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

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

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 Verbal Ability

Electronic Devices and VLSI

PN Junction Semiconductor Physics IC Basics and MOSFET BJT and FET

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 Complex Variable Probability and Statistics Differential Equations Numerical Methods Transform Theory

Microprocessors

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