GATE EE 2010 | Calculus Question 25 | Engineering Mathematics

GATE EE 2010

MCQ (Single Correct Answer)

-0.6

The value of the quantity, where $$P = \int\limits_0^1 {x{e^x}\,dx\,\,\,} $$ is

$$0$$

$$1$$

$$e$$

$$1/e$$

GATE EE 2009

MCQ (Single Correct Answer)

-0.6

If $$(x, y)$$ is continuous function defined over $$\left( {x,y} \right) \in \left[ {0,1} \right] \times \left[ {0,1} \right].\,\,\,$$ Given two constants, $$\,x > {y^2}$$ and $$\,y > {x^2},$$ the volume under $$f(x, y)$$ is

$$\,\,\int\limits_{y = 0}^{y = 1} {\int\limits_{x = {y^2}}^{x = \sqrt y } {f\left( {x,y} \right)dx\,dy\,\,} } $$

$$\int\limits_{y = {x^2}}^{y = 1} {\int\limits_{x = {y^2}}^{x = 1} {f\left( {x,y} \right)dx\,dy\,\,} } $$

$$\int\limits_{y = 0}^{y = 1} {\int\limits_{x = 0}^{x = 1} {f\left( {x,y} \right)dx\,dy\,\,} } $$

$$\int\limits_{x = 0}^{y = \sqrt x } {\int\limits_{x = 0}^{x = \sqrt y } {f\left( {x,y} \right)dx\,dy\,\,} } $$

GATE EE 2007

MCQ (Single Correct Answer)

-0.6

The integral $$\,\,{1 \over {2\pi }}\int\limits_0^{2\Pi } {Sin\left( {t - \tau } \right)\cos \tau \,d\tau \,\,\,} $$ equals

$$Sin\,t\cos t$$

$$0$$

$${1 \over 2}\,\,\cos \,t$$

$${1 \over 2}\,\,\sin \,t$$

GATE EE 2006

MCQ (Single Correct Answer)

-0.6

The expression $$V = \int\limits_0^H {\pi {R^2}{{\left( {1 - {h \over H}} \right)}^2}dh\,\,\,} $$ for the volume of a cone is equal to _________.

$$\int\limits_0^R {\pi {R^2}{{\left( {1 - {h \over H}} \right)}^2}dr\,\,\,} $$

$$\int\limits_0^R {\pi {R^2}{{\left( {1 - {h \over H}} \right)}^2}dh\,\,\,} $$

$$\int\limits_0^H {\,\,2\pi rH\left( {1 - {r \over R}} \right)dh\,\,\,} $$

$$\int\limits_0^R {\,\,2\pi rH{{\left( {1 - {r \over R}} \right)}^2}dr\,\,\,} $$

GATE EE Subjects

Electromagnetic Fields

Time Varying Fields Electrostatics Magnetostatics

Signals and Systems

Continuous and Discrete Time Signals Linear Time Invariant Systems Continuous Time Signal Fourier Transform Discrete Time Signal Z Transformation Continuous Time Signal Laplace Transform Sampling Theorem Continuous Time Periodic Signal Fourier Series Miscellaneous

Engineering Mathematics

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

General Aptitude

Verbal Ability Logical Reasoning Numerical Ability

Power Electronics

Choppers and Commutation Techniques Single and Three Phase Rectifier Power Semiconductor Devices Ac Voltage Controllers Inverters

Power System Analysis

Parameters and Performance of Transmission Lines Power Generation Cost Power System Stability Symmetrical Components and Symmetrical and Unsymmetrical Faults Circuit Breaker Switch Gear and Protection Per Unit System Load Flow Studies High Voltage Dc Transmission Generating Power Station

Analog Electronics

Diode Circuits and Applications Bjt and Mosfet Biasing Small Signal Modeling Feedback Amplifiers and Oscillator Circuits Operational Amplifier Frequency Response 555 Timer

Control Systems

Block Diagram and Signal Flow Graph Polar Nyquist and Bode Plot State Variable Analysis Basics of Control System Routh Hurwitz Stability Time Response Analysis Root Locus Techniques Controller and Compensator

Digital Electronics

Sequential Circuits Microprocessor Boolean Algebra Analog to Digital and Digital to Analog Converter Combinational Circuits Minimization Logic Families and Memories Logic Gates

Electrical Machines

Induction Machines D.C Machines Synchronous Machines Transformers

Electric Circuits

Three Phase Circuits Transient Response Graph Theory Two Port Networks Sinusoidal Steady State Analysis Network Elements Network Theorems

Electrical and Electronics Measurement

Basic of Indicating Instruments Error Analysis and Measurement Measurement of Resistance and A.C Bridges Measurement of Energy and Power Digital Voltmeters Questions Potentiometer and Instrument Transformers Cathode Ray Oscilloscope