GATE EE 2009 | Calculus Question 27 | Engineering Mathematics

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

Electric Circuits

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

Electromagnetic Fields

Time Varying Fields Electrostatics Magnetostatics

Signals and Systems

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

Electrical Machines

Induction Machines D.C Machines Synchronous Machines Transformers

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 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

Electrical and Electronics Measurement

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

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

Power Electronics

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

Digital Electronics

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