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

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

Engineering Mathematics

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

General Aptitude

Verbal Ability Logical Reasoning Numerical Ability

Power Electronics

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

Power System Analysis

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

Analog Electronics

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

Control Systems

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

Digital Electronics

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

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

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