GATE CE 1998 | Calculus Question 36 | Engineering Mathematics

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GATE CE 1998

MCQ (Single Correct Answer)

-0.3

The Taylor's series expansion of sin $$x$$ is ______.

$$1 - {{{x^2}} \over {2!}} + {{{x^4}} \over {4!}} - ......$$

$$1 + {{{x^2}} \over {4!}} + {{{x^4}} \over {4!}} + ......$$

$$x + {{{x^3}} \over {3!}} + {{{x^5}} \over {5!}} + ......$$

$$x - {{{x^3}} \over {3!}} + {{{x^5}} \over {5!}} - ......$$

GATE CE 1998

MCQ (Single Correct Answer)

-0.3

The continuous function $$f(x, y)$$ is said to have saddle point at $$(a, b)$$ if

$${f_x}\left( {a,\,b} \right) = {f_y}\left( {a,\,b} \right) = 0$$
$$f_{xy}^2 - {f_{xx}}{f_{yy}} < 0$$ at $$(a, b)$$

$${f_x}\left( {a,\,b} \right) = 0,{f_y}\left( {a,\,b} \right) = 0$$
$$f_{xy}^2 - {f_{xx}}{f_{yy}} > 0$$ at $$(a, b)$$

$${f_x}\left( {a,\,b} \right) = 0,{f_y}\left( {a,\,b} \right) = 0,$$
$${f_{xx}}$$ and $${f_{yy}} < 0$$ at $$(a, b)$$

$${f_x}\left( {a,\,b} \right) = 0,{f_y}\left( {a,\,b} \right) = 0$$
$$f_{xy}^2 - {f_{xx}}{f_{yy}} = 0\,\,$$ at $$(a, b)$$

GATE CE 1997

MCQ (Single Correct Answer)

-0.3

If $$y = \left| x \right|$$ for $$x < 0$$ and $$y=x$$ for $$x \ge 0$$ then

$${{dy} \over {dx}}$$ is discontinuous at $$x=0$$

$$y$$ is discontinuous at $$x=0$$

$$y$$ is not defined at $$x=0$$

Both $$y$$ and $${{dy} \over {dx}}$$ are discontinuous at $$x=0$$

GATE CE 1997

MCQ (Single Correct Answer)

-0.3

If $$\varphi \left( x \right) = \int\limits_0^{{x^2}} {\sqrt t \,dt\,} $$ then $${{d\varphi } \over {dx}} = \_\_\_\_\_\_\_.$$

$$2\,{x^2}$$

$$\sqrt x $$

$$0$$

$$1$$

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GATE CE Subjects

Engineering Mechanics

Work Energy Principle and Impulse Momentum Equation Equilibrium of Force Systems

Strength of Materials Or Solid Mechanics

Centroid and Moment of Inertia Torsion Pure Bending Shear Stress In Beams Strain Energy Method Columns and Struts Complex Stress Deflection of Beams Thin Cylinder Simple Stresses Shear Force and Bending Moment Propped Cantilever Beam

Structural Analysis

Energy Principle Truss Stability and Static Indeterminacy Methods of Analysis Indeterminacy Arches and Cable Slope Deflection Method Matrix Method Moment Distribution Method Influence Line Diagram Plastic Analysis

Construction Material and Management

Critical Path Method Construction Materials Program Evolution Review Technique

Reinforced Cement Concrete

Doubly Reinforced Sections Limit State of Collapse Shear Footings Bond Slabs Limit State of Collapse Torsion Limit State of Serviceability Prestressed Concrete Singly Reinforced Sections Workmenship and Fundamentals Flanged Beams Limit State of Collapse Compression

Steel Structures

Materials and Specifications Tension Members Riveted Joints and Bolted Joints Welded Connections Eccentric Connections Compression Members Beams Plate Girder

Geotechnical Engineering

Origin of Soils Definitions and Properties of Soils

Fluid Mechanics and Hydraulic Machines

Properties of Fluids Fluid Statics

Hydrology

Evaporation and Transpiration Precipitation and Frequency of Rainfall Data

Irrigation

Water Requirement of Crops Gravity Dams and Spillways

Geomatics Engineering Or Surveying

Angular Measurements and Compass Survey Basic Concepts Linear Measurements and Chain Survey

Environmental Engineering

Sources and Coveyances Water Water Demand Quality Control of Water

Transportation Engineering

Highway Devolopment and Planning Highway Geometric Design

Engineering Mathematics

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

General Aptitude

Numerical Ability Logical Reasoning Verbal Ability