GATE CE 1998 | Calculus Question 33 | 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

Construction Material and Management

Critical Path Method Construction Materials Program Evolution Review Technique

Geomatics Engineering Or Surveying

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

Engineering Mechanics

Equilibrium of Force Systems Work Energy Principle and Impulse Momentum Equation

Hydrology

Evaporation and Transpiration Precipitation and Frequency of Rainfall Data

Transportation Engineering

Highway Geometric Design Highway Devolopment and Planning

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

Reinforced Cement Concrete

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

Steel Structures

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

Irrigation

Gravity Dams and Spillways Water Requirement of Crops

Environmental Engineering

Sources and Coveyances Water Water Demand Quality Control of Water

Engineering Mathematics

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

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

Geotechnical Engineering

Origin of Soils Definitions and Properties of Soils

Fluid Mechanics and Hydraulic Machines

Properties of Fluids Fluid Statics

General Aptitude

Verbal Ability Numerical Ability