GATE CE 1997 | Differential Equations Question 40 | Engineering Mathematics

GATE CE 1997

MCQ (Single Correct Answer)

-0.3

For the differential equation $$f\left( {x,y} \right){{dy} \over {dx}} + g\left( {x,y} \right) = 0\,\,$$ to be exact is

$$\,{{\partial f} \over {\partial y}} = {{\partial g} \over {\partial x}}$$

$${{\partial f} \over {\partial x}} = {{\partial g} \over {\partial y}}$$

$$f=g$$

$${{{\partial ^2}f} \over {\partial {x^2}}} = {{{\partial ^2}g} \over {\partial {y^2}}}$$

GATE CE 1995

MCQ (Single Correct Answer)

-0.3

The differential equation $${y^{11}} + {\left( {{x^3}\,\sin x} \right)^5}{y^1} + y = \cos {x^3}\,\,\,\,$$ is

homogeneous

non-linear

$$2$$^nd order linear

non-homogeneous with constant coefficients

GATE CE 1994

MCQ (Single Correct Answer)

-0.3

The necessary & sufficient condition for the differential equation of the form $$\,\,M\left( {x,y} \right)dx + N\left( {x,y} \right)dy = 0\,\,$$ to be exact is

$$M=N$$

$${{\partial M} \over {\partial x}} = {{\partial N} \over {\partial y}}$$

$${{\partial M} \over {\partial y}} = {{\partial N} \over {\partial x}}$$

$${{{\partial ^2}M} \over {\partial {x^2}}} = {{{\partial ^2}N} \over {\partial {y^2}}}$$

GATE CE Subjects

Construction Material and Management

Critical Path Method Construction Materials Program Evolution Review Technique

Geomatics Engineering Or Surveying

Levelling Traversing Theodolites and Plane Table Surveying Measurement of Area, Volume and Theory of Errors and Survey Adjustment Field Astronomy and Photogrammetric Surveying Basics of GIS, GPS and Remote Sensing Angular Measurements and Compass Survey Basic Concepts Linear Measurements and Chain Survey

Engineering Mechanics

Work Energy Principle and Impulse Momentum Equation Equilibrium of Force Systems

Hydrology

Precipitation and Frequency of Rainfall Data Evaporation and Transpiration Infiltration Hydrograph Flood Estimation and Flood Routing

Transportation Engineering

Highway Devolopment and Planning Highway Geometric Design Traffic Engineering Highway Materials Pavement Design Railway, Runway and Taxiway Design

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

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

Irrigation

Water Requirement of Crops Gravity Dams and Spillways

Environmental Engineering

Sources and Coveyances Water Quality Control of Water Treatment of Water Water Demand Waste Water Characteristics Treatment of Sewage Disposal of Sewage Effluent Solid Waste Management Air Pollution Noise Pollution

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 Classification of Soils and Clay Mineralogy Effective Stress and Permeability Seepage Analysis Compaction of Soil Compressibility and Consolidation Shear Strength of Soil Stress Distribution of Soil Retaining Wall and Earth Pressure Stability of Slopes Shallow Foundation Pile Foundation Soil Stabilization

Fluid Mechanics and Hydraulic Machines

Fluid Pressure and Measurement Fluid Dynamics Boundary Layer Theory Drag and Lift Flow Through Pipes Open Channel Flow Hydraulic Machines Properties of Fluids Fluid Statics

General Aptitude

Numerical Ability Logical Reasoning Verbal Ability