GATE CE 1997 | Calculus Question 45 | Engineering Mathematics

GATE CE 1997

MCQ (Single Correct Answer)

-0.3

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

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

$$\sqrt x $$

$$0$$

$$1$$

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 1995

MCQ (Single Correct Answer)

-0.3

The function $$f\left( x \right) = \left| {x + 1} \right|$$ on the interval $$\left[ { - 2,0} \right]$$ is __________.

continuous and differentiable

continuous on the interval but not differentiable at all points

Neither continuous nor differentiable

Differentiable but not continuous

GATE CE 1995

MCQ (Single Correct Answer)

-0.3

The function $$f\left( x \right) = {x^3} - 6{x^2} + 9x + 25$$ has

a maxima at $$x=1$$ and a minima at $$x=3$$

a maxima at $$x=3$$ and a minima at $$x=1$$

no maxima, but a minima at $$x=3$$

a maxima at $$x=1,$$ but no minima

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GATE CE Subjects

Engineering Mechanics

Equilibrium of Force Systems Work Energy Principle and Impulse Momentum Equation

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

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

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

Hydrology

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

Irrigation

Gravity Dams and Spillways Water Requirement of Crops

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

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

Transportation Engineering

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