GATE CE 2025 Set 2 | Calculus Question 1 | Engineering Mathematics

GATE CE 2025 Set 2

MCQ (Single Correct Answer)

-0.33

Integration of $\ln (x)$ with $x$ i.e.

$$ \int \ln (x) d x= $$__________

$x \cdot \ln (x)-x+$ Constant

$x-\ln (x)+$ Constant

$x \cdot \ln (x)+x+$ Constant

$\ln (x)-x+$ Constant

GATE CE 2024 Set 2

MCQ (Single Correct Answer)

-0.33

The function $f(x) = x^3 - 27x + 4$, $1 \leq x \leq 6$ has

Maxima point

Minima point

Saddle point

Inflection point

GATE CE 2024 Set 1

MCQ (Single Correct Answer)

-0.33

The smallest positive root of the equation $$x^5 - 5 x^4 - 10 x^3 + 50 x^2 + 9 x - 45 = 0$$ lies in the range

0 < x ≤ 2

2 < x ≤ 4

6 ≤ x ≤ 8

10 ≤ x ≤ 100

GATE CE 2023 Set 1

MCQ (Single Correct Answer)

-0.33

For the integral $\rm I=\displaystyle\int^1_{-1}\frac{1}{x^2}dx$

which of the following statements is TRUE?

I = 0

I = 2

I = -2

The integral does not converge

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 Curves 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 Well Hydraulics and River Gauging

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

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

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 Sewage System and Sewer Appurtenances 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

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

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 Hydrostatic Forces Fluid Dynamics Boundary Layer Theory Drag and Lift Dimensional Analysis Flow Through Pipes Open Channel Flow Hydraulic Machines Properties of Fluids Fluid Statics

General Aptitude

Numerical Ability Logical Reasoning Verbal Ability