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

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Irrigation

Gravity Dams and Spillways Water Requirement of Crops

Engineering Mechanics

Equilibrium of Force Systems Work Energy Principle and Impulse Momentum Equation

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Numerical Ability Logical Reasoning Verbal Ability

Transportation Engineering

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

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Precipitation and Frequency of Rainfall Data Evaporation and Transpiration Infiltration Hydrograph Flood Estimation and Flood Routing Well Hydraulics and River Gauging

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

Steel Structures

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

Engineering Mathematics

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

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Reinforced Cement Concrete

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

Construction Material and Management

Program Evolution Review Technique Critical Path Method Construction Materials

Strength of Materials Or Solid Mechanics

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

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