GATE CE 2025 Set 1 | Calculus Question 4 | Engineering Mathematics

GATE CE 2025 Set 1

Numerical

-0

The maximum value of the function $h(x)=-x^3+2 x^2$ in the interval $[-1,1.5]$ is equal to _________ . (rounded off to 1 decimal place)

Your input ____

GATE CE 2024 Set 2

Numerical

-0

The expression for computing the effective interest rate $(i_{eff})$ using continuous compounding for a nominal interest rate of 5% is

$i_{eff} = \lim\limits_{m \to \infty} \left(1 + \frac{0.05}{m}\right)^m - 1$

The effective interest rate (in percentage) is ___________ (rounded off to 2 decimal places).

Your input ____

GATE CE 2023 Set 1

MCQ (More than One Correct Answer)

-0

For the function f(x) = ex |sin x|; x ∈ ℝ, which of the following statements is/are TRUE?

The function is continuous at all x

The function is differentiable at all x

The function is periodic

The function is bounded

GATE CE 2017 Set 2

MCQ (Single Correct Answer)

-0.6

Consider the following definite integral $$${\rm I} = \int\limits_0^1 {{{{{\left( {{{\sin }^{ - 1}}x} \right)}^2}} \over {\sqrt {1 - {x^2}} }}dx} $$$
The value of the integral is

$${{{\pi ^3}} \over {24}}$$

$${{{\pi ^3}} \over {12}}$$

$${{{\pi ^3}} \over {48}}$$

$${{{\pi ^3}} \over {64}}$$

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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

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

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

Construction Material and Management

Critical Path Method Construction Materials Program Evolution Review Technique

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

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

Hydrology

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

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 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

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

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