1
GATE CE 2024 Set 1
MCQ (More than One Correct Answer)
+1
-0.33
For the following partial differential equation,
$x \frac{\partial^2 f}{\partial x^2} + y \frac{\partial^2 f}{\partial y^2} = \frac{x^2 + y^2}{2}$
which of the following option(s) is/are CORRECT?
2
GATE CE 2023 Set 2
Numerical
+1
-0
The steady-state temperature distribution in a square plate ABCD is governed by the 2-dimensional Laplace equation. The side AB is kept at a temperature of 100°C and the other three sides are kept at a temperature of 0°C. Ignoring the effect of discontinuities in the boundary conditions at the corners, the steady-state temperature at the center of the plate is obtained as T0°C. Due to symmetry, the steady-state temperature at the center will be same (T0°C), when any one side of the square is kept at a temperature of 100°C and the remaining three sides are kept at a temperature of 0°C. Using the principle of superposition, the value of T0 is _________ (rounded off to two decimal places).
Your input ____
3
GATE CE 2023 Set 1
Numerical
+1
-0
In the differential equation $\frac{dy}{dx}+\alpha\ x\ y =0, \alpha$ is a positive constant. If y = 1.0 at x = 0.0, and y = 0.8 at x = 1.0, the value of α is ________ (rounded off to three decimal places).
Your input ____
4
GATE CE 2022 Set 2
MCQ (Single Correct Answer)
+1
-0.33
The function f(x, y) satisfies the Laplace equation
$$\Delta$$2f(x, y) = 0
on a circular domain of radius r = 1 with its center at point P with coordinates x = 0, y = 0. The value of this function on the circular boundary of this domain is equal to 3. The numerical value of f/(0, 0) is :
Questions Asked from Differential Equations (Marks 1)
Number in Brackets after Paper Indicates No. of Questions
GATE CE 2024 Set 2 (2)
GATE CE 2024 Set 1 (2)
GATE CE 2023 Set 2 (1)
GATE CE 2023 Set 1 (1)
GATE CE 2022 Set 2 (1)
GATE CE 2022 Set 1 (2)
GATE CE 2017 Set 1 (3)
GATE CE 2016 Set 1 (1)
GATE CE 2014 Set 2 (1)
GATE CE 2011 (1)
GATE CE 2010 (2)
GATE CE 2009 (1)
GATE CE 2007 (2)
GATE CE 2006 (1)
GATE CE 2001 (1)
GATE CE 1999 (1)
GATE CE 1997 (1)
GATE CE 1995 (1)
GATE CE 1994 (1)
GATE CE Subjects
Engineering Mechanics
Strength of Materials Or Solid Mechanics
Structural Analysis
Construction Material and Management
Reinforced Cement Concrete
Steel Structures
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
Hydrology
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
Transportation Engineering
Engineering Mathematics
General Aptitude