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1
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 :

A
1
B
0
C
2
D
3
2
GATE CE 2022 Set 1
MCQ (Single Correct Answer)
+1
-0.33

Consider the following expression:

z = sin(y + it) + cos(y $$-$$ it)

where z, y, and t are variables, and $$i = \sqrt { - 1} $$ is a complex number. The partial differential equation derived from the above expression is

A
$${{{\partial ^2}z} \over {\partial {t^2}}} + {{{\partial ^2}z} \over {\partial {y^2}}} = 0$$
B
$${{{\partial ^2}z} \over {\partial {t^2}}} - {{{\partial ^2}z} \over {\partial {y^2}}} = 0$$
C
$${{\partial z} \over {\partial t}} - i{{\partial z} \over {\partial y}} = 0$$
D
$${{\partial z} \over {\partial t}} + i{{\partial z} \over {\partial y}} = 0$$
3
GATE CE 2022 Set 1
MCQ (Single Correct Answer)
+1
-0.33

For the equation

$${{{d^3}y} \over {d{x^3}}} + x{\left( {{{dy} \over {dx}}} \right)^{3/2}} + {x^2}y = 0$$

the correct description is

A
an ordinary differential equation of order 3 and degree 2.
B
an ordinary differential equation of order 3 and degree 3.
C
an ordinary differential equation of order 2 and degree 3.
D
an ordinary differential equation of order 3 and degree 3/2.
4
GATE CE 2017 Set 1
MCQ (Single Correct Answer)
+1
-0.3
The solution of the equation $$\,{{dQ} \over {dt}} + Q = 1$$ with $$Q=0$$ at $$t=0$$ is
A
$$Q\left( t \right) = {e^{ - t}} - 1$$
B
$$\,Q\left( t \right) = 1 + {e^{ - t}}$$
C
$$Q\left( t \right) = 1 - {e^t}$$
D
$$Q\left( t \right) = 1 - {e^{ - t}}$$
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Questions Asked from Marks 1
GATE CE 2025 Set 2 (1) GATE CE 2025 Set 1 (1) 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
Fluid Mechanics and Hydraulic Machines
Hydrology
Irrigation
Geomatics Engineering Or Surveying
Environmental Engineering
Transportation Engineering
Engineering Mathematics
General Aptitude