1
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 ____
2
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 ____
3
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
4
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
$${{\partial z} \over {\partial t}} + i{{\partial z} \over {\partial y}} = 0$$
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