1
GATE CE 2024 Set 1
MCQ (More than One Correct Answer)
+1
-0

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?

A

elliptic for $x > 0$ and $y > 0$

B

parabolic for $x > 0$ and $y > 0$

C

elliptic for $x = 0$ and $y > 0$

D

hyperbolic for $x < 0$ and $y > 0$

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 :

A
1
B
0
C
2
D
3
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