1
GATE CE 2025 Set 1
MCQ (Single Correct Answer)
+1
-0.33
Which of the following equations belong/belongs to the class of second-order, linear, homogeneous partial differential equations:
A
$\frac{\partial^2 u}{\partial t^2}=c^2\left(\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}\right)+x y$
B
$\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}+\frac{\partial^2 u}{\partial z^2}=0$
C
$\frac{\partial u}{\partial t}=c \frac{\partial u}{\partial x}$
D
$\left(\frac{\partial^2 u}{\partial t^2}\right)^2=c^2 \frac{\partial^2 u}{\partial x^2}$
2
GATE CE 2025 Set 1
MCQ (Single Correct Answer)
+2
-0.67

$$ \text { The value of }\mathop {\lim }\limits_{x \to \infty } \left(x-\sqrt{x^2+x}\right) \text { is equal to }$$

A
-1
B
-0.5
C
-2
D
0
3
GATE CE 2025 Set 1
Numerical
+2
-0

Let $y$ be the solution of the initial value problem $y^{\prime}+0.8 y+0.16 y=0$ where $y(0)=3$ and $y^{\prime}(0)=4.5$. Then, $y(1)$ is equal to__________ (rounded off to 1 decimal place).

Your input ____
4
GATE CE 2025 Set 1
Numerical
+2
-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 ____
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