1
GATE ME 2025
MCQ (Single Correct Answer)
+1
-0.33
Let $A$ and $B$ be real symmetric matrices of same size. Which one of the following options is correct?
A
$A^{\top}=A^{-1}$
B
$\mathrm{AB}=\mathrm{BA}$
C
$(\mathrm{AB})^{\top}=\mathrm{B}^{\top} \mathrm{A}^{\top}$
D
$\mathrm{A}=\mathrm{A}^{-1}$
2
GATE ME 2025
MCQ (Single Correct Answer)
+1
-0.33

For the differential equation given below, which one of the following options is correct?

$$ \frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}=0,0 \leq x \leq 1,0 \leq y \leq 1 $$

A
$u=e^{x+y}$ is a solution for all $x$ and $y$
B
$u=e^x \sin y$ is a solution for all $x$ and $y$
C
$u=\sin x \sin y$ is a solution for all $x$ and $y$
D
$u=\cos x \cos y$ is a solution for all $x$ and $y$
3
GATE ME 2025
MCQ (Single Correct Answer)
+1
-0.33
The divergence of the curl of a vector field is
A
the magnitude of this vector field
B
the argument of this vector field
C
the magnitude of the curl of this vector field
D
Zero
4
GATE ME 2025
MCQ (Single Correct Answer)
+1
-0.33
If two unbiased coins are tossed, then what is the probability of having at least one head?
A
0.25
B
0.5
C
0.675
D
0.75
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