1
GATE CE 2025 Set 2
MCQ (Single Correct Answer)
+1
-0.33

For the matrix $[\mathrm{A}]$ given below, the transpose is $\qquad$ .

$$ [A]=\left[\begin{array}{lll} 2 & 3 & 4 \\ 1 & 4 & 5 \\ 4 & 3 & 2 \end{array}\right] $$

A
$\left[\begin{array}{lll}2 & 1 & 4 \\ 3 & 4 & 3 \\ 4 & 5 & 2\end{array}\right]$
B
$\left[\begin{array}{lll}4 & 3 & 2 \\ 5 & 4 & 1 \\ 2 & 3 & 4\end{array}\right]$
C
$\left[\begin{array}{lll}4 & 2 & 3 \\ 5 & 1 & 4 \\ 2 & 4 & 3\end{array}\right]$
D
$\left[\begin{array}{lll}2 & 3 & 4 \\ 1 & 4 & 5 \\ 4 & 3 & 2\end{array}\right]$
2
GATE CE 2025 Set 2
MCQ (Single Correct Answer)
+1
-0.33

Integration of $\ln (x)$ with $x$ i.e.

$$ \int \ln (x) d x= $$__________

A
$x \cdot \ln (x)-x+$ Constant
B
$x-\ln (x)+$ Constant
C
$x \cdot \ln (x)+x+$ Constant
D
$\ln (x)-x+$ Constant
3
GATE CE 2025 Set 2
MCQ (More than One Correct Answer)
+1
-0

Consider a velocity vector, $\vec{V}$ in ( $\mathrm{x}, \mathrm{y}, \mathrm{z}$ ) coordinates given below. Pick one or more CORRECT statement(s) from the choices given below:

$$ \vec{V}=u \vec{x}+v \vec{y} $$

A
z-component of Curl of velocity; $\nabla \times \vec{V}=\left(\frac{\partial u}{\partial x}-\frac{\partial u}{\partial y}\right) \vec{z}$
B
z-component of Curl of velocity; $\nabla \times \vec{V}=\left(\frac{\partial u}{\partial x}-\frac{\partial v}{\partial y}\right) \vec{z}$
C
Divergence of velocity; $\nabla \cdot \vec{V}=\left(\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}\right)$
D
Divergence of velocity; $\nabla \cdot \vec{V}=\left(\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}\right)$
4
GATE CE 2025 Set 2
MCQ (More than One Correct Answer)
+1
-0
Given that $A$ and $B$ are not null sets, which of the following statements regarding probability is/are CORRECT?
A
$P(A \cap B)=P(A) P(B)$, if $A$ and $B$ are mutually exclusive.
B
Conditional probability, $\mathrm{P}(\mathrm{A} \mid \mathrm{B})=1$ if $\mathrm{B} \subset \mathrm{A}$.
C
$P(A \cup B)=P(A)+P(B)$, if $A$ and $B$ are mutually exclusive.
D
$P(A \cap B)=0$, if $A$ and $B$ are independent.