1
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.
2
GATE CE 2025 Set 2
Numerical
+1
-0

The "order" of the following ordinary differential equation is $\qquad$ .

$$ \frac{d^3 y}{d x^3}+\left(\frac{d^2 y}{d x^2}\right)^6+\left(\frac{d y}{d x}\right)^4+y=0 $$

Your input ____
3
GATE CE 2025 Set 2
MCQ (Single Correct Answer)
+2
-0.67
Pick the CORRECT solution for the following differential equation $\frac{d y}{d x}=e^{x-y}$
A
$y=\ln \left(e^x+\right.$ Constant $)$
B
$\ln (y)=x+$ Constant
C
$\ln (y)=\ln \left(e^x\right)+$ Constant
D
$y=x+$ Constant
4
GATE CE 2025 Set 2
MCQ (More than One Correct Answer)
+2
-0

Consider the function given below and pick one or more CORRECT statement(s) from the following choices.

$$ f(x)=x^3-\frac{15}{2} x^2+18 x+20 $$

A
$f(x)$ has a local minimum at $x=3$
B
$f(x)$ has a local maximum at $x=3$
C
$f(x)$ has a local minimum at $x=2$
D
$f(x)$ has a local maximum at $x=2$
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