1
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $A=\int_0^{\infty} \frac{1+x^2}{1+x^4} d x, B=\int_0^1 \frac{1+x^2}{1+x^4} d x$, then
A
$2 A=B$
B
$A=B$
C
$2 B=A$
D
$2 B+A=0$
2
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $(a, \beta)$ is the stationary point of the curve $y=2 x-x^2$, then the area bounded by the curves $y=2^x, y=2 x-x^2, x=0$ and $x=\alpha$ is

A
$\frac{3 \log 2+4}{2}$
B
$\frac{3+\log 4}{6}$
C
$\frac{3-\log 4}{3 \log 2}$
D
$\frac{1}{\log 2}+\frac{3}{4}$
3
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
Among the options given below from which option a differential equation of order two can be formed ?
A
All circles passing through origin
B
All parabolas passing through origin and having focus on X-axis
C
All the lines passing through the origin
D
All the hyperbolas of the form $x^2-y^2=K^2$
4
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The differential equation for which $a x+b y=1$ is general solution is
A
$\frac{d y}{d x}=x+c$
B
$y \frac{d^2 y}{d x^2}+x=1$
C
$\frac{d^2 y}{d x^2}=0$.
D
$\frac{d^3 y}{d x^3}=0$
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