1
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int_0^\pi \frac{x \sin x}{4 \cos ^2 x+3 \sin ^2 x} d x$ is equal to
A
$\frac{\pi^2}{6 \sqrt{3}}$
B
$\frac{\pi}{3 \sqrt{3}}$
C
$\frac{\pi^2}{3 \sqrt{3}}$
D
$\sqrt{3} \pi^2$
2
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
$2 B+A=0$
3
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
$\frac{1}{\log 2}+\frac{3}{4}$
4
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 $x^2-y^2=K^2$
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