1
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $y=\left(\tan ^{-1} 2 x\right)^2+\left(\cot ^{-1} 2 x\right)^2$, then $\left(1+4 x^2\right)^2 y^{\prime \prime}-16$ is equal to
A
$8 x y^{\prime}$
B
$-8 x\left(1+4 x^2\right) y^{\prime}$
C
$8 x\left(1+4 x^2\right) y^{\prime}$
D
$-8 x y^{\prime}$
2
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\int_0^{2 \pi}\left(\sin ^4 x+\cos ^4 x\right) d x=K \int_0^\pi \sin ^2 x d x+L \int_0^{\frac{\pi}{2}} \cos ^2 x d x$ and $K, L \in N$, then the number of possible ordered pairs ( $K, L$ ) is

A
1
B
2
C
3
D
4
3
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
$\sqrt{3} \pi^2$
4
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
$2 B+A=0$
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