1
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\int \frac{\sqrt[4]{x}}{\sqrt{x}+\sqrt[4]{x}} d x=$ $\frac{2}{3}\left[A \sqrt[4]{x^3}+B \sqrt[4]{x^2}+C \sqrt[4]{x}+D \log (1+\sqrt[4]{x})\right]+K$, then $\frac{2}{3}(A+B+C+D)$ is equal to
A
$2 / 3$
B
$-2 / 3$
C
$4 / 3$
D
$-4 / 3$
2
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int(\log x)^m x^n d x$ is equal to
A
$\int t^m e^{n t} d t, \quad t=e^x$
B
$\int t^m e^{(n+1) t} d t, \quad t=e^x$
C
$\int t^m e^{(n+1) t} d t, \quad x=e^t$
D
$\int t^m e^{n t} d t, \quad x=e^t$
3
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \sin ^{-1}\left(\sqrt{\frac{x-a}{x}}\right) d x$ is equal to
A
$x \cos ^{-1} \sqrt{\frac{a}{x}}-\sqrt{a x-a^2}+c$
B
$x \sec ^{-1} \cdot \sqrt{\frac{a}{x}}+\sqrt{x^2-a x}+c$
C
$x \sin ^{-1} \sqrt{\frac{x}{a}}+\sqrt{x^2+a x}+c$
D
$\frac{x}{a} \sin ^{-1} \frac{x}{a}+\frac{x^2}{a} \sqrt{1+a^2}+c$
4
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\int \frac{\sin x \cos x}{\sqrt{\cos ^4 x-\sin ^4 x}} d x=-\frac{f(x)}{2}+c$, then domain of $f(x)$ is
A
$[2 n \pi,(2 n+1) \pi], n=0,1,2 \ldots$
B
$\left[(4 n-1) \frac{\pi}{2} \cdot(4 n+1) \frac{\pi}{2}\right], n=0,1,2 \ldots$
C
$\left[(4 n-1) \frac{\pi}{4} \cdot(4 n+1) \frac{\pi}{4}\right], n=0,1,2 \ldots$
D
$\left[\left(2 n \frac{\pi}{4} 1 .(2 n+1) \frac{\pi}{4}\right], n=0,1,2 \ldots\right.$
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