1
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{\operatorname{cosec} x}{3 \cos x+4 \sin x} d x=$
A
$\frac{1}{2} \log \left|\frac{\cos x}{3 \sin x+4 \cos x}\right|+c$
B
$\frac{1}{3} \log \left|\frac{\sin x}{3 \cos x+4 \sin x}\right|+c$
C
$\frac{1}{3} \log \left|\frac{3 \cos x+\sin x}{3 \cos x+4 \sin x}\right|+c$
D
$\frac{1}{2} \log \left|\frac{\cos x+4 \sin x}{3 \cos x+4 \sin x}\right|+c$
2
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int e^{2 x+3} \sin 6 x d x=$
A
$\frac{e^{2 x+3}}{40}(2 \sin (x x+6 \cos 6 x)+c$
B
$\frac{e^{2 v+3}}{40}(2 \cos 6 x+6 \sin 6 x)+c$
C
$\frac{e^{2 n+3}}{20}(\sin 6 x-3 \cos 6 x)+c$
D
$\frac{e^{2 n 3}}{20}(\cos 8 x-3 \sin 6 x)+c$
3
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\lim \limits_{n \rightarrow+\infty}\left[{\frac{1}{n^4}+\frac{1}{\left(n^2+1\right)^{\frac{3}{2}}}+\frac{1}{\left(n^2+4\right)^{\frac{3}{2}}}+\frac{1}{\left(n^2+9\right)^{\frac{3}{2}}}}{+\ldots \ldots+\frac{1}{4 \sqrt{2} n^5}}\right]=$
A
$\frac{3}{4 \sqrt{2}}$
B
$\frac{3 \sqrt{2}}{4}$
C
$\frac{5}{6 \sqrt{2}}$
D
$\frac{5 \sqrt{2}}{6}$
4
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int_{\log 4}^{\log 4} \frac{e^{2 x}+e^x}{e^{2 r}-5 e^x+6} d x=$
A
$\log \left(\frac{64}{9}\right)$
B
$\log \left(\frac{256}{81}\right)$
C
$\log \left(\frac{32}{3}\right)$
D
$\log \left(\frac{128}{27}\right)$
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