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TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $f(x)=\int \frac{\sin 2 x+2 \cos x}{4 \sin ^2 x+5 \sin x+1} d x$ and $f(0)=0$, then $f(\pi / 6)=$
A
$\log \frac{3}{4}$
B
$2 \log 2$
C
$\frac{1}{2} \log 3$
D
1
2
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int_{-2}^2 x^4\left(4-x^2\right)^{\frac{7}{2}} d x=$
A
$4 \pi$
B
$\frac{\pi}{16}$
C
$28 \pi$
D
$\frac{3 \pi}{128}$
3
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int_0^{\pi / 4} \frac{\sec x}{1+2 \sin ^2 x} d x= $$

A
$\frac{1}{3} \log (\sqrt{2}+1)+\frac{\pi \sqrt{2}}{12}$
B
$\frac{2}{3} \log (\sqrt{2}+1)+\frac{\pi \sqrt{2}}{6}$
C
$\frac{1}{6} \log (\sqrt{2}-1)+\frac{\pi}{12}$
D
$\frac{1}{4} \log (\sqrt{2}-1)-\frac{\pi \sqrt{3}}{6}$
4
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \lim\limits_{n \rightarrow \infty}\left[\frac{1}{n^2} \sec ^2 \frac{1}{n^2}+\frac{2}{n^2} \sec ^2 \frac{4}{n^2}+\ldots \ldots+\frac{1}{n} \sec ^2 1\right]= $$

A
$\frac{1}{2} \sec (1)$
B
$\frac{1}{2} \operatorname{cosec}(1)$
C
$\tan (1)$
D
$\frac{1}{2} \tan (1)$
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