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1
TG EAPCET 2024 (Online) 9th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{d x}{9 \cos ^2 2 x+16 \sin ^2 2 x}=$
A
$\frac{1}{25} \tan ^{-1}\left(\frac{3}{4} \sec ^2 2 x\right)+c$
B
$\frac{1}{25} \tan ^{-1}\left(\frac{4}{3} \sec ^2 2 x\right)+c$
C
$\frac{1}{24} \tan ^{-1}\left(\frac{3}{4} \tan 2 x\right)+c$
D
$\frac{1}{24} \tan ^{-1}\left(\frac{4}{3} \tan 2 x\right)+c$
2
TG EAPCET 2024 (Online) 9th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{2 \cos 3 x-3 \sin 3 x}{\cos 3 x+2 \sin 3 x} d x=$
A
$\frac{7}{15} \log |\cos 3 x+2 \sin 3 x|-\frac{4}{5} x+c$
B
$-\frac{4}{5} \log |\cos 3 x+2 \sin 3 x|+\frac{7 x}{5}+c$
C
$\frac{7}{5} \log |\cos 3 x+2 \sin 3 x|-\frac{4}{5} x+c$
D
$-\frac{8}{15} \log |\cos 3 x+2 \sin 3 x|+\frac{x}{5}+c$
3
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\frac{x^4}{\left(x^2+1\right)(x-2)}=f(x)+\frac{A x+B}{x^2+1}+\frac{C}{x-2}$, then $f(14)+2 A-B=$
A
$5 C$
B
$4 C$
C
$6 C$
D
$7 C$
4
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$\int(\sqrt{1-\sin x}+\sqrt{1+\sin x}) d x=f(x)+c$, where $c$ is the constant of integration. If $\frac{5 \pi}{2}$<$x<\frac{7 \pi}{2}$ and $$ f\left(\frac{8 \pi}{3}\right)=-2, \text { then } f^{\prime}\left(\frac{8 \pi}{3}\right)= $$

A
1
B
$\sqrt{3}$
C
0
D
-1
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