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