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1
AP EAPCET 2025 - 21st May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{\sin 2 x}{\sin ^2 x+3 \cos x-3} d x $$

A

$2 \log \left|\frac{\cos x-2}{\cos x-1}\right|+C$

B

$\log \left(\frac{(\cos x-2)^2}{(\cos x-1)^4}\right)+C$

C

$\log \left(\frac{(\cos x-2)^2}{|\cos x-1|}\right)+C$

D

$\log \left(\frac{(\cos x-2)^4}{(\cos x-1)^2}\right)+C$

2
AP EAPCET 2025 - 21st May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\int \frac{d x}{\sin ^3 x+\cos ^3 x}=A \log \left|\frac{\sqrt{2}+t}{\sqrt{2}-t}\right|+B \tan ^{-1}(t)+C$, then $\left(\frac{B}{A}, t\right)=$

A

$(3 \sqrt{2}, \sin x-\cos x)$

B

$(2 \sqrt{2}, \sin x-\cos x)$

C

$\left(\frac{\sqrt{2}}{3}, \sin x-\cos x\right)$

D

$\left(\frac{3}{\sqrt{2}}, \sin x+\cos x\right)$

3
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$\frac{4 x^2+5}{(x-2)^4}=\frac{A}{(x-2)}+\frac{B}{(x-2)^2}+\frac{C}{(x-2)^3}+\frac{D}{(x-2)^4}$, then $\sqrt{\frac{A}{C}+\frac{B}{C}+\frac{D}{C}}$ is equal to

A
$\frac{\sqrt{29}}{4}$
B
$\frac{\sqrt{23}}{4}$
C
$\frac{5}{4}$
D
$\frac{4}{5}$
4
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
$-4 / 3$
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