1
AP EAPCET 2025 - 26th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \sec \left(x-\frac{\pi}{3}\right) \sec \left(x+\frac{\pi}{6}\right) d x= $$

A

$\log \left|\frac{\sec \left(x-\frac{\pi}{3}\right)}{\sec \left[x+\frac{\pi}{6}\right]}\right|+C$

B

$\log \left|\frac{\cos \left(x-\frac{\pi}{3}\right)}{\cos \left(x+\frac{\pi}{6}\right)}\right|+C$

C

$\log \left|\frac{\operatorname{cosec}\left(x-\frac{\pi}{3}\right)}{\operatorname{cosec}\left(x+\frac{\pi}{6}\right)}\right|+C$

D

$\log \left|\frac{\sin \left(x-\frac{\pi}{3}\right)}{\sin \left(x+\frac{\pi}{6}\right)}\right|+C$

2
AP EAPCET 2025 - 26th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\int \frac{a \cos x+3 \sin x}{5 \cos x+2 \sin x} d x=\frac{26}{29} x-\frac{k}{29} \log |5 \cos x+2 \sin x|+\ldots$ then $|a+k|=$

A

3

B

11

C

12

D

2

3
AP EAPCET 2025 - 26th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\int \frac{d x}{1-\sin ^4 x}=A \tan x+B \tan ^{-1}(\sqrt{2} \tan x)+C$, then $A^2-B^2=$

A

$\frac{1}{2}$

B

$\frac{3}{4}$

C

$\frac{1}{4}$

D

$\frac{1}{8}$

4
AP EAPCET 2025 - 27th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\frac{x^2}{\left(x^2+2\right)\left(x^4-1\right)}=\frac{A}{x^2-1}+\frac{B}{x^2+1}+\frac{C}{x^2+2}$, then $A+B-C=$

A

0

B

$\frac{4}{3}$

C

$\frac{3}{4}$

D

2

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