1
AP EAPCET 2025 - 22nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $\frac{a x+5}{\left(x^2+b\right)(x+3)}=\frac{x+21}{12\left(x^2+b\right)}+\frac{c}{12(x+3)}$, then $b^2=$

A

$a^3-c$

B

$a^2+c$

C

$a-c$

D

$a+c$

2
AP EAPCET 2025 - 22nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int\left(\sum_{r=0}^{\infty} \frac{x^r 2^r}{r!}\right) d x= $$

A

$e^x+C$

B

$\frac{-2}{1-2 x}+C$

C

$2 e^{2 x}+C$

D

$\frac{e^{2 x}}{2}+C$

3
AP EAPCET 2025 - 22nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{d x}{12 \cos x+5 \sin x}= $$

A

$\frac{1}{13} \log \left|\tan \left(\frac{\pi}{4}+\frac{x}{2}-\frac{1}{2} \tan ^{-1} \frac{5}{12}\right)\right|+C$

B

$\frac{5}{12} \log \left|\tan \left(\frac{\pi}{4}+\frac{x}{2}-\frac{1}{2} \tan ^{-1} \frac{5}{12}\right)\right|+C$

C

$\frac{1}{13} \log \left|\tan \left(\frac{\pi}{4}+\frac{x}{2}+\frac{1}{2} \tan ^{-1} \frac{5}{12}\right)\right|+C$

D

$\frac{5}{12} \log \left|\tan \left(\frac{\pi}{4}+\frac{x}{2}+\frac{1}{2} \tan ^{-1} \frac{5}{12}\right)\right|+C$

4
AP EAPCET 2025 - 22nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $\int \frac{\cos ^3 x}{\sin ^2 x+\sin ^4 x} d x=c-\operatorname{cosec} x-f(x)$, then $f\left(\frac{\pi}{2}\right)=$

A

1

B

0

C

$\pi / 2$

D

$\pi$

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