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

$$ \int_0^1 \frac{2 x+5}{x^2+3 x+2} d x= $$

A

$\log \left(\frac{16}{3}\right)$

B

0

C

$\log \left(\frac{3}{16}\right)$

D

$4 \log 2-2 \log 3$

2
AP EAPCET 2025 - 27th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The area (in sq units) of the region given by $R=\left\{(x, y) ; \frac{y^2}{2} \leq x \leq y+4\right\}$ is

A

16

B

18

C

24

D

30

3
AP EAPCET 2025 - 27th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int_0^1 x^{\frac{5}{2}}(1-x)^{\frac{3}{2}} d x= $$

A

$\frac{5 \pi}{256}$

B

$\frac{3 \pi}{256}$

C

$\frac{3 \pi}{128}$

D

$\frac{5 \pi}{128}$

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

$$ \lim _{n \rightarrow \infty}\left[\begin{array}{c} \frac{1}{n^2} \sec ^2 \frac{1}{n^2}+\frac{2}{n^2} \sec ^2 \frac{4}{n^2}+\frac{3}{n^2} \sec ^2 \\ \frac{9}{n^2}+\ldots+\frac{1}{n^2} \sec ^2 1 \end{array}\right]= $$

A

$\tan ^{-1} 1$

B

$\frac{1}{2} \tan ^{-1} 1$

C

$\frac{1}{2} \tan 1$

D

$\frac{1}{2} \sec 1$