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

If $k \in N$, then $\lim\limits_{n \rightarrow \infty}\left[\frac{1}{n+1}+\frac{1}{n+2}+\frac{1}{n+3}+\ldots .+\frac{1}{k n}\right]=$

A

$\log (k+1)$

B

$\log k$

C

$\log (k+5)$

D

$\log (k+1)-\log 6$

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

$$ \int_{-1}^4 \sqrt{\frac{4-x}{x+1}} d x= $$

A

0

B

$\frac{\pi}{2}$

C

$\frac{3 \pi}{2}$

D

$\frac{5 \pi}{2}$

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

$$ \int_0^{\pi / 4} \frac{\cos ^2 x}{\cos ^2 x+4 \sin ^2 x} d x= $$

A

$\frac{\pi}{2}-\frac{1}{3} \tan ^{-1} 2$

B

$-\frac{\pi}{4}-\frac{4}{3} \tan ^{-1} 2$

C

$\frac{\pi}{6}+\frac{2}{3} \tan ^{-1} 2$

D

$-\frac{\pi}{12}+\frac{2}{3} \tan ^{-1} 2$

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

$$ \int_{5 \pi}^{25 \pi}|\sin 2 x+\cos 2 x| d x= $$

A

$20 \sqrt{2}$

B

$10 \sqrt{2}$

C

$40 \sqrt{2}$

D

$80 \sqrt{2}$

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