1
TG EAPCET 2025 (Online) 4th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $\int_0^{\frac{\pi}{2}} \tan ^{14}\left(\frac{x}{2}\right) d x=2\left[\sum_{n=1}^7 f(n)-\frac{\pi}{4}\right]$, then $f(n)=$

A

$\frac{(-1)^n}{n-1}$

B

$\frac{(-1)^n}{2 n+1}$

C

$\frac{(-1)^{n+1}}{2 n-1}$

D

$\frac{(-1)^{n+1}}{n+1}$

2
TG EAPCET 2025 (Online) 4th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int_{-4}^5 \frac{1}{\sqrt{20+x-x^2}} d x= $$

A

$\frac{81 \pi}{8}$

B

$\frac{9 \pi}{2}$

C

$\pi$

D

$\frac{\pi}{10}$

3
TG EAPCET 2025 (Online) 4th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int_0^{\frac{\pi}{2}} \frac{d x}{\cos x-\sqrt{3} \sin x}= $$

A

0

B

$\frac{1}{2} \log (2-\sqrt{3})$

C

$\frac{1}{2} \log (2+\sqrt{3})$

D

$\frac{1}{2} \log (2 \sqrt{3}-3)$

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

$$ \int_0^{\frac{\pi}{2}} \sqrt{\tan x d x}= $$

A

$\frac{\pi}{\sqrt{2}}$

B

$\frac{\pi}{2}$

C

$\sqrt{2} \pi$

D

$2 \pi$

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