1
TS EAMCET 2020 (Online) 11th September Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{25 x^2+8}{\sqrt{25 x^2+9}} d x= $$

A

$\frac{x}{2} \sqrt{25 x^2+9}+\frac{11}{10} \sinh ^{-1}\left(\frac{5 x}{3}\right)+C$

B

$\frac{x}{2} \sqrt{25 x^2+9}-\frac{7}{10} \log \left(\frac{5 x+\sqrt{25 x^2+9}}{3}\right)+C$

C

$\frac{x}{2} \sqrt{25 x^2+9}+\frac{7}{10} \sinh ^{-1}\left(\frac{5 x}{3}\right)+C$

D

$\frac{x}{2} \sqrt{25 x^2+9}+\frac{11}{10} \log \left(\frac{5 x-\sqrt{25 x^2+9}}{3}\right)+C$

2
TS EAMCET 2020 (Online) 11th September Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ I_{m, n}=\int x^m(\log x)^n d x= $$

A

$\frac{x^{m+1}}{m+1}(\log x)^n-\frac{n}{m+1} I_{m, n-1}$

B

$\frac{x^m}{m}(\log x)^n-\frac{n-1}{m+1} I_{m+1, n-1}$

C

$\frac{x^{m+1}}{m} \frac{(\log x)^{n+1}}{n+1}-\frac{n}{m+1} I_{m, n-1}$

D

$x^m \frac{(\log x)^{n+1}}{n+1}-\frac{n}{m+1} I_{m, n-1}$

3
TS EAMCET 2020 (Online) 11th September Morning Shift
MCQ (Single Correct Answer)
+1
-0

The positive integer $n \leq 5$ for which $\int_0^1 e^x(x-1)^n d x=16-6 e$ is

A

5

B

4

C

3

D

2

4
TS EAMCET 2020 (Online) 11th September Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $f(x)=\sin ^6 x+\cos ^6 x+2 \sin ^3 x \cos ^3 x$, then $\int_0^{\pi / 4} \frac{\sin ^2 2 x}{f(x)} d x=$

A

2

B

$2 / 3$

C

$-2 / 3$

D

$1 / 6$

TS EAMCET Papers

All year-wise previous year question papers