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

If $f(x)=x e^{x(1-x)}, x \in R$, then $f(x)$ is

A

increasing on $\left[-\frac{1}{2}, 1\right]$

B

decreasing on $R$

C

increasing on $R$

D

decreasing on $\left[-\frac{1}{2}, 1\right]$

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

The angle between the curves $y^2=x$ and $x^2=y$ at the point $(1,1)$ is

A

$\tan ^{-1}\left(\frac{4}{3}\right)$

B

$\tan ^{-1}\left(\frac{3}{4}\right)$

C

$90^{\circ}$

D

$45^{\circ}$

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

If $\int \frac{5 \tan x}{\tan x-2} d x=a x+b \log |\sin x-2 \cos x|+c$, then $a+b=$

A

2

B

3

C

4

D

-1

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

$$ \int x \cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right) d x(x>0)= $$

A

$-x+\left(1+x^2\right) \tan ^{-1} x+C$

B

$x-\left(1+x^2\right) \cot ^{-1} x+C$

C

$-x+\left(1+x^2\right) \cot ^{-1} x+C$

D

$x-\left(1+x^2\right) \tan ^{-1} x+C$