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

If $f(x)=x+\log \left(\frac{x-1}{x+1}\right)$ is a well-defined real valued function, then $f$ is

A

monotonically decreasing function

B

monotonically increasing function

C

increasing in $(1, \infty)$ and decreasing in $(-\infty,-1)$

D

decreasing in $(1, \infty)$ and increasing in $(-\infty,-1)$

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

A real valued function $f(x)=\left|x^2-3 x+2\right|+2 x-3$ is defined on $[-2,1]$. If $m$ and $M$ are absolute minimum and absolute maximum values of $f$ respectively, then $M-4 m=$

A

0

B

1

C

15

D

10

3
TG EAPCET 2025 (Online) 2nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{2 \sin x-3 \cos x}{4 \cos x-3 \sin x} d x= $$

A

$\frac{1}{25}[17 \log |4 \cos x-3 \sin x|-6 x]+C$

B

$\frac{1}{25}[x-18 \log |4 \cos x-3 \sin x|]+C$

C

$\frac{1}{25}[\log |4 \cos x-3 \sin x|-18 x]+C$

D

$\frac{1}{25}[17 x-6 \log |4 \cos x-3 \sin x|]+C$

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

$$ \int e^{4 x}(\sin 3 x-\cos 3 x) d x= $$

A

$\frac{e^{4 x}}{25}(7 \sin 3 x-\cos 3 x)+C$

B

$\frac{e^{4 x}}{25}(\sin 3 x-7 \cos 3 x)+C$

C

$\frac{e^{4 x}}{5}(7 \sin 3 x+\cos 3 x)+C$

D

$\frac{e^{4 x}}{5}(\sin 3 x+7 \cos 3 x)+C$

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