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1
MHT CET 2025 19th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{x \mathrm{~d} x}{(x-1)(x-2)}= $$

A
$\log \left(\frac{x-1}{x-2}\right)+\mathrm{c}$, where c is the constant of integration
B
$\quad \log \left(\frac{x-2}{(x-1)^2}\right)+\mathrm{c}$, where c is the constant of integration
C
$\log \left(\frac{x-2}{x-1}\right)+\mathrm{c}$, where c is the constant of integration
D
$\quad \log \left(\frac{(x-2)^2}{x-1}\right)+\mathrm{c}$, where c is the constant of integration
2
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
$$\int \frac{\mathrm{d} x}{2 \mathrm{e}^{2 x}+3 \mathrm{e}^x+1}=$$
A
$x+\log \left(\mathrm{e}^x+1\right)-2 \log \left(2 \mathrm{e}^x+1\right)+\mathrm{c}$, where c is the constant of integration
B
$x-\log \left(\mathrm{e}^x+1\right)+4 \log \left(\mathrm{e}^x+1\right)+\mathrm{c}$, where c is the constant of integration
C
$x+\log \left(\mathrm{e}^x+1\right)-4 \log \left(2 \mathrm{e}^x+1\right)+\mathrm{c}$, where c is the constant of integration
D
$x-\log \left(\mathrm{e}^x+1\right)+2 \log \left(2 \mathrm{e}^x+1\right)+\mathrm{c}$, where c is the constant of integration
3
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
$$\int \frac{\mathrm{e}^{2030 \log x}-\mathrm{e}^{2029 \log x}}{\mathrm{e}^{2028 \log x}-\mathrm{e}^{2027 \log x}} \mathrm{~d} x=\ldots$$
A
$\frac{x^2}{2}+c$, where $c$ is the constant of integration
B
$x+c$, where $c$ is the constant of integration
C
$\frac{x^3}{3}+c$, where $c$ is the constant of integration
D
$\frac{x}{3}+c$, where $c$ is the constant of integration
4
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
 $$\int \frac{\sin 2 x}{(a+b \cos x)^2} d x=$$
A
$\frac{2}{a^2}\left[\log (a+b \cos x)-\frac{a}{a+b \cos x}\right]+c$ where c is the constant of integration.
B
$\frac{-1}{a^2}\left[\log (a+b \cos x)+\frac{a}{a+b \cos x}\right]+c$, where c is the constant of integration.
C
$\frac{-2}{b^2}\left[\log (a+b \cos x)+\frac{a}{a+b \cos x}\right]+c$ where c is the constant of integration.
D
$\frac{-2}{b^2}\left[\log (a+b \cos x)-\frac{a}{a+b \cos x}\right]+c$, where c is the constant of integration.
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