1
MHT CET 2025 23rd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{\mathrm{d} x}{\sqrt{x}+x}= $$

A
$\log \sqrt{x}+c$, where $c$ is the constant of integration.
B
$\quad \log (\sqrt{x}+x)+\mathrm{c}$, where c is the constant of integration.
C
$\quad \log (1+\sqrt{x})+\mathrm{c}$, where c is the constant of integration.
D
$\quad 2 \log (1+\sqrt{x})+\mathrm{c}$, where c is the constant of integration.
2
MHT CET 2025 23rd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

With usual notations, in $\triangle \mathrm{ABC}$, the lengths of two sides are 10 cm and 9 cm respectively. If angles $\mathrm{A}, \mathrm{B}, \mathrm{C}$ are in A.P. then perimeter of $\triangle \mathrm{ABC}$ is

A
$24+2 \sqrt{6} \mathrm{~cm}$
B
$24+\sqrt{6} \mathrm{~cm}$
C
$24-2 \sqrt{6} \mathrm{~cm}$
D
$22-\sqrt{6} \mathrm{~cm}$
3
MHT CET 2025 23rd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{\mathrm{d} x}{\mathrm{e}^x-1}= $$

A
$\quad \log \left(\mathrm{e}^{\mathrm{x}}-1\right)+x+\mathrm{c}$, where c is the constant of integration.
B
$\quad \log \left(\mathrm{e}^{\mathrm{x}}-1\right)-x+\mathrm{c}$, where c is the constant of integration.
C
$\quad x-\log \left(\mathrm{e}^x-1\right)+\mathrm{c}$, where c is the constant of integration.
D
$\log \left(\mathrm{e}^{\mathrm{x}}-1\right)-x \mathrm{e}^{\mathrm{x}}+\mathrm{c}$, where c is the constant of integration.
4
MHT CET 2025 23rd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The maximum value of $x^{2 / 3}+(x-2)^{2 / 3}$ is

A
0
B
2
C
$2^{\frac{2}{3}}$
D
1
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