1
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\frac{\mathrm{d} y}{\mathrm{~d} x}=y+3, y+3>0$ and $y(0)=2$, then $y(\log 2)$ is equal to

A
13
B
$-$2
C
7
D
5
2
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The assets of a person are reduced in his business such that the rate of reduction is proportional to the square root of the existing assets. If the assets were initially ₹$10,00,000$ and due to loss they reduce to ₹$ 10,000$ after 3 years, then the number of years required for the person to go bankrupt will be

A
$\frac{10}{3}$
B
 $\frac{10}{9}$
C
$\frac{20}{9}$
D
$\frac{20}{3}$
3
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $f(1)=1, f^{\prime}(1)=5$, then the derivative of $\mathrm{f}(\mathrm{f}(\mathrm{f}(x)))+(\mathrm{f}(x))^2$ at $x=1$ is

A
125
B
1250
C
135
D
35
4
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The abscissa of the point on the curve $y=\mathrm{a}\left(\mathrm{e}^{\frac{x}{a}}+\mathrm{e}^{-\frac{x}{a}}\right)$ where the tangent is parallel to the X -axis is

A
0
B
a
C
2a
D
$-$2a
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