1
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $y=\log \left[\mathrm{e}^{5 x}\left(\frac{3 x-4}{x+5}\right)^{\frac{4}{3}}\right]$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to

A
$5+\frac{4}{3 x-4}-\frac{4}{3(x+5)}$
B
$5+\frac{4}{3(3 x-4)}-\frac{4}{3(x+5)}$
C
$5 x+\frac{4}{3 x-4}-\frac{4}{3(x+5)}$
D
$5+\frac{12}{3 x-4}-\frac{4}{(x+5)}$
2
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0
 

Let $f$ be a twice differentiable function such that $\mathrm{f}^{\prime \prime}(x)=-\mathrm{f}(x), \mathrm{f}^{\prime}(x)=\mathrm{g}(x)$ and $\mathrm{h}(x)=[\mathrm{f}(x)]^2+[\mathrm{g}(x)]^2$. If $\mathrm{h}(5)=1$, then $\mathrm{h}(10)$ is __________.

A
2
B
4
C
$-$1
D
1
3
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The area (in sq. units) of the parallelogram whose diagonals are along the vectors $8 \hat{\mathrm{i}}-6 \hat{\mathrm{j}}$ and $3 \hat{i}+4 \hat{j}-12 \hat{k}$, is

A
52
B
26
C
65
D
20
4
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The line L given by $\frac{x}{5}+\frac{y}{b}=1$ passes through the point $(13,32)$. The line K is parallel to L and has the equation $\frac{x}{c}+\frac{y}{3}=1$. Then the distance between $L$ and $K$ is

A
$\frac{23}{\sqrt{15}}$
B
$\sqrt{17}$
C
$\frac{17}{\sqrt{15}}$
D
$\frac{23}{\sqrt{17}}$
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