1
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

For $N \in \mathbb{N}, \frac{\mathrm{~d}^{\mathrm{n}}}{\mathrm{d} x^{\mathrm{n}}}(\log x)=$

A
$\frac{(n-1)!}{x^n}$
B
$\frac{n!}{x^n}$
C
$\frac{(\mathrm{n}-2)!}{x^{\mathrm{n}}}$
D
$\quad(-1)^{n-1} \frac{(n-1)!}{x^n}$
2
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

In a single toss of a fair die, the odds against the event that number 4 or 5 turns up is

A
$2: 1$
B
$1: 3$
C
$2: 3$
D
$1: 1$
3
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}(x)=x \cdot \mathrm{e}^{x(1-x)}$, then $\mathrm{f}(x)$ is

A
increasing in $\mathbb{R}$
B
increasing in $\left(\frac{-1}{2}, 1\right)$
C
decreasing in $\mathbb{R}$
D
decreasing in $\left[-\frac{1}{2}, 1\right]$
4
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The approximate value of $\sqrt[3]{64 \cdot 04}$ is

A
4.00043
B
4.00076
C
4.00083
D
4.00064
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