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

For each $x \in \mathbb{R}$, Let $[x]$ represent greatest integer function, then $\lim _{x \rightarrow 0^{-}} \frac{x([x]+|x|) \sin [x]}{|x|}$ is equal to

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

If order and degree of the differential equation $\left(\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}\right)^5+4 \frac{\left(\frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}\right)^5}{\left(\frac{\mathrm{~d}^3 y}{\mathrm{~d} x^3}\right)}+\frac{\mathrm{d}^3 y}{\mathrm{~d} x^3}=\sin x$, are $m$ and $n$ respectively, then the value of $\left(\mathrm{m}^2+\mathrm{n}^2\right)$ is equal to

A
29
B
13
C
5
D
8
3
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A student scores the following marks in five tests : $54,45,41,43,57$. His score is not known for the sixth test. If the mean score is 48 in six tests, then the standard deviation of marks in six tests is

A
$\frac{100}{\sqrt{3}}$
B
$\frac{10}{\sqrt{3}}$
C
$\frac{100}{3}$
D
$\frac{10}{3}$
4
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $y=\tan ^{-1}\left(\frac{3+2 x}{2-3 x}\right)+\tan ^{-1}\left(\frac{3 x}{1+4 x^2}\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to

A
$\frac{1}{1+16 x^2}$
B
$\frac{4}{1+16 x^2}$
C
$\frac{1}{1+4 x^2}$
D
$\frac{4}{1+4 x^2}$
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