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

If the function $\mathrm{f}(x)=\left(\frac{5 x-8}{8-3 x}\right)^{\frac{3}{2 x-4}}$ if $x \neq 2$. $=\mathrm{k}$ if $x=2$. is continuous at $x=2$, then $\mathrm{k}=$

A
$\mathrm{e}^6$
B
$\mathrm{e}^2$
C
$e^{-6}$
D
$\mathrm{e}^{-2}$
2
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
$-\sin 1$
3
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $\mathrm{f}(x)=\frac{1-\tan x}{4 x-\pi}, x \neq \frac{\pi}{4}, x \in\left[0, \frac{1}{2}\right], \quad \mathrm{f}(x)$ is continuous in $\left[0, \frac{\pi}{2}\right]$, then $\mathrm{f}\left(\frac{\pi}{4}\right)$ is

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

Let $\alpha(a)$ and $\beta(a)$ be the roots of the equation $$(\sqrt[3]{1+a}-1) x^2+(\sqrt{1+a}-1) x+(\sqrt[6]{1+a}-1)=0$$ where $a>-1$ then $\lim _\limits{a \rightarrow 0^{+}} \alpha(a)$ and $\lim _\limits{a \rightarrow 0^{+}} \beta(a)$ respectively are

A
1 and $-\frac{5}{2}$
B
$-$1 and $-\frac{1}{2}$
C
2 and $-\frac{7}{2}$
D
3 and $-\frac{9}{2}$
MHT CET Subjects
EXAM MAP