1
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $\mathrm{f}(x)=x\left[\frac{x}{2}\right]$, for $-10< x<10$, where $[t]$ denotes the greatest integer function. Then the number of points of discontinuity of $f$ is equal to

A
10
B
9
C
6
D
8
2
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\lim\limits_{x \rightarrow \infty}\left(\frac{x^2+x+1}{x+1}-a x-b\right)=4$ then

A
$\mathrm{a}=1, \mathrm{~b}=4$
B
$\mathrm{a}=1, \mathrm{~b}=-4$
C
$\mathrm{a}=2, \mathrm{~b}=-3$
D
$\mathrm{a}=2, \mathrm{~b}=3$
3
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let k be a non-zero real number. If $f(x)=\left\{\begin{array}{cl}\frac{\left(\mathrm{e}^x-1\right)^2}{\sin \left(\frac{x}{k}\right) \log \left(1+\frac{x}{4}\right)} & , x \neq 0 \\ 12 & , x=0\end{array}\right.$ is a continuous function, then the value of $k$ is

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

If $\mathrm{f}(x)=\frac{x+x^2+x^3+\ldots \ldots \ldots \ldots+x^{\mathrm{n}}-\mathrm{n}}{x-1}$, for $x \neq 1$ is continuous at $x=1$, then $\mathrm{f}(1)=$

A
$\frac{\mathrm{n}(\mathrm{n}+1)(4 \mathrm{n}-1)}{6}$
B
$\frac{\mathrm{n}(\mathrm{n}+1)}{2}$
C
$\frac{\mathrm{n}(\mathrm{n}+1)(2 \mathrm{n}+1)}{6}$
D
$\frac{\mathrm{n}(2 \mathrm{n}+1)}{4}$
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