1
MHT CET 2026 20th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
$\lim\limits_{x \to 0}\left[\dfrac{x \cdot \log(1 + 4x)}{\left(e^{4x} - 1\right)^2}\right] = \cdots$
A
$\dfrac{1}{4}$
B
$\dfrac{1}{16}$
C
$\dfrac{1}{3}$
D
$\dfrac{1}{9}$
2
MHT CET 2026 20th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
Let $[x]$ denotes the greatest integer less than or equal to x and $f(x) = [\tan^2 x]$, then which of the following is true ?
A
$\lim\limits_{x \to 0} f(x)$ does not exist
B
$f(x)$ is continuous at $x = 0$
C
$f(x)$ is not differentiable at $x = 0$
D
$f'(0) = 1$
3
MHT CET 2025 5th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\quad f(x)=\left\{\begin{array}{cc}\frac{9^x-2 \cdot 3^x+1}{\log (1+3 x) \cdot \tan 2 x} & , \text { if } x \neq 0 \\ a(\log b)^c & , \text { if } x=0\end{array}\right.$ is continuous at $x=0$, then $\mathrm{a}+\mathrm{b}+\mathrm{c}=$

A

$\frac{31}{6}$

B

$\frac{1}{6}$

C

$\frac{5}{6}$

D

$\frac{3}{20}$

4
MHT CET 2025 5th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Define $f(x)=\left\{\begin{array}{cl}b-a x & , \text { if } x<2 \\ 3 & , \text { if } x=2 \\ a+2 b x & , \text { if } x>2\end{array}\right.$ and if $\lim _{x \rightarrow 2} f(x)$ exists, then $\frac{a}{b}=$

A

1

B

-1

C

$\frac{2}{3}$

D

$\frac{3}{2}$

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