1
MHT CET 2025 19th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}(x)=\frac{(27-2 x)^{\frac{1}{3}}-3}{9-3(243+5 x)^{\frac{1}{5}}}, x \neq 0$ is continuous at $x=0$, then the value of $\mathrm{f}(0)$ is

A
$\frac{2}{3}$
B
6
C
2
D
$\frac{1}{3}$
2
MHT CET 2025 19th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \mathop {\lim }\limits_{x \to 0} \frac{|x|}{|x|+x^2}= $$

A
0
B
1
C
-1
D
$\frac{1}{2}$
3
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
$\lim _\limits{x \rightarrow 3} \frac{(84-x)^{\frac{1}{4}}-3}{x-3}$ is
A
$\frac{-1}{108}$
B
$\frac{-1}{84}$
C
$\frac{-1}{27}$
D
$\frac{-1}{4}$
4
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
If $\mathrm{f}(x)$ is continuous at point $x=0$ where $$ f(x)=\left\{\begin{array}{cc} \frac{3 \sin x+5 \tan x}{\mathrm{a}^x-1} & , x<0 \\ \frac{2}{\log 2} & , x=0 \\ \frac{8 x+2 x \cos x}{\mathrm{~b}^x-1} & , x>0 \end{array}\right. $$ then the values of a and b , respectively, are __________
A
4, 5
B
16, 32
C
8, 10
D
16, 16
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