1
MHT CET 2019 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the function $f(x)=\frac{\left(e^{k x}-1\right) \tan k x}{4 x^2}, x \neq 0$

$$\qquad \qquad=16 \qquad x=0$$

is continuous at $x=0$, then $k=\ldots \ldots$

A
$\pm \frac{1}{8}$
B
$\pm 4$
C
$\pm 2$
D
$\pm 8$
2
MHT CET 2019 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $f(x)=[x]$, where $[x]$ is the greatest integer not greater than $x$, then $f^{\prime}\left(1^{+}\right)=$ ...........

A
1
B
2
C
0
D
$-$1
3
MHT CET 2019 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If function

$$\begin{aligned} f(x) & =x-\frac{|x|}{x}, x<0 \\ & =x+\frac{|x|}{x}, x>0 \\ & =1, \quad x=0, \text { then } \end{aligned}$$

A
$\lim _\limits{x \rightarrow 0^{-}} f(x)$ does not exist
B
$\lim _\limits{x \rightarrow 0^{+}} f(x)$ does not exist
C
$f(x)$ is continuous at $x=0$
D
$\lim _\limits{x \rightarrow 0^{-}} f(x) \neq \lim _\limits{x \rightarrow 0^{+}} f(x)$
4
MHT CET 2019 2nd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Which of the following function is not continuous at $x=0$ ?

A
$$\begin{aligned} f(x) & =(1+2 x)^{1 / x}, & & x \neq 0 \\ & =e^2, & & x=0 \end{aligned}$$
B
$$\begin{aligned} f(x) & =\sin x-\cos x, & & x \neq 0 \\ & =-1, & & x=0 \end{aligned}$$
C
$$\begin{array}{rlr} f(x) & =\frac{e^{1 / x}-1}{e^{1 / x}+1}, & x \neq 0 \\ & =-1, & x=0 \end{array}$$
D
$$\begin{array}{rlr} f(x) & =\frac{e^{5 x}-e^{2 x}}{\sin 3 x}, & x \neq 0 \\ & =1, & x=0 \end{array}$$
MHT CET Subjects
EXAM MAP