1
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

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

A
$-\frac{1}{2}$
B
$\frac{1}{2}$
C
1
D
$-$1
2
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the function $f(x)= \begin{cases}-2 \sin x & \text {, if } x \leq \frac{-\pi}{2} \\ A \sin x+B & , \text { if } \frac{-\pi}{2}< x<\frac{\pi}{2} \\ \cos x & , \text { if } x \geq \frac{\pi}{2}\end{cases}$ is continuous everywhere, then the values of $A$ and B are respectively

A
$1,-1$.
B
$-1,1$.
C
$1,1 .$
D
$-1,-1$.
3
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\lim _\limits{x \rightarrow 2} \frac{3^x+3^{3-x}-12}{3^{3-x}-3^{\frac{x}{2}}}=$$

A
$-\frac{4}{3}$
B
$\frac{4}{3}$
C
$\frac{2}{3}$
D
$-\frac{4}{9}$
4
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $f:[-1,3] \rightarrow \mathbb{R}$ be defined as

$$\left\{\begin{array}{lc} |x|+[x], & -1 \leqslant x<1 \\ x+|x|, & 1 \leqslant x<2 \\ x+[x], & 2 \leqslant x \leqslant 3 \end{array}\right.$$

where $[t]$ denotes the greatest integer function. Then $f$ is discontinuous at

A
only two points
B
only three points
C
four or more points
D
only one point
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