1
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}(x)=\left(\frac{1+\tan x}{1+\sin x}\right)^{\operatorname{cosec} x}$ is continuous at $x=0$ then $f(0)$ is equal to

A
0
B
1
C
$\mathrm{e}$
D
$\mathrm{\frac{1}{e}}$
2
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\lim _\limits{x \rightarrow 0} \frac{9^x-4^x}{x\left(9^x+4^x\right)}=$$

A
$\log \left(\frac{3}{2}\right)$
B
$\frac{1}{2} \log \left(\frac{3}{2}\right)$
C
$2 \log \left(\frac{3}{2}\right)$
D
$2 \log \left(\frac{9}{4}\right)$
3
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The values of $a$ and $b$, so that the function

$$f(x)= \begin{cases}x+\mathrm{a} \sqrt{2} \sin x & , 0 \leq x \leq \frac{\pi}{4} \\ 2 x \cot x+b & , \frac{\pi}{4} \leq x \leq \frac{\pi}{2} \\ \mathrm{a} \cos 2 x-\mathrm{b} \sin x & , \frac{\pi}{2}< x \leq \pi\end{cases}$$

is continuous for $0 \leq x \leq \pi$, are respectively given by

A
$+\frac{\pi}{12},-\frac{\pi}{6}$
B
  $-\frac{\pi}{6},-\frac{\pi}{12}$
C
$\frac{\pi}{6}, \frac{\pi}{12}$
D
$\frac{\pi}{6},-\frac{\pi}{12}$
4
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The approximate value of $x^3-2 x^2+3 x+2$ at $x=2.01$ is

A
8.07
B
8.27
C
8.007
D
8.17
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