1
MHT CET 2023 10th May Morning Shift
+2
-0

The value of $$\lim _\limits{x \rightarrow a} \frac{\sqrt{a+2 x}-\sqrt{3 x}}{\sqrt{3 a+x}-2 \sqrt{x}}$$ is

A
$$\frac{1}{3 \sqrt{3}}$$
B
$$\frac{2}{\sqrt{3}}$$
C
$$\frac{2}{3 \sqrt{3}}$$
D
$$\frac{4}{3 \sqrt{3}}$$
2
MHT CET 2023 10th May Morning Shift
+2
-0

If the function $$\mathrm{f}(x)$$ is continuous in $$0 \leq x \leq \pi$$, then the value of $$2 a+3 b$$ is where

$$f(x)= \begin{cases}x+a \sqrt{2} \sin x & \text { if } 0 \leq x < \frac{\pi}{4} \\ 2 x \cot x+b & \text { if } \frac{\pi}{4} \leq x \leq \frac{\pi}{2} \\ \operatorname{acos} 2 x-b \sin x & \text { if } \frac{\pi}{2} < x \leq \pi\end{cases}$$

A
$$\frac{\pi}{12}$$
B
$$\frac{\pi}{6}$$
C
$$\frac{\pi}{4}$$
D
$$\frac{\pi}{10}$$
3
MHT CET 2023 9th May Evening Shift
+2
-0

$$\lim _\limits{x \rightarrow 0} \frac{(1-\cos 2 x) \cdot \sin 5 x}{x^2 \sin 3 x}$$ is

A
$$\frac{10}{3}$$
B
$$\frac{5}{3}$$
C
$$\frac{5}{6}$$
D
$$\frac{2}{3}$$
4
MHT CET 2023 9th May Evening Shift
+2
-0

$$f(x)=\left\{\begin{array}{ll} \frac{1-\cos k x}{x^2}, & \text { if } x \leq 0 \\ \frac{\sqrt{x}}{\sqrt{16+\sqrt{x}}-4}, & \text { if } x>0 \end{array}\right. \text { is continuous at }$$ $$x=0$$, then the value of $$\mathrm{k}$$ is

A
4
B
2
C
$$-$$1
D
$$-$$3
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