1
MHT CET 2021 24th September Evening Shift
+2
-0

$$\lim _\limits{x \rightarrow 0} \frac{\sqrt{1-\cos x^2}}{1-\cos x}=$$

A
$$\sqrt{2}$$
B
$$\frac{1}{\sqrt{2}}$$
C
0
D
$$\frac{1}{2}$$
2
MHT CET 2021 24th September Evening Shift
+2
-0

If $$\mathrm{f}(\mathrm{x})=\mathrm{x}, \quad$$ for $$\mathrm{x} \leq 0$$

$$=0,\quad$$ for $$x>0$$, then the function $$f(x)$$ at $$x=0$$ is

A
not continuous and not differentiable.
B
not continuous but differentiable.
C
continuous but not differentiable.
D
continuous and differentiable.
3
MHT CET 2021 24th September Morning Shift
+2
-0

$$\lim _\limits{x \rightarrow 1} \frac{a b^x-a^x b}{x^2-1}=$$

A
$$\frac{-a b}{2} \log \left(\frac{b}{a}\right)$$
B
$$\frac{\mathrm{ab}}{2} \log \left(\frac{\mathrm{b}}{\mathrm{a}}\right)$$
C
ab $$\log \left(\frac{\mathrm{b}}{\mathrm{a}}\right)$$
D
$$-\mathrm{ab} \log \left(\frac{\mathrm{b}}{\mathrm{a}}\right)$$
4
MHT CET 2021 24th September Morning Shift
+2
-0

If the function

$$\begin{array}{rlrl} f(x) & =3 a x+b, & & \text { for } x<1 \\ & =11, & & \text { for } x=1 \\ & =5 a x-2 b, & \text { for } x>1 \end{array}$$

is continuous at $$x=1$$. Then, the values of $$a$$ and $$b$$ are

A
$$\mathrm{a}=2, \mathrm{~b}=3$$
B
$$\mathrm{a=3, b=3}$$
C
$$\mathrm{a=2, b=2}$$
D
$$\mathrm{a}=3, \mathrm{~b}=2$$
EXAM MAP
Medical
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