1
MHT CET 2022 11th August Evening Shift
+2
-0

$$\matrix{ {f(x) = a{x^2} + bx + 1,} & {if} & {\left| {2x - 3} \right| \ge 2} \cr { = 3x + 2,} & {if} & {{1 \over 2} < x < {5 \over 2}} \cr }$$

is continuous on its domain, then $$a+b$$ has the value

A
$$\frac{13}{5}$$
B
$$\frac{31}{5}$$
C
$$\frac{23}{5}$$
D
$$\frac{1}{5}$$
2
MHT CET 2022 11th August Evening Shift
+2
-0

If $$\lim _\limits{x \rightarrow 1} \frac{x^2-a x+b}{(x-1)}=5$$, then $$(a+b)$$ is equal to

A
$$-$$4
B
$$-$$7
C
7
D
$$-$$3
3
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
$$\frac{1}{2}$$
4
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.
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