1
MHT CET 2021 24th September Evening Shift
MCQ (Single Correct Answer)
+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.
2
MHT CET 2021 24th September Morning Shift
MCQ (Single Correct Answer)
+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
$$-\mathrm{ab} \log \left(\frac{\mathrm{b}}{\mathrm{a}}\right)$$
3
MHT CET 2021 24th September Morning Shift
MCQ (Single Correct Answer)
+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
$$\mathrm{a}=3, \mathrm{~b}=2$$
4
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\begin{aligned} & \text { If the function given by} \mathrm{f}(\mathrm{x}) \\ & =-2 \sin \mathrm{x} \quad-\pi \leq \mathrm{x}<-(\pi / 2) \\ & =a \sin x+b \quad-(\pi / 2)< x<(\pi / 2) \\ & =\cos x \quad(\pi / 2) \leq x \leq \pi \\ \end{aligned}$$

is continuous in $$[-\pi, \pi]$$, then the value of $$(3 a+2 b)^3$$ is

A
1
B
8
C
$$-$$1
D
$$-$$8
MHT CET Subjects
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12