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

If $$f(x)=\frac{1-\sin x+\cos x}{1+\sin x+\cos x}$$, for $$x \neq \pi$$ is continuous at $$x=\pi$$, then the value of $$f(\pi)$$ is

A
$$\frac{-1}{2}$$
B
$$-1$$
C
1
D
$$\frac{1}{2}$$
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