1
MHT CET 2023 12th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\lim _\limits{x \rightarrow 0} \frac{\cos 7 x^{\circ}-\cos 2 x^{\circ}}{x^2}$$ is

A
$$\frac{-45}{2} \pi^2$$
B
$$\frac{-45}{2} \pi$$
C
$$\frac{-\pi^2}{1440}$$
D
$$\frac{-\pi^2}{2880}$$
2
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\text { If } l=\lim _\limits{x \rightarrow 0} \frac{x}{|x|+x^2} \text {, then the value of } l \text { is }$$

A
1
B
$$-$$1
C
2
D
non-existant
3
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\mathrm{f}(x)=\left\{\begin{array}{cc}\frac{x-3}{|x-3|}+\mathrm{a} & , \quad x < 3 \\ \mathrm{a}+\mathrm{b} & , \quad x=3 \\ \frac{|x-3|}{x-3}+\mathrm{b}, & x>3\end{array}\right.$$

Is continuous at $$x=3$$, then the value of $$\mathrm{a}-\mathrm{b}$$ is

A
$$-$$1
B
0
C
1
D
2
4
MHT CET 2023 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\lim _\limits{x \rightarrow 2}\left[\frac{1}{x-2}-\frac{2}{x^3-3 x^2+2 x}\right]$$ is equal to

A
$$\frac{2}{3}$$
B
$$\frac{-2}{3}$$
C
$$\frac{3}{2}$$
D
$$\frac{-3}{2}$$
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