1
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The set of all points, where the derivative of the functions $$\mathrm{f}(x)=\frac{x}{1+|x|}$$ exists, is

A
$$(-\infty, \infty)$$
B
$$[0, \infty)$$
C
$$(-\infty, 0) \cup(0, \infty)$$
D
$$(0, \infty)$$
2
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

In triangle $$\mathrm{ABC}$$ with usual notations $$\mathrm{b}=\sqrt{3}, \mathrm{c}=1, \mathrm{~m} \angle \mathrm{A}=30^{\circ}$$, then the largest angle of the triangle is

A
$$135^{\circ}$$
B
$$90^{\circ}$$
C
$$60^{\circ}$$
D
$$120^{\circ}$$
3
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A fair die is tossed twice in succession. If $$\mathrm{X}$$ denotes the number of fours in two tosses, then the probability distribution of $$\mathrm{X}$$ is given by

A
$$\mathrm{X}=x_i$$ 0 1 2
$$\mathrm{P_i}$$ $$\frac{1}{36}$$ $$\frac{25}{36}$$ $$\frac{5}{18}$$
B
$$\mathrm{X}=x_i$$ 0 1 2
$$\mathrm{P_i}$$ $$\frac{25}{36}$$ $$\frac{1}{36}$$ $$\frac{5}{18}$$
C
$$\mathrm{X}=x_i$$ 0 1 2
$$\mathrm{P_i}$$ $$\frac{25}{36}$$ $$\frac{5}{18}$$ $$\frac{1}{36}$$
D
$$\mathrm{X}=x_i$$ 0 1 2
$$\mathrm{P_i}$$ $$\frac{5}{18}$$ $$\frac{1}{36}$$ $$\frac{25}{36}$$
4
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\mathrm{f}(x)=\frac{3 x+4}{5 x-7}$$ and $$\mathrm{g}(x)=\frac{7 x+4}{5 x-3}$$, then $$\mathrm{f}(\mathrm{g}(x))=$$

A
$$\frac{x^3+1}{x^2+2}$$
B
$$41 x$$
C
$$\mathrm{g}(\mathrm{f}(x))$$
D
$$\frac{5 x-7}{41}$$
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