1
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$y=\operatorname{cosec}^{-1}\left[\frac{\sqrt{x}+1}{\sqrt{x}-1}\right]+\cos ^{-1}\left[\frac{\sqrt{x}-1}{\sqrt{x}+1}\right]$$, then $$\frac{d y}{d x}=$$

A
0
B
1
C
$$\frac{2}{\sqrt{x}+1}$$
D
$$\frac{1}{2(\sqrt{x}-1)}$$
2
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$f(x)=|x-1|+|x-2|+|x-3|, \forall x \in[1,4]$$, then $$\int_\limits1^4 f(x) d x=$$

A
$$\frac{1}{2}$$
B
7
C
$$\frac{9}{2}$$
D
$$\frac{19}{2}$$
3
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The general solution of the differential equation $$\frac{d y}{d x}=\frac{x+2 y-1}{x+2 y+1}$$ is

A
$$3(x+y)+4 \log |3 x+6 y-1|=K$$
B
$$3(x-y)+4 \log |3 x+6 y-1|=K$$
C
$$6(-x+y)+4 \log |3 x+6 y-1|=K$$
D
$$6(x+y)+4 \log |3 x+6 y-1|=K$$
4
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$\mathrm{X}$$ is a random variable with p.m.f. as follows.

$$\begin{aligned} \mathrm{P}(\mathrm{X}=\mathrm{x}) & =\frac{5}{16}, \mathrm{x}=0,1 \\ & =\frac{\mathrm{kx}}{48}, \mathrm{x}=2, \quad \text { then } \mathrm{E}(\mathrm{x})= \\ & =\frac{1}{4}, \mathrm{x}=3 \end{aligned}$$

A
1.1875
B
1.3125
C
1.5625
D
0.5625
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