1
MHT CET 2021 24th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$y=\tan ^{-1}\left[\frac{\log \left(\frac{e}{x^2}\right)}{\log \left(e x^2\right)}\right]+\tan ^{-1}\left[\frac{3+2 \log x}{1-6 \log x}\right]$$, then $$\frac{d^2 y}{d x^2}=$$

A
$$\frac{2}{1+x^2}$$
B
$$\frac{1}{1+x^2}$$
C
$$\frac{3}{1+x^2}$$
D
0
2
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
$$\mathrm{a}=3, \mathrm{~b}=2$$
3
MHT CET 2021 24th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$\mathrm{P}(\mathrm{A})=\frac{3}{10}, \mathrm{P}(\mathrm{B})=\frac{2}{5}, \mathrm{P}(\mathrm{A} \cup \mathrm{B})=\frac{3}{5}$$, then $$\mathrm{P}(\mathrm{A} / \mathrm{B}) \times \mathrm{P}(\mathrm{B} / \mathrm{A})=$$

A
$$\frac{1}{3}$$
B
$$\frac{1}{12}$$
C
$$\frac{1}{10}$$
D
$$\frac{1}{4}$$
4
MHT CET 2021 24th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int_\limits0^{\pi / 2} \log \left(\frac{4+3 \sin x}{4+3 \cos x}\right) d x=$$

A
0
B
4log3
C
$$\frac{1}{2}$$
D
2log4
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