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

If $$\mathrm{A}$$ and $$\mathrm{B}$$ are two events such that $$\mathrm{P}(\mathrm{A})=\frac{1}{3}, \mathrm{P}(\mathrm{B})=\frac{1}{5}, \mathrm{P}(\mathrm{A} \cup \mathrm{B})=\frac{1}{3}$$, then the value of $$\mathrm{P}\left(\mathrm{A}^{\prime} / \mathrm{B}^{\prime}\right)+\mathrm{P}\left(\mathrm{B}^{\prime} / \mathrm{A}^{\prime}\right)$$ is

A
$$\frac{5}{6}$$
B
1
C
$$\frac{1}{6}$$
D
$$\frac{11}{6}$$
2
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the general solution of the equation $$\frac{\tan 3 x-1}{\tan 3 x+1}=\sqrt{3}$$ is $$x=\frac{\mathrm{n} \pi}{\mathrm{p}}+\frac{7 \pi}{\mathrm{q}}, \mathrm{n}, \mathrm{p}, \mathrm{q}, \in \mathrm{Z}$$, then $$\frac{p}{q}$$ is

A
12
B
$$\frac{1}{12}$$
C
3
D
36
3
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the area of the parallelogram with $$\bar{a}$$ and $$\bar{b}$$ as two adjacent sides is $$16 \mathrm{sq}$$. units, then the area of the parallelogram having $$3 \overline{\mathrm{a}}+2 \overline{\mathrm{b}}$$ and $$\overline{\mathrm{a}}+3 \overline{\mathrm{b}}$$ as two adjacent sides (in sq. units) is

A
96
B
112
C
144
D
128
4
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of $$\int(1-\cos x) \cdot \operatorname{cosec}^2 x d x$$ is

A
$$\frac{1}{2} \tan \frac{x}{2}+\mathrm{c}$$, where c is a constant of integration.
B
$$\tan \frac{x}{2}+\mathrm{c}$$, where c is a constant of integration.
C
$$2 \cot \frac{x}{2}+\mathrm{c}$$, where c is a constant of integration.
D
$$\cot \frac{x}{2}+\mathrm{c}$$, where c is a constant of integration.
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