1
MHT CET 2023 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\log _2 x+\log _4 x+\log _8 x+\log _{16} x=\frac{25}{36}$$ and $$x=2^{\mathrm{k}}$$ then $$\mathrm{k}$$ is

A
1
B
$$\frac{1}{2}$$
C
$$\frac{1}{3}$$
D
$$\frac{1}{8}$$
2
MHT CET 2023 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\left|\begin{array}{ccc}\cos (A+B) & -\sin (A+B) & \cos (2 B) \\ \sin A & \cos A & \sin B \\ -\cos A & \sin A & \cos B\end{array}\right|=0$$, then the value of $$B$$ is

A
$$\mathrm{n} \pi, \mathrm{n} \in \mathbb{Z}$$
B
$$(2 \mathrm{n}+1) \frac{\pi}{2}, \mathrm{n} \in \mathbb{Z}$$
C
$$(2 \mathrm{n}+1) \frac{\pi}{4}, \mathrm{n} \in \mathbb{Z}$$
D
$$2 \mathrm{n} \frac{\pi}{3}, \mathrm{n} \in \mathbb{Z}$$
3
MHT CET 2023 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

General solution of the differential equation $$\log \left(\frac{d y}{d x}\right)=a x+b y$$ is

A
$$a e^{b y}+b e^{a x}=c_1$$, where $$c_1$$ is a constant.
B
$$a e^{-b y}+b^{-a x}=c_1$$, where $$c_1$$ is a constant.
C
$$a e^{-b y}+b e^{a x}=c_1$$, where $$c_1$$ is a constant.
D
$$a e^{b y}+b e^{-a x}=c_1$$, where $$c_1$$ is a constant.
4
MHT CET 2023 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int(\sqrt{\tan x}+\sqrt{\cot x}) d x=$$

A
$$\sqrt{2} \sin ^{-1}(\sin x-\cos x)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
B
$$\frac{1}{\sqrt{2}} \sin ^{-1}(\sin x-\cos x)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
C
$$\sin ^{-1}(\sin x-\cos x)+c$$, where c is a constant of integration.
D
$$2 \sin ^{-1}(\sin x-\cos x)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
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