1
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The maximum value of $\left(\cos \alpha_1\right) \cdot\left(\cos \alpha_2\right) \ldots .\left(\cos \alpha_n\right)$ under the constraints $0 \leq \alpha_1, \alpha_2, \ldots ., \alpha_n \leq \frac{\pi}{2}$ and $\left(\cot \alpha_1\right) \cdot\left(\cot \alpha_2\right) \ldots\left(\cot \alpha_n\right)=1$ is

A
$\frac{1}{2^{\left(\frac{n}{2}\right)}}$
B
$\frac{1}{2^n}$
C
$2^n$
D
$2^{\frac{n}{2}}$
2
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{A}+\mathrm{B}=225^{\circ}$, then $\frac{\cot \mathrm{A}}{1+\cot \mathrm{A}} \cdot \frac{\cot \mathrm{B}}{1+\cot \mathrm{B}}$, if it exists, is equal to

A
0
B
1
C
2
D
$\frac{1}{2}$
3
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\begin{aligned} \cos \left(18^{\circ}-\mathrm{A}\right) \cos \left(18^{\circ}+\mathrm{A}\right) -\cos \left(72^{\circ}-\mathrm{A}\right) \cos \left(72^{\circ}+\mathrm{A}\right) \text { is equal to }\end{aligned}$

A
$\cos 54^{\circ}$
B
$\cos 36^{\circ}$
C
$\sin 54^{\circ}$
D
$\sin 36^{\circ}$
4
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$ \cos ^3\left(\frac{\pi}{8}\right) \cos \left(\frac{3 \pi}{8}\right)+\sin ^3\left(\frac{\pi}{8}\right) \sin \left(\frac{3 \pi}{8}\right)=$$

A
$\frac{1}{2 \sqrt{2}}$
B
$\frac{1}{\sqrt{2}}$
C
$\frac{1}{2}$
D
$\frac{\sqrt{3}}{2}$
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