1
JEE Main 2022 (Online) 25th July Evening Shift
+4
-1

$$2 \sin \left(\frac{\pi}{22}\right) \sin \left(\frac{3 \pi}{22}\right) \sin \left(\frac{5 \pi}{22}\right) \sin \left(\frac{7 \pi}{22}\right) \sin \left(\frac{9 \pi}{22}\right)$$ is equal to :

A
$$\frac{3}{16}$$
B
$$\frac{1}{16}$$
C
$$\frac{1}{32}$$
D
$$\frac{9}{32}$$
2
JEE Main 2022 (Online) 28th June Evening Shift
+4
-1

If cot$$\alpha$$ = 1 and sec$$\beta$$ = $$- {5 \over 3}$$, where $$\pi < \alpha < {{3\pi } \over 2}$$ and $${\pi \over 2} < \beta < \pi$$, then the value of $$\tan (\alpha + \beta )$$ and the quadrant in which $$\alpha$$ + $$\beta$$ lies, respectively are :

A
$$- {1 \over 7}$$ and IVth quadrant
B
C
$$-$$7 and IVth quadrant
D
$${1 \over 7}$$ and Ist quadrant
3
JEE Main 2022 (Online) 27th June Evening Shift
+4
-1

$$\alpha = \sin 36^\circ$$ is a root of which of the following equation?

A
$$16{x^4} - 10{x^2} - 5 = 0$$
B
$$16{x^4} + 20{x^2} - 5 = 0$$
C
$$4{x^4} - 20{x^2} + 5 = 0$$
D
$$4{x^4} - 10{x^2} + 5 = 0$$
4
JEE Main 2022 (Online) 27th June Morning Shift
+4
-1

The value of $$\cos \left( {{{2\pi } \over 7}} \right) + \cos \left( {{{4\pi } \over 7}} \right) + \cos \left( {{{6\pi } \over 7}} \right)$$ is equal to :

A
$$-$$1
B
$$-$$$${1 \over 2}$$
C
$$-$$$${1 \over 3}$$
D
$$-$$$${1 \over 4}$$
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