1
JEE Main 2023 (Online) 10th April Morning Shift
+4
-1 $$96\cos {\pi \over {33}}\cos {{2\pi } \over {33}}\cos {{4\pi } \over {33}}\cos {{8\pi } \over {33}}\cos {{16\pi } \over {33}}$$ is equal to

A
4
B
2
C
1
D
3
2
JEE Main 2023 (Online) 8th April Evening Shift
+4
-1 The value of $$36\left(4 \cos ^{2} 9^{\circ}-1\right)\left(4 \cos ^{2} 27^{\circ}-1\right)\left(4 \cos ^{2} 81^{\circ}-1\right)\left(4 \cos ^{2} 243^{\circ}-1\right)$$ is :

A
18
B
36
C
54
D
27
3
JEE Main 2023 (Online) 30th January Morning Shift
+4
-1 If $$\tan 15^\circ + {1 \over {\tan 75^\circ }} + {1 \over {\tan 105^\circ }} + \tan 195^\circ = 2a$$, then the value of $$\left( {a + {1 \over a}} \right)$$ is :

A
$$5 - {3 \over 2}\sqrt 3$$
B
$$4 - 2\sqrt 3$$
C
2
D
4
4
JEE Main 2023 (Online) 29th January Evening Shift
+4
-1 The set of all values of $$\lambda$$ for which the equation $${\cos ^2}2x - 2{\sin ^4}x - 2{\cos ^2}x = \lambda$$ has a real solution $$x$$, is :

A
$$\left[ { - 2, - 1} \right]$$
B
$$\left[ { - {3 \over 2}, - 1} \right]$$
C
$$\left[ { - 2, - {3 \over 2}} \right]$$
D
$$\left[ { - 1, - {1 \over 2}} \right]$$
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