1
JEE Main 2021 (Online) 24th February Morning Shift
+4
-1
If $${e^{\left( {{{\cos }^2}x + {{\cos }^4}x + {{\cos }^6}x + ...\infty } \right){{\log }_e}2}}$$ satisfies the equation t2 - 9t + 8 = 0, then the value of
$${{2\sin x} \over {\sin x + \sqrt 3 \cos x}}\left( {0 < x < {\pi \over 2}} \right)$$ is :
A
$$\sqrt 3$$
B
$${3 \over 2}$$
C
2$$\sqrt 3$$
D
$${1 \over 2}$$
2
JEE Main 2020 (Online) 5th September Evening Slot
+4
-1
If L = sin2$$\left( {{\pi \over {16}}} \right)$$ - sin2$$\left( {{\pi \over {8}}} \right)$$ and
M = cos2$$\left( {{\pi \over {16}}} \right)$$ - sin2$$\left( {{\pi \over {8}}} \right)$$, then :
A
L = $$- {1 \over {2\sqrt 2 }} + {1 \over 2}\cos {\pi \over 8}$$
B
M = $${1 \over {2\sqrt 2 }} + {1 \over 2}\cos {\pi \over 8}$$
C
M = $${1 \over {4\sqrt 2 }} + {1 \over 4}\cos {\pi \over 8}$$
D
L = $${1 \over {4\sqrt 2 }} - {1 \over 4}\cos {\pi \over 8}$$
3
JEE Main 2020 (Online) 2nd September Evening Slot
+4
-1
If the equation cos4 $$\theta$$ + sin4 $$\theta$$ + $$\lambda$$ = 0 has real solutions for $$\theta$$, then $$\lambda$$ lies in the interval :
A
$$\left[ { - {3 \over 2}, - {5 \over 4}} \right]$$
B
$$\left( { - {1 \over 2}, - {1 \over 4}} \right]$$
C
$$\left( { - {5 \over 4}, - 1} \right]$$
D
$$\left[ { - 1, - {1 \over 2}} \right]$$
4
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
If $$x = \sum\limits_{n = 0}^\infty {{{\left( { - 1} \right)}^n}{{\tan }^{2n}}\theta }$$ and $$y = \sum\limits_{n = 0}^\infty {{{\cos }^{2n}}\theta }$$

for 0 < $$\theta$$ < $${\pi \over 4}$$, then :
A
x(1 + y) = 1
B
y(1 – x) = 1
C
y(1 + x) = 1
D
x(1 – y) = 1
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