1
JEE Main 2021 (Online) 26th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The value of

$$2\sin \left( {{\pi \over 8}} \right)\sin \left( {{{2\pi } \over 8}} \right)\sin \left( {{{3\pi } \over 8}} \right)\sin \left( {{{5\pi } \over 8}} \right)\sin \left( {{{6\pi } \over 8}} \right)\sin \left( {{{7\pi } \over 8}} \right)$$ is :
A
$${1 \over {4\sqrt 2 }}$$
B
$${1 \over 4}$$
C
$${1 \over 8}$$
D
$${1 \over {8\sqrt 2 }}$$
2
JEE Main 2021 (Online) 26th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If $${\left( {\sqrt 3 + i} \right)^{100}} = {2^{99}}(p + iq)$$, then p and q are roots of the equation :
A
$${x^2} - \left( {\sqrt 3 - 1} \right)x - \sqrt 3 = 0$$
B
$${x^2} + \left( {\sqrt 3 + 1} \right)x + \sqrt 3 = 0$$
C
$${x^2} + \left( {\sqrt 3 - 1} \right)x - \sqrt 3 = 0$$
D
$${x^2} - \left( {\sqrt 3 + 1} \right)x + \sqrt 3 = 0$$
3
JEE Main 2021 (Online) 26th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
A hall has a square floor of dimension 10 m $$\times$$ 10 m (see the figure) and vertical walls. If the angle GPH between the diagonals AG and BH is $${\cos ^{ - 1}}{1 \over 5}$$, then the height of the hall (in meters) is :

JEE Main 2021 (Online) 26th August Evening Shift Mathematics - Vector Algebra Question 140 English
A
5
B
2$$\sqrt {10} $$
C
5$$\sqrt {3} $$
D
5$$\sqrt {2} $$
4
JEE Main 2021 (Online) 26th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The value of $$\int\limits_{ - {\pi \over 2}}^{{\pi \over 2}} {\left( {{{1 + {{\sin }^2}x} \over {1 + {\pi ^{\sin x}}}}} \right)} \,dx$$ is
A
$${\pi \over 2}$$
B
$${{5\pi } \over 4}$$
C
$${{3\pi } \over 4}$$
D
$${{3\pi } \over 2}$$
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