1
JEE Main 2021 (Online) 26th August Evening Shift
+4
-1
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 :

A
5
B
2$$\sqrt {10}$$
C
5$$\sqrt {3}$$
D
5$$\sqrt {2}$$
2
JEE Main 2021 (Online) 26th August Morning Shift
+4
-1
Let $$\overrightarrow a = \widehat i + \widehat j + \widehat k$$ and $$\overrightarrow b = \widehat j - \widehat k$$. If $$\overrightarrow c$$ is a vector such that $$\overrightarrow a \times \overrightarrow c = \overrightarrow b$$ and $$\overrightarrow a .\overrightarrow c = 3$$, then $$\overrightarrow a .(\overrightarrow b \times \overrightarrow c )$$ is equal to :
A
$$-$$2
B
$$-$$6
C
6
D
2
3
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
Let $$\overrightarrow a$$, $$\overrightarrow b$$ and $$\overrightarrow c$$ be three vectors such that $$\overrightarrow a$$ = $$\overrightarrow b$$ $$\times$$ ($$\overrightarrow b$$ $$\times$$ $$\overrightarrow c$$). If magnitudes of the vectors $$\overrightarrow a$$, $$\overrightarrow b$$ and $$\overrightarrow c$$ are $$\sqrt 2$$, 1 and 2 respectively and the angle between $$\overrightarrow b$$ and $$\overrightarrow c$$ is $$\theta \left( {0 < \theta < {\pi \over 2}} \right)$$, then the value of 1 + tan$$\theta$$ is equal to :
A
$$\sqrt 3 + 1$$
B
2
C
1
D
$${{\sqrt 3 + 1} \over {\sqrt 3 }}$$
4
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
Let $$\overrightarrow a = \widehat i + \widehat j + 2\widehat k$$ and $$\overrightarrow b = - \widehat i + 2\widehat j + 3\widehat k$$. Then the vector product $$\left( {\overrightarrow a + \overrightarrow b } \right) \times \left( {\left( {\overrightarrow a \times \left( {\left( {\overrightarrow a - \overrightarrow b } \right) \times \overrightarrow b } \right)} \right) \times \overrightarrow b } \right)$$ is equal to :
A
$$5(34\widehat i - 5\widehat j + 3\widehat k)$$
B
$$7(34\widehat i - 5\widehat j + 3\widehat k)$$
C
$$7(30\widehat i - 5\widehat j + 7\widehat k)$$
D
$$5(30\widehat i - 5\widehat j + 7\widehat k)$$
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