1
JEE Main 2022 (Online) 26th June Evening Shift
+4
-1 If the plane $$2x + y - 5z = 0$$ is rotated about its line of intersection with the plane $$3x - y + 4z - 7 = 0$$ by an angle of $${\pi \over 2}$$, then the plane after the rotation passes through the point :

A
(2, $$-$$2, 0)
B
($$-$$2, 2, 0)
C
(1, 0, 2)
D
($$-$$1, 0, $$-$$2)
2
JEE Main 2022 (Online) 26th June Evening Shift
+4
-1 If the lines $$\overrightarrow r = \left( {\widehat i - \widehat j + \widehat k} \right) + \lambda \left( {3\widehat j - \widehat k} \right)$$ and $$\overrightarrow r = \left( {\alpha \widehat i - \widehat j} \right) + \mu \left( {2\widehat i - 3\widehat k} \right)$$ are co-planar, then the distance of the plane containing these two lines from the point ($$\alpha$$, 0, 0) is :

A
$${2 \over 9}$$
B
$${2 \over 11}$$
C
$${4 \over 11}$$
D
2
3
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1 If the two lines $${l_1}:{{x - 2} \over 3} = {{y + 1} \over {-2}},\,z = 2$$ and $${l_2}:{{x - 1} \over 1} = {{2y + 3} \over \alpha } = {{z + 5} \over 2}$$ are perpendicular, then an angle between the lines l2 and $${l_3}:{{1 - x} \over 3} = {{2y - 1} \over { - 4}} = {z \over 4}$$ is :

A
$${\cos ^{ - 1}}\left( {{{29} \over 4}} \right)$$
B
$${\sec ^{ - 1}}\left( {{{29} \over 4}} \right)$$
C
$${\cos ^{ - 1}}\left( {{2 \over {29}}} \right)$$
D
$${\cos ^{ - 1}}\left( {{2 \over {\sqrt {29} }}} \right)$$
4
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1 Let the plane 2x + 3y + z + 20 = 0 be rotated through a right angle about its line of intersection with the plane x $$-$$ 3y + 5z = 8. If the mirror image of the point $$\left( {2, - {1 \over 2},2} \right)$$ in the rotated plane is B(a, b, c), then :

A
$${a \over 8} = {b \over 5} = {c \over { - 4}}$$
B
$${a \over 4} = {b \over 5} = {c \over { - 2}}$$
C
$${a \over 8} = {b \over { - 5}} = {c \over 4}$$
D
$${a \over 4} = {b \over 5} = {c \over 2}$$
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