1
JEE Main 2022 (Online) 29th June Morning Shift
+4
-1 If the mirror image of the point (2, 4, 7) in the plane 3x $$-$$ y + 4z = 2 is (a, b, c), then 2a + b + 2c is equal to:

A
54
B
50
C
$$-$$6
D
$$-$$42
2
JEE Main 2022 (Online) 28th June Evening Shift
+4
-1 Let the plane ax + by + cz = d pass through (2, 3, $$-$$5) and is perpendicular to the planes
2x + y $$-$$ 5z = 10 and 3x + 5y $$-$$ 7z = 12. If a, b, c, d are integers d > 0 and gcd (|a|, |b|, |c|, d) = 1, then the value of a + 7b + c + 20d is equal to :

A
18
B
20
C
24
D
22
3
JEE Main 2022 (Online) 28th June Morning Shift
+4
-1 If two distinct point Q, R lie on the line of intersection of the planes $$- x + 2y - z = 0$$ and $$3x - 5y + 2z = 0$$ and $$PQ = PR = \sqrt {18}$$ where the point P is (1, $$-$$2, 3), then the area of the triangle PQR is equal to

A
$${2 \over 3}\sqrt {38}$$
B
$${4 \over 3}\sqrt {38}$$
C
$${8 \over 3}\sqrt {38}$$
D
$$\sqrt {{{152} \over 3}}$$
4
JEE Main 2022 (Online) 28th June Morning Shift
+4
-1 The acute angle between the planes P1 and P2, when P1 and P2 are the planes passing through the intersection of the planes $$5x + 8y + 13z - 29 = 0$$ and $$8x - 7y + z - 20 = 0$$ and the points (2, 1, 3) and (0, 1, 2), respectively, is

A
$${\pi \over 3}$$
B
$${\pi \over 4}$$
C
$${\pi \over 6}$$
D
$${\pi \over 12}$$
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